Happy New Year!

2015:

Complete the formula: 10  9  8  7  6  5  4  3  2  1  0  =  2015.

Possible solutions:

(10 + 9) * (8 + 7) * 6 + 5 * (4 ^ 3 - 2 - 1 - 0) = 2015.
(10 + 9) * (8 + 7 + 6) * 5 + 4! - 3! + 2! - 1! + 0! = 2015.
10 * 9 * (8 + 7 + 6) + 5 * (4! + 3 - 2 - 1 * 0) = 2015.
10 * 9! / (8 * 7 * 6 * 5) - (4! * 3! + 2 - 1 - 0) = 2015.
(10 * 9 * 8 * 7 / (6 * 5)) * 4 * 3 - 2 + 1 ^ 0 = 2015. (@alexbellos)

2015 = 11111011111 base 2.

10987654321098765...10987 (2015 digits) is prime.

2014^2 + 2015^2 and 2015^2 + 2016^2 is prime.

2015 = (69-4) x (38-7) (uses each digit once). (@alexbellos)
2015 = 2^11 - 2^5 - 2^0 (only uses 2, 0, 1, and 5). (@brianucsd)
2015 = 31*5*13 = 13*5*31 (palindromic products). (@druizaguilera)
2015 = 31*(32+33) (consecutive numbers). (@juanripu)

2014:

Complete the formula: 10  9  8  7  6  5  4  3  2  1  0  =  2014.

Possible solutions:

(10 + 9) * (8 * 7 - 6 * (5 - 4) + 3) * (2 * 1 + 0) = 2014.

-10 + 9 + 8 * 7 * 6 * (5 - 4) * 3 * (2 + 1 * 0) = 2014.

(10 + 9) * ( (8 + 7) * 6 + 5 + 4 * 3 - 2 + 1 + 0) = 2014.

2014 = 13^3 - 13^2 - 13^1 - 13^0.

2013 = 3*11*61.
2014 = 2*19*53.
2015 = 5*13*31.
(run of three 3-almost primes)

January 1st (1st Day of the Year)

Jan 1st, 1/1.

11^n is a palindrome for n = 0,1,2,3,4.

11 is of the form 2p+1 (p = 5) and if 11 = p, 2p + 1 is also prime (2*11+1 = 23).

11 describes the number 1 ("one one"), and it's the 1st Day of the Year.

6^11 + 5^11 is prime (Note: 6+5 = 11).

11 is the 5th prime. (5 is prime.) 5 is the 3rd prime. (3 is prime.) 3 is the 2nd prime. (2 is prime.)

11 is a prime of the form R_n where R_n is 11...111 with n 1's. (What's the next R_n prime?)

There are 11 primes less than 2^5.

11! + 1 is prime. (What's the next number with this property? Next prime?)

11, 11+2, 11+6, and 11+8 are all prime.

11 is the smallest natural number with 3 syllables.

If a number is a multiple of 11, its reverse is also a multiple of 11.

There are 11 spacetime dimensions in M-theory.

Apollo 11 was the first manned spacecraft to land on the Moon.

There are 11 players on a US soccer or football field during play.

World War 1 ended in an armistice on the 11th hour of the 11th day of the 11th month of the year.

The maple leaf on the flag of Canada has 11 points.

Clocks on the Canadian currency show 11:00.

11:11 is known as a lucky time of the day that one may make a wish.

The secret formula for Kentucky Fried Chicken includes 11 herbs and spices.

11 + 2n^2 gives prime for the first 11 whole numbers.

There are 11 letters in "prime number".

10! - 11 and 10! + 11 are two consecutive primes (Note: 10 and 11 are consecutive). (What other consecutive numbers have this property?)

11 is the only number such that 11 +- 8 and 11 +- 6 are prime.

11 is the smallest prime where 2^11 - 1 is composite.

11^11+11^11*11+1 is prime (Note: 11 ones are used).

The sum of the 11 primes after 11 is another palindromic prime.

The 2002 All-Star baseball game was determined a tie after 11 innings.

The sum of the first 11 primes ending with a 1 is a prime beginning with 11.

11! + 11! + 11! + 11! + 11! + 1 is prime (Again, there are 11 ones).

2! + 3! + 5! = 7 mod 11 (Note: 2,3,5,7,11 are the first 5 primes).

12345678910 - 11 is prime. (What other number has this property?)

11 is the concatenation of the first 2 Fibonacci numbers.

11 = 1b2 + 11b2 + 111b2 where b represents "base".

1st Day of the Year.

1^n = 1 for all real numbers n.

1 was originally considered prime before 1900; today it is nonprime (neither prime nor composite).

1 written in any nontrivial base is 1.

0.999.... = 1.

1 begins the Fibonacci sequence.

1 is the only known perfect number not ending in a 6 or 8.

1 is the lowest number an NHL jersey could have (as 0 and 00 were banned).

January 2nd (2nd Day of the Year)

Jan 2nd, 1/2.

12 = (10-9)*(8+7)-6*(5-4)+(3*(2-1))

12 = (10+9)-(8-7)-(6+5)+(4+(3-2)*1)

12 = (10*9)/(8+7)+(6-5)*(4+3-2+1)

12 = (10-9)*(8-7) + (6+5)*(-4+3*2-1)

12 = 3!*2!*1!*0!

12^2 + 12 + 1 and 12^3 + 12 + 1 are prime.

12 is divisible by 1+2 and 1*2. (What's the next number with this property?)

12! - 1 is prime (Note: 11! + 1 was prime). (What's another number where n! - 1 is prime and (n-1)! + 1 is prime?)

12^2 + 13^2 is prime.

12^4 + 12^3 + 12^2 + 12^1 + 1 is prime.

12 written in base 12 is 10 (Thus, 12b10 = 10b12 where b should be read "base"). (Do other numbers have this property?)

12 = 3*4 (1,2,3,4 are in order).

There are 12 months in a year.

12 strikes are needed for a perfect game in bowling.

The most common font for articles or essays is 12 point font.

A standard clock is based on mod 12 .

There are 12 ounces in a troy pound (a common measurement for metals).

12 is the largest number with just one syllable.

There are normally 12 pairs of ribs in the human body.

12 inches are in a foot.

2nd Day of the Year.

2 is the only even prime (this makes it "the oddest prime of them all").

2 is prime. 2*2+1 = 5 is prime. 2*5+1 = 11 is prime. 2*11+1 = 23 is prime. 2*23+1 = 47 is prime.

2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...

2^2^2^2 - 2^2^2 divides n^2^2^2 - n^2^2 for all n.

(One of) Euler's formula is V - E + F = 2 for a convex polyhedron, meaning the number of faces and vertices of the object is two more than the number of edges.

x^n + y^n = z^n only works for n = 1 or n = 2.

2 is the only prime of the form n^n + n. (Why?)

There is no prime between n! + 2 and n! + n for any n. (Why? Proof?)

2! is the only prime factorial.

Mars is the only known planet to have two known natural satellites.

2 is the only prime without the letter "e" in its English spelling.

2 = 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + ... where the denominators are the triangular numbers 1,3,6,10,15,21,28,36,... (Proof?)

pi(2^pi) = pi(pi^2) where pi( ) is the prime counting function.

January 3rd (3rd Day of the Year)

Jan 3rd, 1/3.

13 = (10+9)-(8-7+6-5+4-3+2+1)

13 = (10-9)*(8+7-6)+(5-4+3)*(2-1)

13 = (10*9)/(8+7)+6*(5-4)+(3-2)*1

13 has the property is 1 < 3.

13^2 = 169 (1 < 6 < 9).

13^2 = 169 and 31^2 = 961.

2^13 - 1 is prime.

2^13 - 13 is prime.

11 and 13 are the first two-digit twin primes.

There are 13 primes between 2^6 and 2^7 (Note: 6+7 = 13).

13 is of the form 2^n + 3^n (n=2). Only one other known prime is of this form. (What is it?)

13 is of the form 4n+1 (n=3, prime) and 4*13 + 1 is prime.

13 is of the form n^2 + 4 (n=3, prime) and 13^2 + 4 is prime.

(What's another prime with both these properties?)

13 is the smallest number with eight letters in its English spelling (8 and 13 are consecutive Fibonacci numbers).

13 is the smallest emirp (prime written backwards is a different prime).

13 is usually the age when a boy becomes a man, either in religion or psychologically/physiologically.

The number 13 is mainly seen as unlucky; buildings over 13 floors sometimes even skip the number 13 when naming the floors (an elevator will say Floor 1, Floor 2, ... Floor 11, Floor 12, Floor 14, Floor 15, ....).

The American flag has 13 stripes, honoring the original 13 colonies.

Apollo 13 was a "successful failure", the astronauts were unable to land on the Moon; they returned home safely.

Dan Marino in the NFL has the number 13 retired.

The fear of the number 13 is known as triskaidekaphobia.

A baker's dozen is 13, not 12. The 13th is usually for the baker, himself or herself.

(3^3 - 1^3)/(3-1) = 13.

13 written in base 4 is 31 (Note: 1+3 = 4).

The olive branch on the back of a US dollar bill has 13 leaves.

The longest recorded flight of a chicken is 13 seconds.

131211109876543212345678910111213 is prime. (What other numbers have this property?)

ELEVEN + TWO = TWELVE + ONE (mathematically correct and grammatically correct, look at the letters).

The Beatles recorded 13 albums throughout their career together.

The sum of the primes up to 13 equals the 13th prime.

13 is the largest known Fibonacci prime index of a Fibonacci prime.

13333333333333/13 is prime (the numerator has one 1 and thirteen 3's).

pi(13) = 1!*3! where pi( ) is the prime counting function).

The 13th Mersenne prime is 2^521 - 1 and the 13th Lucas number is 521.

13 is the smallest Fibonacci emirp.

1313131313131313131313131 is prime (This is thirteen 13's with the last 3 deleted).

There are 13 composite numbers between 13 and 31.

PG-13 is a movie rating that states it is for people over the age of 13 unless accompanied by an adult.

13 = 3^2 + 3^1 + 3^0

13^13 - pi(13)^pi(13) is prime (This is the largest known prime with this property, guaranteed for numbers less than 10^50000).

3rd Day of the Year.

3 is the first odd prime.

Octopuses have 3 hearts.

1 + 2 = 3.

3^2 + 4^2 = 5^2.

3^3 + 4^3 + 5^3 = 6^3.

It is the only prime triangular number.

Earth is the 3rd planet from the Sun.

3 is a prime number, triangular number, Fibonacci number, Fermat number, and 3! is a perfect number.

3 is the only number where 3! + 1 and 3! - 1 is prime.

There are 3 primary colors (red, green, blue).

3^2^1 = 3! + 2! + 1!

3 begins the only twin prime triplet (3,5,7). (Why isn't there another one?)

3 begins the only cousin prime triplet (3,7,11). (Why isn't there another one?)

3 is the closest integer to pi and e.

pi(3^2) = (pi(3))^2.

3 is the first Fermat prime, first Mersenne prime, and the first lucky prime.

Every integer is the sum of at most 3 triangular numbers.

A triathlon consists of three events: running, swimming, and biking.

A hat-trick in NHL is when a player scores 3 goals in a game; usually the crowd will toss a hat onto the ice.

3 is the only prime of the form n^2 - 1. (Why?)

2^3 + 3 is prime (3 is the smallest prime with this property). (What's the next prime with this property?)

January 4th (4th Day of the Year)

Jan 4th, 1/4.

14 = 3^2 + 2^2 + 1^2

14 = 3^3 - 3^2 - 3^1 - 3^0.

14^2 + 1, 14^2 - 14 - 1, and 14^2 + 14 + 1 are prime.

n^14 + n + 1 is composite for all n > 1.

3.14 is the most common approximation for pi.

14! - 1 is prime.

+- 1 +- 2 +- 3 +- 4 +- 5 +- 6 +- 7 +- 8 = 0 has 14 solutions.

14^2 + 15^2 is prime.

14 is the concatenation of the first two squares (1^2//2^2).

14^6 + 14^5 + 14^4 + 14^3 + 14^2 + 14^1 + 1 is prime.

The sum of the first 14 primes is prime.

14 is the only semiprime Catalan number.

14 is the maximum number of electrons that can fit in an F sublevel.

There are 14 days in a fortnight (two weeks).

There are 14 lines in a sonnet.

4th Day of the Year.

4 has four letters (the only number with this property).

All insects with wings have four wings. Flies are the only exception (they have two).

We live in four dimensions, three dimensions of space and one dimension of time.

Humans have four canines, four incisors, and four wisdom teeth.

Most furniture has 4 legs (chairs, tables, couches,...).

In music, time is constructed in 4 beats.

Tetris is a game comprised of many shapes, all made from four blocks.

The Beatles were known as the "Fab-Four" (John Lennon, Ringo Starr, Paul McCartney, George Harrison).

Many things have 4 of something:

There are 4 basic rules of arithmetic: addition, subtraction, multiplication, and division.

There are 4 seasons: fall, winter, spring, and summer.

There are 4 cardinal directions: north, south, east, and west.

There are 4 suits of playing cards: diamonds, spades, hearts, and clubs.

There are 4 chambers in a mammalian heart.

There are 4 basic states of matter: solid, liquid, gas, and plasma.

There are 4 elements of alchemy: earth, water, air, and fire.

There are 4 fundamental forces: electromagnetism, gravitational, weak nuclear and strong nuclear.

There are 4 giant gas planets: Jupiter, Saturn, Uranus, and Neptune.

There are 4 nucleobase types in DNA: adenine, guanine, cytosine, and thymine.

There are 4 human blood types: A, AB, B, and O.

There are 4 terrestrial planets: Mercury, Venus, Earth, and Mars.

There are 4 giant gas planets: Jupiter, Saturn, Uranus, and Neptune.

There are 4 elementary logical statements: conditional, inverse, converse, and contrapositive.

(Note: there are 14 groups of things above^....unintentional!)

January 5th (5th Day of the Year)

Jan 5th, 1/5.

15 = 1+2+3+4+5 (Note the beginning term is 1, ending term is 5).

15 is the first number of the form 2^n-1 that is not prime.

15 = 1*3*5 (as an odd factorial...1*3*5*7*9*...)

15 is the product of the first two twin primes 3 and 5.

15^2 + 15 + 1 and 15^3 + 15 + 1 are prime.

15^3 + 15 + 1 and 15^3 - 15 - 1 are prime.

15 is the difference of consecutive fourth powers: 15 = 2^4 - 1^4.

15 = 2^3 + 2^2 + 2^1 + 1.

There are 15 primes less than 7^2.

15 written in base 3 is 5!.

In tennis, the first point is worth 15.

"uncopyrightable" is the longest word that does not repeat letters; it is 15 letters long (There are three other examples).

5th Day of the Year.

On average, a human has 5 fingers and 5 toes on each hand/foot.

5*n ends in either a 5 or a 0.

5 is the fifth Fibonacci number (Only prime n that is the nth Fibonacci number).

5 is the only number that is a part of two twin prime pairs, (3,5) and (5,7).

There exists a quadratic, cubic, and quartic formula for finding the roots of said polynomials. However, it is proven for degrees 5 or more, no such formula exists.

5 is the atomic element of boron (Boron has 5 letters).

A Category-5 is the strongest hurricane on Earth. An F-5 is the strongest tornado on Earth.

There are five main senses: seeing, hearing, touching, tasting, smelling.

The Olympic Games has 5 rings, symbolizing the participating continents (North America and South America are counted as one).

Joe DiMaggio from the New York Yankees wore jersey number 5.

In hockey, the area between the goaltender's legs is known as the five-hole.

January 6th (6th Day of the Year)

Jan 6th, 1/6.

16 = 2^4 = 4^2 (only number x^y where x^y = y^x for different x and y values).

16^2 + 1 is prime (Even stronger, 2^8 + 1 is prime -- 2*8 = 16).

16^4 + 1 is prime (Even stronger, 2^16 + 1 is prime).

16!! - 1 is prime.

16 = (2^2)^2 = 2^(2^2)

16^2 - 16 - 1 is prime.

There are 16 digits in the first 10 primes.

16 written in bases 2, 3, and 4 are also squares (10000, 121, and 100 respectively).

16 ounces are in one pound.

16 is the most common minimum age in which a driver's license may be issued to someone.

16 is sometimes seen as the "coming of age" (sweet sixteen).

There are 16 regular season games in the NFL.

The University of Alabama once had 16 different sports teams on probation all at the same time.

There are 16 pawns in a chess set and each player starts with 16 pieces.

Most bank card numbers are 16 digits long.

6th Day of the Year.

6^n for any natural number n will end in a 6.

6 is the first perfect number (with divisors 1,2,3, 1+2+3 = 6, the number itself).

6 = 1*2*3 = 1+2+3

6b10 = 10b6 where 'b' should be read "base"

All primes > 3 are of the form 6n +/- 1.

There are 6 basic trigonometric functions.

A standard guitar has 6 strings.

Insects have 6 legs.

In particle physics, there are 6 types of quark and 6 types of lepton.

There are 6 ice hockey players on the ice per team (including the goalie).

The standard term for office for a US senator is 6 years.

In three dimensions, there are 6 cardinal directions: up, down, left, right, backward, and forward.

January 7th (7th Day of the Year)

Jan 7th, 1/7.

17 = 1^4 + 2^4

17^3 + 17 + 1 is prime.

17 and 71 are prime.

3 is the largest prime factor of 17^2 - 1 (17 is the largest number with this property).

(17^10 + 17^9 + 17^8 + 17^7 + (17^6 + 17^5 + (17^4 + 17^3 + (17^2 + 17 + 1))))... Each expression in parentheses is prime.

17^2 - 17 - 1 is prime.

2^2^2^2^2^2^2 has 17 different values depending on where the parentheses go.

17 is the first number where (11^n-1)/10 is prime (where n = 17).

17 = 2+3+5+7 (first four primes).

n^2 + n + 17 is prime for all n < 17 (n is positive).

17 is the minimum number of givens needed to obtain a unique solution for a sudoku puzzle. This was proven in 2012.

At MIT, in a survey, people were asked to choose a random number between 1 and 20. The most common number was 17.

There are 17 syllables in a haiku.

17^3 = 4913 and 4+9+1+3 = 17 (17 is the largest known prime with this property).

Also, 1+7 is a cube.

A smile uses 17 muscles :-)

17 is the smallest number in which, when written in bases 2,3,4,5,6,7,8, all digit sums are primes.

17+2^1, 17+2^1+2^2, 17+2^1+2^2+2^3, 17+2^1+2^2+2^3+2^4, and 17+2^1+2^2+2^3+2^4+2^5 are all prime.

The first four digits of 2^(17+17) is 1717.

(17^17+1)/(17+1) is prime. (What's another prime with this form?)

No odd Fibonacci number is divisible by 17.

There are 17 ways to express 17 as the sum of one or more primes.

17 is the smaller twin prime (with 19). 71 is the smaller twin prime (with 73). (What's another prime with the same property?)

tan(cos(sin(x))) = .017... for any x when x is in degrees.

17 is the (1*7)th prime.

The sum of the first 17 composite numbers is prime.

Apollo 17 was the last manned Moon landing space mission.

10^17 - 3 and 10^17 + 3 are both primes (known as sexy primes). (What's another power with this property?)

7th Day of the Year.

4^7 - 3^7 is prime (Note: 4+3 = 7). (Do other numbers have this property?)

7 written in base 3 is 21 (Note: 3*7 = 21).

The 7th dimension is the only dimension (besides 3) is well-defined for the cross product.

There are seven Clay Mathematics Millenium Prize Problems for the 2000-3000 years. So far, six remain unsolved.

James Bond's secret agent number is 007.

There are seven days in a week.

There are 7 horizontal rows on the periodic table.

There are 7 colors in a rainbow: red, orange, yellow, green, blue, indigo, and violet.

TUESDAY is the only day that contains 7 letters (a prime number). Also, Tuesday (at least in 2014) is the 7th Day of the Year.

7! - 6! + 5! - 4! + 3! - 2! + 1! is prime. (What's another prime of this form?)

There are 7 prime happy numbers less than 100.

There are 7 indeterminate forms involving 0, 1, and infinity.

14459929 = 1^7 + 4^7 + 4^7 + 5^7 + 9^7 + 9^7 + 2^7 + 9^7.

(77+777)/(7+7) = 61 is prime (Note: there are seven 7s used and 6+1 = 7).

The sum of seven consecutive primes beginning with 7 is seven times the seventh prime.

1!*2!*3!*4!*5!*6!*7! +/- 1 are twin primes. (Are there other numbers with this property as well?)

7 = 2^5 - 5^2 (Also, 2+5 = 7).

(123456789+987654321) +/- 7 are both prime. (Does this happen with other numbers?)

January 8th (8th Day of the Year)

Jan 8th, 1/8.

There are 18 primes less than 2^6.

18^3 + 18 + 1 is prime.

10^18 + 3 is prime.

18 is the only number (besides 0) equal to twice the sum of its decimal digits.

In most countries, at the age of 18, one may vote.

There are 18 holes in a regulation golf course.

8th Day of the Year.

8 is the only cube > 1 that is also a Fibonacci number.

8 is the only nonzero perfect power that is one less than a different perfect power.

Hanukkah is a Jewish festival holiday that lasts eight days and nights.

If written sideways, it's values becomes huge!

8 is the maximum number of electrons that can occupy a valence shell.

All arachnids (spiders) have 8 legs.

There are 8 octants in three dimensions that split up an R^3 space.

8 is considered a lucky in China. In fact, the Summer Olympics in Beijing started at 8:08:08 pm (local time) on 8/8/08.

An octave is interval between two notes with the same letter name (one has double the frequency of the other).

Each side of a chess game has 8 pawns.

Baseball hall of famer Cal Ripken, Jr. wore number 8 when he played for the Baltimore Orioles.

The number 8 has not been retired from the NBA.

A byte is 8 bits, in computer programming and technology.

There are 8 fluid ounces in a cup and 8 pints in a gallon.

January 9th (9th Day of the Year)

Jan 9th, 1/9.

19 = 9*((1/9)*(9/9)+(9+9)/9)*(9/9) (nine 9s and one 1)

1111111111111111111 is prime (There are 19 ones. The next smallest prime of this form is 11).

19 is prime, and so are 191, 193, 197, and 199.

19 is the largest prime less than e^3.

There are 19 primes less than 100 that do not contain a 9.

19^2 + 20^2 is prime.

(5^19-3^19)/2 is prime.

(8^19-3^19)/5 is prime.

(11^19-3^19)/8 is prime.

90*19 + 37 and 90*19 + 73 are both prime.

(5^19-3^19)/2 and (5^19-2^19)/3 are both prime.

Major League Soccer has 19 teams.

19 = (1*9) + (1+9)

19^2 = 361 and 1+9 = 3+6+1.

1111*111^11 + 111111111 + 1 is prime (there are 19 ones).

The 19th Amendment of the Constitution gave women the right to vote.

2^1 + 3^2 + 5^3 + 7^4 + 11^5 + 13^6 + 17^7 + 19^8 is prime.

19 = 4! - 3! + 2! - 1!

19^5 + 19^2 + 19^1 + 19^3 + 19^5 + 19^6 + 19^4 + 19^0 = 52135640

19^19 begins with the digits 19.

2^19 + 3^19 + 5^19 + 7^19 is prime.

19 + 18 + ... + 1 + 0 = 190.

19, 109, 1009, and 10009 are all prime.

19^0 + 19^1 + 19^2 + ... + 19^18 is prime.

The last 19 digits of 17^18 form a prime.

9th Day of the Year.

There are 9 circles of Hell in Dante's "Divine Comedy".

9 = 3^2^1

A nine-point circle is formed by using properties of a triangle.

There were 9 planets in out solar system, before 2006.

0.9999999.... = 1.

January 10th (10th Day of the Year)

Jan 10th, 1/10.

110 = 101 + (10-1)

110 = 11*10

110 = 10^(1+1+0) + 1*10

110 = (10-1)*(10+1) + (11+0)

110 = (11+10)*(10/(1+1)) + (10/(1+1))

110 = (10/(1+1+0))*(11*(1+1))

110^2 + 1 is prime.

110^2 + 110 + 1 is prime.

110^2 + 111^2 is prime.

110^4 + 110^3 + 110^2 + 110 + 1 is prime.

There are 110 triangles (of all sizes) in a regular hexagon if you connect all the vertices.

110^23 + 110^21 + 110^19 + 110^17 + 110^15 + 110^13 + 110^11 + 110^9 + 110^7 + 110^5 + 110^3 + 110 + 1 is prime.

There are 110 primes of the from x^4 + 1 for 1 < x < 1000.

There are 110 primes between 8000 and 9000.

110 = 5^2 + 6^2 + 7^2

A supercentenarian is someone who passes his or her 110th birthday.

There were 110 stories on each World Trade Center in New York.

The expression "give 110%" is usually said to ensure he or she will give it his/her all.

In base 2 and base 3, 110 begins with 110.

10th Day of the Year.

Base 10 was created because humans had 10 fingers on both hands.

10 is also used as a scale value ("From 1 to 10...").

10 = 1+2+3+4 (first four natural numbers)

10 = 2+3+5 (first three primes)

10 = 0!+1!+2!+3! (first four factorials)

10 in base 2 is 10 times 10 in base 3.

There are 10 spacetime dimensions, the 11th dimension in theorized.

The top of the rim of a basketball hoop is 10 feet above the ground.

10 pins are used in most bowling games.

10^2 + 1 is prime.

January 11th (11th Day of the Year)

Jan 11th, 1/11.

111 = 11 + (11-1)^(1+1/1)

111 = 11*11 - (11-1)

111 = 11*(11-1) + 1

111 = (1+1+1)*((1+1+1)*(11+1)+1)

111 = (11+1)*(11-(1+1)) + (1+1+1)

111, 111^2, and 111^3 are all palindromes. (What's the next number with the same property?)

111 = 37*3 (373 is also a palindrome).

111^2 + 111 + 1 is prime.

3^3^3^3^3^3^3^3 has 111 distinct values depending on where you put parentheses.

DigitSum(111^1) = 3 = 3^1

DigitSum(111^2) = 9 = 3^2

DigitSum(111^3) = 27 = 3^3

(What's another number with this property? Can you have fourth powers?)

There are 111 primes less than 610.

111 is divisible by the sum of its digits. (What's another repdigit with this property?)

111 = (1/6)*(1+2+3+....+36)

111, said "eleventy-one", is the age when Bilbo Baggins leaves the Shire in J.R.R. Tolkien's "The Fellowship of the Ring".

There are 111 primes that pass on a clock from 1:00 to 12:59

11th Day of the Year.

11^n is a palindrome for n = 0,1,2,3,4.

11 is of the form 2p+1 (p = 5) and if 11 = p, 2p + 1 is also prime (2*11+1 = 23).

11 describes the number 1 ("one one"), and it's the 1st Day of the Year.

6^11 + 5^11 is prime (Note: 6+5 = 11).

11 is the 5th prime. (5 is prime.) 5 is the 3rd prime. (3 is prime.) 3 is the 2nd prime. (2 is prime.)

11 is a prime of the form R_n where R_n is 11...111 with n 1's. (What's the next R_n prime?)

There are 11 primes less than 2^5.

11! + 1 is prime. (What's the next number with this property? Next prime?)

11, 11+2, 11+6, and 11+8 are all prime.

11 is the smallest natural number with 3 syllables.

If a number is a multiple of 11, its reverse is also a multiple of 11.

There are 11 spacetime dimensions in M-theory.

Apollo 11 was the first manned spacecraft to land on the Moon.

There are 11 players on a US soccer or football field during play.

World War 1 ended in an armistice on the 11th hour of the 11th day of the 11th month of the year.

The maple leaf on the flag of Canada has 11 points.

Clocks on the Canadian currency show 11:00.

11:11 is known as a lucky time of the day that one may make a wish.

The secret formula for Kentucky Fried Chicken includes 11 herbs and spices.

11 + 2n^2 gives prime for the first 11 whole numbers.

There are 11 letters in "prime number".

10! - 11 and 10! + 11 are two consecutive primes (Note: 10 and 11 are consecutive). (What other consecutive numbers have this property?)

11 is the only number such that 11 +- 8 and 11 +- 6 are prime.

11 is the smallest prime where 2^11 - 1 is composite.

11^11+11^11*11+1 is prime (Note: 11 ones are used).

The sum of the 11 primes after 11 is another palindromic prime.

The 2002 All-Star baseball game was determined a tie after 11 innings.

The sum of the first 11 primes ending with a 1 is a prime beginning with 11.

11! + 11! + 11! + 11! + 11! + 1 is prime (Again, there are 11 ones).

2! + 3! + 5! = 7 mod 11 (Note: 2,3,5,7,11 are the first 5 primes).

12345678910 - 11 is prime. (What other number has this property?)

11 is the concatenation of the first 2 Fibonacci numbers.

11 = 1b2 + 11b2 + 111b2 where b represents "base".

January 12th (12th Day of the Year)

Jan 12th, 1/12.

112 = 121 - (11-2)

112 = 11*12 - (21-1)

112 = 11^2 - (12-(1+2))

112 = (1+1+2)*(12 + (1*1*2)^(1+1+2))

112 = 12 + 11 + 21 + (1*1*2)*(12 + 11*2)

112 = (1+12) + (11*2) + (11+12) + (21+1) + (21+11)

112^4 contains all odd digits (excluding the ones digit, of course). (Do other numbers share the same property?)

112*211 is palindromic. (What others numbers are like this?)

112^32 + 1 is prime. (What's another number with the same property?)

There are 112 ways to place 5 nonattacking bishops on a 4 by 4 board.

There are 112 primes between 9000 and 10000.

112 = 11 + 13 + 17 + 19 + 23 + 29 (six consecutive primes).

A British long hundredweight is 112 pounds.

112 written in base 36 is less than 36 (34, actually).

112 contains a letter when written in base 11 (the first base that may have letters).

12th Day of the Year.

12 = (10-9)*(8+7)-6*(5-4)+(3*(2-1))

12 = (10+9)-(8-7)-(6+5)+(4+(3-2)*1)

12 = (10*9)/(8+7)+(6-5)*(4+3-2+1)

12 = (10-9)*(8-7) + (6+5)*(-4+3*2-1)

12 = 3!*2!*1!*0!

12^2 + 12 + 1 and 12^3 + 12 + 1 are prime.

12 is divisible by 1+2 and 1*2. (What's the next number with this property?)

12! - 1 is prime (Note: 11! + 1 was prime). (What's another number where n! - 1 is prime and (n-1)! + 1 is prime?)

12^2 + 13^2 is prime.

12^4 + 12^3 + 12^2 + 12^1 + 1 is prime.

12 = 3*4 (1,2,3,4 are in order).

There are 12 months in a year.

12 strikes are needed for a perfect game in bowling.

The most common font for articles or essays is 12 point font.

A standard clock is based on mod 12 .

There are 12 ounces in a troy pound (a common measurement for metals).

12 is the largest number with just one syllable.

There are normally 12 pairs of ribs in the human body.

12 inches are in a foot.

January 13th (13th Day of the Year)

Jan 13th, 1/13.

113 = 131 - 3*(3*(1+1))

113 = 31*(1+1+3) - (31+11)

113 = 13*(1+1+3) + 31 + (1+1)^3 + 3^(1+1)

113 = (13+31)*(1+1+3) - 11^(3-1) + (1+13)

113 = (31-13)*(1+1+3) + (11-(1-13))

113 = 11*3 + 31*1 + 1*13 + (3*(1+1))^(3-1^1)

113^3 = 1442897 (contains two squares concatenated....144 and 289). (Do other numbers have this property?)

113 and 311 are primes. (What's another number with the same property?)

Eliminating any digit in 113 still results in a prime. (What's another number like this?)

Any two digit number generated from 113 is prime. (What other numbers display this property?)

113 is the smallest prime factor of 12345678910111213 (concatenation of first 13 natural numbers).

A113 is the license plate on Andy's mom's car in the movie Toy Story.

13th Day of the Year.

13 = (10+9)-(8-7+6-5+4-3+2+1)

13 = (10-9)*(8+7-6)+(5-4+3)*(2-1)

13 = (10*9)/(8+7)+6*(5-4)+(3-2)*1

13 has the property is 1 < 3.

13^2 = 169 (1 < 6 < 9).

13^2 = 169 and 31^2 = 961.

2^13 - 1 is prime.

2^13 - 13 is prime.

11 and 13 are the first two-digit twin primes.

There are 13 primes between 2^6 and 2^7 (Note: 6+7 = 13).

13 is of the form 2^n + 3^n (n=2). Only one other known prime is of this form. (What is it?)

13 is of the form 4n+1 (n=3, prime) and 4*13 + 1 is prime.

13 is of the form n^2 + 4 (n=3, prime) and 13^2 + 4 is prime.

(What's another prime with both these properties?)

13 is the smallest number with eight letters in its English spelling (8 and 13 are consecutive Fibonacci numbers).

13 is the smallest emirp (prime written backwards is a different prime).

13 is usually the age when a boy becomes a man, either in religion or psychologically/physiologically.

The number 13 is mainly seen as unlucky; buildings over 13 floors sometimes even skip the number 13 when naming the floors (an elevator will say Floor 1, Floor 2, ... Floor 11, Floor 12, Floor 14, Floor 15, ....).

The American flag has 13 stripes, honoring the original 13 colonies.

Apollo 13 was a "successful failure", the astronauts were unable to land on the Moon; they returned home safely.

Dan Marino in the NFL has the number 13 retired.

The fear of the number 13 is known as triskaidekaphobia.

A baker's dozen is 13, not 12. The 13th is usually for the baker, himself or herself.

(3^3 - 1^3)/(3-1) = 13.

13 written in base 4 is 31 (Note: 1+3 = 4).

The olive branch on the back of a US dollar bill has 13 leaves.

The longest recorded flight of a chicken is 13 seconds.

131211109876543212345678910111213 is prime. (What other numbers have this property?)

ELEVEN + TWO = TWELVE + ONE (mathematically correct and grammatically correct, look at the letters).

The Beatles recorded 13 albums throughout their career together.

The sum of the primes up to 13 equals the 13th prime.

13 is the largest known Fibonacci prime index of a Fibonacci prime.

13333333333333/13 is prime (the numerator has one 1 and thirteen 3's).

pi(13) = 1!*3! where pi( ) is the prime counting function.

The 13th Mersenne prime is 2^521 - 1 and the 13th Lucas number is 521.

13 is the smallest Fibonacci emirp.

1313131313131313131313131 is prime (This is thirteen 13's with the last 3 deleted).

There are 13 composite numbers between 13 and 31.

PG-13 is a movie rating that states it is for people over the age of 13 unless accompanied by an adult.

13 = 3^2 + 3^1 + 3^0

13^13 - pi(13)^pi(13) is prime (This is the largest known prime with this property, guaranteed for numbers less than 10^50000).

13 is the only prime of the form n^2 + n + 1 (n=3) and 13^2 + 13 + 1 is prime.

January 14th (14th Day of the Year)

Jan 14th, 1/14.

114 = 141 - 14 - (14-1)

114 = 11*4 + 41*1 + 1*14 + (1+14)

114 = (1+14)*(1+1+4) + 11 - (1-14)

114 = 41 - (1-14)*(1+1+4) - (4+1)

114 = 11*14 - (41-1)

114 = (1+14) + (11+4) + (41+1) + (4+11) + 41 - 14

The sum of the first 114 primes is prime.

There are 114 primes less than 25^2.

114^32 + 1 is prime. (What's the next number with this property?)

3^114 + 10 is prime. (What's the next number with the same property?)

4^4^4^4^4^4^4^4 has 114 different values (depending on where you put the parentheses).

There are 114 primes between 5000 and 6000.

114 written in base 36 is 36. (What other numbers have this property for other bases?)

14th Day of the Year.

14 = 3^2 + 2^2 + 1^2

14 = 3^3 - 3^2 - 3^1 - 3^0.

14^2 + 1, 14^2 - 14 - 1, and 14^2 + 14 + 1 are prime.

n^14 + n + 1 is composite for all n > 1.

3.14 is the most common approximation for pi.

14! - 1 is prime.

+- 1 +- 2 +- 3 +- 4 +- 5 +- 6 +- 7 +- 8 = 0 has 14 solutions.

14^2 + 15^2 is prime.

14 is the concatenation of the first two squares (1^2//2^2).

14^6 + 14^5 + 14^4 + 14^3 + 14^2 + 14^1 + 1 is prime.

The sum of the first 14 primes is prime.

14 is the only semiprime Catalan number.

14 is the maximum number of electrons that can fit in an F sublevel.

There are 14 days in a fortnight (two weeks).

There are 14 lines in a sonnet.

January 15th (15th Day of the Year)

Jan 15th, 1/15.

115 = 5*((1+15) + (1+1+5))

115 = 51 + (1+1)^(11-5)

115 = ((1+1)*5)^(1+1) + 15

115 = 11*15 - (51-1)

115 = 11^(1+1) - (11-5)

115 = 15*(1+1+5) + (1+1)*5

115 = 23*5 (23 > 5 but 2 < 3 < 5). (Do other numbers satisfy this property?)

115 = 23*5 (prime factorization only uses prime numbers). (What's the next highest number with this property?)

115*511 = 58765 (contains a run of '8765') (Are there other numbers with the same property? Run of 5? 6? etc.)

115 has 666 pages on the OEIS (As of January 15th, 2014).

115 + (1+1+5) and 115 + (1*1*5) are one away from a perfect square (11^2). (Do other numbers have this property?)

115^6 + 115^5 + 115^4 + 115^3 + 115^2 + 115 + 1 is prime. (What other numbers are like this?)

5^5^5^5^5^5^5^5 has 115 distinct values (depending on where you put the parentheses).

(The same argument goes for 6,7,8,9, and 10).

115 is composite but its digits are not. (What's another number like this?)

115 = 5! - 5

As of 2013, the oldest verified person is 115 years old. Her name is Misao Okawa. (Curiously, the top ten oldest verified people are all female.)

15th Day of the Year.

15 = 1+2+3+4+5 (Note the beginning term is 1, ending term is 5).

15 is the first number of the form 2^n-1 that is not prime.

15 = 1*3*5 (as an odd factorial...1*3*5*7*9*...)

15 is the product of the first two twin primes 3 and 5.

15^2 + 15 + 1 and 15^3 + 15 + 1 are prime.

15^3 + 15 + 1 and 15^3 - 15 - 1 are prime.

15 is the difference of consecutive fourth powers: 15 = 2^4 - 1^4.

15 = 2^3 + 2^2 + 2^1 + 1.

There are 15 primes less than 7^2.

15 written in base 3 is 5!.

In tennis, the first point is worth 15.

"uncopyrightable" is the longest word that does not repeat letters; it is 15 letters long (There are three other examples).

January 16th (16th Day of the Year)

Jan 16th, 1/16.

116 = 61 + (6-1)*11

116 = 66 + (11-6)*(6-1)*(1+1)

116 = (61+1) + (1+16) + (11+6) + (16+(6-1-1))

116 = 11*16 - (16-1)*(6-1-1)

116 = 11^(1+1) - (6-1*1)

116 = (6-1-1)*(11+16+(1+1))

116^2 = 13456 (1 < 3 < 4 < 5 < 6 and '3456' is a run of 4 consecutive numbers). (Does this happen with other numbers?)

116^2 + 1 is prime. (What's the next number like this?)

116! + 1 is prime. (What's another number with the same property?)

90*116 + 37 and 90*116 + 73 are prime. (What's the next number with both of these properties?)

116^16 + 117^16 is prime. (What's the next number with the same property?)

There are 116 different possible rows/columns in an 11 by 11 crossword puzzle.

The number 1 appears 116 times in the first 1000 digits of pi.

3^116 + 2^115 is prime. (What's the next number with this property?)

116 written as a Roman numeral uses all different letters (CVXI).

The Hundred Years' War between England and France actually lasted 116 years (1337 - 1453).

116 is the record number of wins in Major League Baseball (set by Chicago Cubs in 1906 then Seattle Mariners in 2001).

16th Day of the Year.

16 = 2^4 = 4^2 (only number x^y where x^y = y^x for different x and y values).

16^2 + 1 is prime (Even stronger, 2^8 + 1 is prime).

16^4 + 1 is prime (Even stronger, 2^16 + 1 is prime).

16!! - 1 is prime.

16 = (2^2)^2 = 2^(2^2)

16^2 - 16 - 1 is prime.

There are 16 digits in the first 10 primes.

16 written in bases 2, 3, and 4 are also squares (10000, 121, and 100 respectively).

16 ounces are in one pound.

16 is the most common minimum age in which a driver's license may be issued to someone.

16 is sometimes seen as the "coming of age" (sweet sixteen).

There are 16 regular season games in the NFL.

The University of Alabama once had 16 different sports teams on probation all at the same time.

There are 16 pawns in a chess set and each player starts with 16 pieces.

Most bank card numbers are 16 digits long.

January 17th (17th Day of the Year)

Jan 17th, 1/17.

117 = 71 + (7-1-1)*(7+1+1) + 1

117 = 11 + (11+7) - (1-17) + (71+1)

117 = 11*17 - (7-1-1)*(7*(1+1))

117 = 171 - (7-1*1)*(7+1+1)

117 = (7-1-1)*(1+17) + (7+1+1)*((7-1)/(1+1))

117 = (1+1+7)*11 + (1+17)

117 = (11-7)*(11+7) + (7+1+1)*(7-1-1)

117^2 = 13689 (1 < 3 < 6 < 8 < 9). (Do other numbers larger than 117 have this property?)

117*DigitSum(117) is the first four digit number (for 3-digit numbers, abc). (What's the smallest 2-digit number AB such that AB*DigitSum(AB) is a 3-digit number? 4-digit number?)

117^2 + 117 + 1 is prime. (What's another number with the same property?)

117^4 + 117^3 + 117^2 + 117 + 1 is prime. (What other numbers have this property?)

10^21 + 17 is the first prime after 10^21.

10^23 + 17 is the first prime after 10^23.

117 is a divisor of 999999.

There are 117 primes between 6000 and 7000.

There are 117 primes between 18^3 and 19^3.

The 1992 United States men's Olympic basketball team averaged 117 points per game.

17th Day of the Year.

17 = 1^4 + 2^4

17^3 + 17 + 1 is prime.

17 and 71 are prime.

3 is the largest prime factor of 17^2 - 1 (17 is the largest number with this property).

(17^10 + 17^9 + 17^8 + 17^7 + (17^6 + 17^5 + (17^4 + 17^3 + (17^2 + 17 + 1))))... Each expression in parentheses is prime.

17^2 - 17 - 1 is prime.

2^2^2^2^2^2^2 has 17 different values depending on where the parentheses go.

17 is the first number where (11^n-1)/10 is prime (where n = 17).

17 = 2+3+5+7 (first four primes).

n^2 + n + 17 is prime for all n < 17 (n is positive).

17 is the minimum number of givens needed to obtain a unique solution for a sudoku puzzle. This was proven in 2012.

At MIT, in a survey, people were asked to choose a random number between 1 and 20. The most common number was 17.

There are 17 syllables in a haiku.

17^3 = 4913 and 4+9+1+3 = 17 (17 is the largest known prime with this property).

Also, 1+7 is a cube.

A smile uses 17 muscles :-)

17 is the smallest number in which, when written in bases 2,3,4,5,6,7,8, all digit sums are primes.

17+2^1, 17+2^1+2^2, 17+2^1+2^2+2^3, 17+2^1+2^2+2^3+2^4, and 17+2^1+2^2+2^3+2^4+2^5 are all prime.

The first four digits of 2^(17+17) is 1717.

(17^17+1)/(17+1) is prime. (What's another prime with this form?)

No odd Fibonacci number is divisible by 17.

There are 17 ways to express 17 as the sum of one or more primes.

17 is the smaller twin prime (with 19). 71 is the smaller twin prime (with 73). (What's another prime with the same property?)

tan(cos(sin(x))) = .017... for any x when x is in degrees.

17 is the (1*7)th prime.

The sum of the first 17 composite numbers is prime.

Apollo 17 was the last manned Moon landing space mission.

10^17 - 3 and 10^17 + 3 are both primes (known as sexy primes). (What's another power with this property?)

January 18th (18th Day of the Year)

Jan 18th, 1/18.

118 = 81 + (11+8) + 18

118 = (81+1) + (8-1-1)^(1+1)

118 = (11-8)*(11+8) + (81-1) - (1+18)

118 = 11*8 + 11 + (1+18)

118 = 11*18 + (11-8)^(8/(1+1)) + 1

118 = 181 - (8+1)*(8-1)

118^2 = 13924 (contains 3,2,4 in order-- 324 = 18^2).

118^4 = 193877776 (run of four 7s). (Are there other numbers with this property or a similar property?)

118 = 2*59 (2 < 59 and 2 < 5 < 9). (What's another number satisfying this property?)

118^4 + 118^3 + 118^2 + 118 + 1 is prime (similarly, 117 had the same property). (Are there other pairs of numbers with this property?)

118^4 + 1 = 193877777 is prime.

118^8 + 1 is prime.

118 = 3^5 - 5^3. Also, 5*118 + 3 and 3*118 + 5 is prime.

118^8 + 119^8 is prime.

118!! + 1 is prime.

118!! - 1 is prime.

118!!!! +1 is prime.

(What's another number satisfying one, two, three, ... of these properties? Any satisfying all?)

The number of primes between 118^2 and 119^2 equals the number of primes between 118 and 2*118. (With what other numbers does this happen?)

There are 118 perfect squares less than 24^3.

1 + 2*118 + 3*118^2 + 4*118^3 is prime (Meaning if 118 = n, 1 + 2n + 3n^2 + 4n^3 is prime). (What's the next number like this?)

18th Day of the Year.

There are 18 primes less than 2^6.

18^3 + 18 + 1 is prime.

10^18 + 3 is prime.

18 is the only number (besides 0) equal to twice the sum of its decimal digits.

In most countries, at the age of 18, one may vote.

There are 18 holes in a regulation golf course.

January 19th (19th Day of the Year)

Jan 19th, 1/19.

119 = 91 + 19 +1*1*9

119 = 11*9 + (11+9)

119 = (9+1+1)^(11-9) - (1+1)

119 = (11+9) + (1+19) + (9+11) + (91+1) - (11+19) - (1+1+9) + (9-1*1)

119 = 9^(1+1) + (1+1)*19

119 = 11*19 - 9^(1+1) - 9

119 = (1+1)^(9-1-1) - 1*1*9

119 = (9-1-1)*(9+1+1) + (1+1)*19 + (1+1)^(1+1)

119 = (9-1-1)*(9*1*1) + (11+19) + (19+(9-1-1))

119 = ((9-1-1)-(11-9))! - 1

119^2 + 119 + 1 is prime. (What's the next number displaying the same property?)

1+1+9 = 11 (contained in 119). (What's another number like this?)

There are 119 primes between 4000 and 5000.

2^119 - 119^2 is prime. (What's another number displaying this property?)

10^41 - 119 is the last prime before 10^41.

119^4 + 120^4 is prime. (What's another number with this property?)

The sum of proper divisors of 119 is 25 (1+7+17).

The sum of the divisors of 119 is 144 (1+7+17+119).

(Note: Both are perfect squares).

(Does this happen for other numbers?)

119 is the smallest composite that is 1 less than a factorial (5! - 1).

119 = 17 + 19 + 23 + 29 + 31 (5 consecutive primes).

119 written in bases 2, 5 and 16 are palindromes (1110111, 434, and 77, respectively).

19th Day of the Year.

19 = 9*((1/9)*(9/9)+(9+9)/9)*(9/9) (nine 9s and one 1)

1111111111111111111 is prime (There are 19 ones. The next smallest prime of this form is 11).

19 is prime, and so are 191, 193, 197, and 199.

19 is the largest prime less than e^3.

There are 19 primes less than 100 that do not contain a 9.

19^2 + 20^2 is prime.

(5^19-3^19)/2 is prime.

(8^19-3^19)/5 is prime.

(11^19-3^19)/8 is prime.

90*19 + 37 and 90*19 + 73 are both prime.

(5^19-3^19)/2 and (5^19-2^19)/3 are both prime.

Major League Soccer has 19 teams.

19 = (1*9) + (1+9)

19^2 = 361 and 1+9 = 3+6+1.

1111*111^11 + 111111111 + 1 is prime (there are 19 ones).

The 19th Amendment of the Constitution gave women the right to vote.

2^1 + 3^2 + 5^3 + 7^4 + 11^5 + 13^6 + 17^7 + 19^8 is prime.

19 = 4! - 3! + 2! - 1!

19^5 + 19^2 + 19^1 + 19^3 + 19^5 + 19^6 + 19^4 + 19^0 = 52135640

19^19 begins with the digits 19.

2^19 + 3^19 + 5^19 + 7^19 is prime.

19 + 18 + ... + 1 + 0 = 190.

19, 109, 1009, and 10009 are all prime.

19^0 + 19^1 + 19^2 + ... + 19^18 is prime.

The last 19 digits of 17^18 form a prime.

January 20th (20th Day of the Year)

Jan 20th, 1/20.

120 = 201 - (12-(1+2))^(1*2+0)

120 = (10/2)!

120 = 102 + 2*(20-1*2)

120 = 12*10

120 = (1+20)*(12/(1*2)) - (1+2+0)!

120 = (20-1)*(12-(1+2+0)!) + 12/(1*2)

120 = 1+2+3+...+15 = 1*2*3*4*5 (Note: 15 is a multiple of 5, specifically, (1+2+0)*5 = 15).

120 = 1 + (1+2) + (1+2+3) + ... + (1+2+3+4+5+6+7+8)

120^2 + 1 is prime.

120 is divisible by 1,2,3,4,5,6.

120^4 + 120^3 + 120^2 + 120^1 + 1 is prime.

120 is the factorial of the third prime (Note: 1+2+0=3).

120 written in base 4 is 1320 (Note one and only one of each distinct digit is used).

120 = 59 + 61 = 23 + 29 + 31 + 37 (sum of a multiple number of primes).

120 = 8 + 16 + 32 + 64 (four consecutive powers of 2).

120 = 3 + 9 + 27 + 81 (four consecutive powers of 3).

120 is the smallest multiple of 6 that is not adjacent to a prime.

120 is the smallest number of appear 6 times in Pascal's Triangle (Note: (1+2+0)! = 6).

The height of an NBA basketball hoop is 120 inches.

20th Day of the Year.

20 = 1 + (1+2) + (1+2+3) + (1+2+3+4)

20/20 is often referred to as having perfect vision.

20 is of the form k! - k (k=4).

January 21st (21st Day of the Year)

Jan 21st, 1/21.

121 = 11^2 (uses 1,2,1).

121 = 1*21 + 12*1 + 11*(12-(1+2+1))

121 = 12^(1*2*1) - (12+11)

121 = 12*(12-1) - (12-(1+2)+1)

121 = 21*(1*2+2*1+(1*2*1)) - (1+2)! - 1!

121 = (1+2+1)*(12+21) - 11

121 = 3^4 + 3^3 + 3^2 + 3^1 + 1 (Only square number of this form, given 3 is prime).

DigitSum(121^1) = 4^1.

DigitSum(121^2) = 4^2.

121 and 121^2 are palindromes.

121^2 - 121 - 1 is prime. (What's another palindrome with this property? Square?)

121^1 contains 2 different digits.

121^2 contains 3 different digits.

121^3 contains 4 different digits.

(Are there other numbers with this property?)

121 = 37 + 41 + 43 (three consecutive primes).

121 = 5! + 1 (What's another square with this property? Another palindrome?)

121 written in bases 3, 7, and 8 are palindromes (11111, 232, and 171, respectively). (What's another palindrome with this property?)

121 written in bases 5, 9, 11, 15 and 28 are squares (441, 144, 100, 81, and 49, respectively). (What's another square with this property?)

21st Day of the Year.

21 = 1+2+3+4+5+6

21 written in base 3 is 120 (reverse of which is 21).

21 = 4^2 + 4^1 + 1.

21 is the smallest number not close to a power of 2 (for 2^n, you are "close" if you are within +/- n).

No NFL team has retired the number 21.

We are in 21st century.

Research determined that the average weight of the soul is 21 grams, but the weight is regarded as meaningless.

January 22nd (22nd Day of the Year)

Jan 22nd, 1/22.

122 = 12^2 - 22

122 = (12-2)^((2-1)*2) + 22

122 = (22/(1+2/2))^2 + (1-2+2)

122 = 12*22 - 212 + (12*(1+2+2)) + (12-2)

122 = (1+2+2)*(12*2) - (1-2)*2

122 = (1*2*2)*(22+2^(1+2)) + 2*(2-1)

122 = (1+22)*(1+2+2) + 12-(1+2+2)

122 = (12+2)*((1+2)^2) - (1*2*2)

122 = (22-1)*((1+2)*2) - (1*2*2)

122^4 uses 1,2,3,4,5,6. (Do other numbers have a similar property?)

122^1 has 2 different digits.

122^2 has 3 different digits.

122^3 has 4 different digits.

(What's the next number with all three properties?)

122*221 is a palindrome (26962) and 2 < 6 < 9 > 6 > 2.

122^2 + 123^2 is prime. (What's another number like this?)

122^4 + 122^3 + 122^2 + 122^1 + 1 is prime.

122^6 + 122^5 + 122^4 + 122^3 + 122^2 + 122^1 + 1 is prime.

(Do other numbers have both these properties?)

There are 122 primes less than 26^2.

The numerator of 1 + 1/2 + 1/3 + ... + 1/122 is prime. (What is the prime number on the numerator?)

The number of primes between [122,2*122] equals the number of primes between [122,122^2]. (What's the next number with the same property?)

678901234567890123456.... (122 digits) is prime.

122 is the largest known number in which there are no twin primes between 122^2 and 123^2.

22nd Day of the Year.

Perfect squares can only end in 22 different two-digit ends (00, 01, 04, 09, ...), thus ruling out 78% of all other numbers no matter how large.

Only using one digit endings, you can only rule out 40% of all numbers (numbers ending in 2,3,7,8).

22 written in base 3 and base 4 are reversals of each other (211 and 112, respectively).

There are 22 primes between 76^2 and 77^2.

1 + the sum of the first 22 primes is divisible by 22.

22 is the first two-digit Smith number. 22 = 11*2 and 2+2 = (1+1)+2.

22 is the only number that describes itself (two two).

January 23rd (23rd Day of the Year)

Jan 23rd, 1/23.

123 = 13^2 - (3-2+1)*23

123 = 12^(3-2+1) - (2^3-1)*21

123 = 12*3 + 1*23 + 3*21 + 32*1 - 31

123 = (12+3) + (1+23) + (3+21) + (32+1) + (1+2)^3

123 = (13-2)^(1-2+3) + (3-2+1)

123 = (1+2+3)*((3+2-1)*(3*2-1)) + (3*(2-1))

123 = (1+23)*(3*2-1) - (1-2)*3

123 = (12+3)*(1*2^3) + (12/3-(3-2)/1)

123 = (12-3)*((2^3-1)+(1*2*3)) + (1+2+3)

1*2*3 = 1+2+3

123^4 only has odd digits (disregarding the ones digit). (Are there other numbers with the same property?)

3^123 + 2 is prime and 123^3 +2 is prime (Note: 3 and 2 used here are also in the string '123'). (Are there other numbers that satisfy both these properties?)

10^123 + 3 is prime (Meaning, 1000...0003 where there are 122 zeroes is prime). (What's the next number with the same property?)

10^25 - 123 is the largest prime less than 10^25.

10^63 - 123 is the largest prime less than 10^63.

123^4 + 124^4 is prime.

(Also, 121^4 + 122^4 and 122^4 + 123^4 are prime).

(What's another run of 3 consecutive numbers satisfying this property?)

23rd Day of the Year.

(23-1)/2 = 11 is prime. (11-1)/2 = 5 is prime. (5-1)/2 = 2 is prime.

23 divides the sum of the first 23 primes.

11111111111111111111111 is prime (23 ones).

23 is the first nontrivial prime with all prime digits.

There are 23 primes between 79^2 and 80^2.

The 23rd Fibonacci number is prime (as is 23).

23 is the smallest prime that has a gap of 6 between the next prime.

23 = 3*3*3 - 2*2 (Note: three 3's and two 2's).

23 is prime, an 2+3 = 5 is prime.

23^4 + 23^3 + 23^2 + 23^1 + 1 is prime.

23 is the smallest odd prime that is not a twin prime.

23 = 5 + 7 + 11 (three consecutive primes). Note the first 5 consecutive primes.

23 (along with one other number) cannot be expressed as the sum of fewer than 9 integer cubes.

If you have 23 people in a room, there is a 50% chance two share a birthday.

23! is 23 digits long (Only prime with this property).

Playing darts, 23 is the lowest score that cannot be gained by throwing a single dart.

Julius Caesar was stabbed 23 times.

The floor of e^pi is 23.

Hilbert's Problems are a list of 23 problems mathematician David Hilbert put forth in 1900.

Homo sapiens have 23 pairs of chromosomes.

11111*1111^11 + 11111111111 + 1 (23 ones) is prime.

23! is the smallest factorial where the digits 0,...,9 appear at least once.

If you would be able to fold a standard sheet of paper 23 times in half, it would become over a mile thick.

If 23 = n, n0123456789 is prime (Meaning, 230123456789 is prime).

23 = 0^5 + 1^4 + 2^3 + 3^2 + 4^1 + 5^0

123571113171923 and 231917131175321 are prime (concatenation of the first noncomposites up to 23).

If A = 1, B = 2, ... Z = 26. Then ODD = 15+4+4 = 23. And ODD + ODD = EVEN (46). Note the mathematical truth in this as well.

January 24th (24th Day of the Year)

Jan 24th, 1/24.

124 = 14^2 - 24*(4-2+1)

124 = 12^(4-2*1) - (12+1*2*4)

124 = (14-(4-2+1))^(4-2*1) + (4-2+1)

124 = 12*4 + 1*24 + (42+(4+1)*2)

124 = 4*21 + 42*1 - (4-2*1)

124 = (12+4) + (1+24) + (4+21) + (42+1) + (4-1)*(4+1)

124 = 214 - 2*(42+(4-2+1))

124 = 142 - (4-2)*(4*2+1)

124 = (1+2+4)*(1+2^4) + (4+2-1)

124 = (1*2*4)*(24-(1+2*4)) + (2-1)*4

124 = (12+4)*(2^(4-1)) - 4*(2-1)

124 = (1+24)*(4+2-1) - (4-2-1)

124^2 + 1 is prime. (What's the next number with the same property?)

The sum of the first 124 primes is prime.

3^124 + 28 and 3^124 - 28 are prime. (What's the next number with this property?)

124 written in bases 8 and 9 use the same digits (174 and 147, respectively). (What other numbers share a similar property?)

124 = 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 (8 consecutive primes).

+- 1 +- 2 +- 3 +- 4 +- 5 +- 6 +- 7 +- 8 +- 9 +- 10 +- 11 +- 12 = 0 has 124 solutions.

24th Day of the Year.

24 is divisible by 2+4, 2*4, and 2-4.

24 = 1*2*3*4 = 7+8+9

2^24 does not contain a 0.

24 divides the 24th Fibonacci number.

24 = 4*6 (first two composite numbers).

2^24 is the smallest power of 2 containing 3 of the same digits consecutively.

24 is the smallest number with 8 divisors (Note: 2*4 = 8).

1^2 + 2^2 + ... + 24^2 = 70^2.

There are 24 hours in a day.

The following are prime:

24^2 + 1.

24^2 + 24 + 1.

24^4 + 1  (24*4 + 1 is also prime).

24^2 + 25^2.

24^4 + 24^3 + 24^2 + 24^1 + 1.

January 25th (25th Day of the Year)

Jan 25th, 1/25.

125 = 5^(2+1)

125 = 152 - (5-2)^(2+1)

125 = 215 - 21*5 + 15

125 = 1*25 + 12*5 + (1+2+5)*(5*(2-1))

125 = 5*21 + 52*1 - 1*2^5

125 = (1+2+5)*((1+2)*5) - (1-2)*5

125 = (1*2*5)*(2*(1+5)) + 5*(2-1)

125 = (1+25)*(5*(2-1)) - ((5+1)/2 + (5-2-1))

125 = (12+5)*(2+5) + (5+2-1)

125 = (52+1)*(5-2-1) + (21-(5-2-1))

125 = 2^(5+1) + (52+(5*2-1))

125^n ends in "25" for all positive integers n. (This works for any number ending in 25).

125*521 contains 125. (What's the next number with the same property?)

125 = 5^3.

1+2+5 = 2^3.

(Are there other numbers with both these properties?)

There are 125 primes less than 700.

125^2 + 4 is prime (Note: 125 is of the form p^2 + 4 for prime p as well). (What's another number with both these properties?)

125 equals the third prime to the third power.

There are 125 primes between 19^3 and 20^3.

There are 39 primes between 125^2 and 126^2 and 39 primes between 125 and 2*125.

25th Day of the Year.

There are 25 primes less than 100.

25 = 5^2 (Note the use of 2 and 5).

5/2 = 2.5 (Note the use of 2 and 5).

25^2 + 26^2 is prime (Note: 24^2 + 25^2 was also prime).

25^2 - 25 - 1 is prime (Also, 24^2 + 24 + 1 was prime).

25 = 3^2 + 4^2

5^n ends in 25 for all integers n > 2.

25^n ends in 625 for all integers n > 2.

625^n ends in 0625 for all integers n > 2.

January 26th (26th Day of the Year)

Jan 26th, 1/26.

126 = 2^(1+6) - (6/2-1)

126 = 6^(2+1) - (62+21) - (6+2-1)

126 = 162 - 6^(2*1)

126 = 261 - ((1+2)^(6/2))*(6-(2-1))

126 = (1*26) + (12*6) + (6+2-1)*(6/2+1)

126 = (6*21) + (62*1) - 2*(26+(6-(2-1)))

126 = 612 - 261 - (12+(6-2-1))^(6/2-1)

126 = (1+26) + (12+6) + (6+21) + (62+1) - (1+2+6)

126 = (1+2+6)*(16-2)

126 = (1*2*6)*((6-1)*2) + (6*(2-1))

126 = (12+6)*(6+2-1)

126 = (1+26)*(6/2+1) + (1+2)*6

126 = (62+1)*(6/2-1)

126^3 contains 3 zeroes yet 126 has no zeroes. (126 is the smallest number with this property.)

126^2 + 1 is prime.

Nuclei with 126 protons or neutrons are the largest nuclei that are more stable against nuclear decay.

126^6 + 126^5 + 126^4 + 126^3 + 126^2 + 126^1 + 1 is prime. (What's the next number with this property?)

There are 126 perfect squares less than 25^3 (incl 25^3).

26th Day of the Year.

26 is of the form 5^2 + 1 (5 is prime) and 26^2 + 1 is prime.

26 is the only number sandwiched between a perfect square and a perfect cube (5^2 and 3^3).

26!! - 1 is prime.

There are 26 letters in the English alphabet.

26^6 + 26^5 + 26^4 + 26^3 + 26^2 + 26^1 + 1 is prime.

26 = 2*(3^0) + 2*(3^1) + 2*(3^2)

There are 26 spacetime dimensions in bosonic string theory.

No NBA or NFL team has retired number 26.

There are roughly 26 miles in a marathon.

January 27th (27th Day of the Year)

Jan 27th, 1/27.

127 = 172 - (1*7+2)*(1*7-2)

127 = 217 - (7+2)*(1+2+7)

127 = (1*27) + (12*7) + (12+(7-2-1))

127 = (7*21) + (72*1) - (7-2-1)*(17+(7-2+1))

127 = 2^(7*1) - (7+2+1) - (1+2)*(7-2-1-((7-2)/(12-7)))

127 = (12+7) + (1+27) + (7+21) + (72+1) - (1+2)*7

127 = (12+7)*(7*(2-1)) - (7-(2-1))

127 = (12-7)*((7-2)^(2-1)) + (1+2+7)/(7-2*1)

127 = (1+27)*(7/2+1) + (12/(7*2-2*(2-1)))

127 = (72+1)*((7-2-1)/(2*1)) - (17+2)

127 = (27-1)*(7-2*1) - (7-2-1-(2-1))

127 = (1+2+7)*(7*2-1) - 12 - (7+2*1)

127 = (1*2*7)*(1*2+7) + (17-2^(7-2-1))

127^4 + 127^3 + 127^2 + 127^1 + 1 is prime. (What's another number like this?)

127^16 + 128^16 is prime. (What's the next number satisfying the same property?)

127 is a Mersenne prime (prime of the form 2^p - 1 for a prime p).

Further, 2^127 - 1 is a prime itself. It is the largest prime ever discovered by hand calculations.

127 = 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0.

There are 127 prime days in a leap year.

The numerator of 1 + 1/2 + 1/3 + 1/4 + ... + 1/127 is a prime number.

27th Day of the Year.

27 is of the form x^x (for prime x). It is the only two-digit number with this property.

27! + 1 is prime.

27 = 3^3.
2+7 = 3^2.

27^2 + 27 + 1 is prime.
27^2 - 27 - 1 is prime.

27 is the 8th prime plus 8.

27^2 contains 2 and 7.

90*27 + 73 and 90*27 + 37 are both prime.

27 = 123b4 where b should be read "base".

27 is the first composite number not divisible by any of its digits.

27 makes up the 28th and 29th digit of pi (starting after the decimal place).

No NFL team has retired this number.

There are 27 bones in the human hand.

January 28th (28th Day of the Year)

Jan 28th, 1/28.

128 = 2^(8-1)

128 = (1+2+8)^(12-(1*2+8)) + (8+1-2)

128 = 182 - (8+1)*(8-2)

128 = 218 - (82+8*(2-1))

128 = (8-2)^(2+1) - (81+(8-2+1))

128 = 1*28 + 12*8 + 8/(2*1)

128 = 8*21 - 82*1 * (8-1)*(8-2)

128 = (1+28) + (12+8) + (8+21) + (82+1) - (1+2)*(1+2+8)

128 = (1+2+8)*((8/2-1)*(8/2)) - (8/(2*1))

128 = (1+28)*(8/2*1) + (8-2)*(2/1)

128 = (12+8)*(8-2/1) + 8*(2-1)

128 = (1*2*8)*(8/2*1)

128 = 12^((18/2)-(8-2+1)) - 1*2*8

128 = 2^7. 1*2*8 = 2^4.

The sum of divisors of 128 is also a power of 2 (64 = 2^6).

(Do other numbers have all these properties?)

128^6 + 128^5 + 128^4 + 128^3 + 128^2 + 128^1 + 1 is prime.

128 written in binary (base 2), quaternary (base 4), and hexadecimal (base 16) begins with 1, 2, and 8 (Note the bases; 2 is two times 1, 4 is two times 2, 16 is two times 8).

128 is the largest number that cannot be expressed as the sum of any number of distinct squares.

The Commodore 128 home/personal computer which had 128 KB of memory was released in 1985.

28th Day of the Year.

28 is the second perfect number (Note: the 2nd perfect number with 2 decimal digits).

28 = 1+2+3+4+5+6+7

28 divides 1 + the sum of the first 28 primes.

28^4 + 1 is prime.

28^4 + 28^3 + 28^2 + 28^1 + 1 is prime.

90*28 + 73 and 90*28 + 37 are both prime.

The number e is 2.18281828...

The revolution time on the surface of the sun is 28 days.

The shortest month is February, with 28 days.

In the NFL, the number 28 is retired for St. Louis Rams Marshall Faulk.

January 29th (29th Day of the Year)

Jan 29th, 1/29.

129 = 2^(9-(2*1)) + (12-9) - (12/(9-2-1))

129 = 219 - 9*(9+2-1)

129 = (1*2+9)^(29-(12-9)^(9/(2+1))) + (9+1-2)

129 = 192 - (9*(2-1))*(9-2*1)

129 = 1*29 + 12*9 - (9-(2-1))

129 = 9*21 - 92*1+ 2^((1+9)/2)

129 = (1+29) + (12+9) + (92+1) + (9+21) - 9*((12-9)+(12/(9-2-1)))

129 = (1+2+9)*(9+2*1) - (9/(2+1))

129 = (1*2*9)*(9-2*1) + (12-9)

129 = (1+29)*(12/(12-9)) + 9*(2-1)

129 = (12+9)*(9-2-1) + (9/(2+1))

129^2 is the concatenation of 3 squares (16//64//1).

129^4 + 129^3 + 129^2 + 129 + 1 is prime. (What's the next number like this?)

2*129 + 19 and 2*129 - 19 are prime (Note the use of 2 and 19, digits in 1,2,9). (Are there other numbers that share a similar property?)

There are 129 primes less than 27^2 (or 3^6, a stronger fact).

129^8 + 130^8 is prime.

129^4 + 130^4 is prime.

(Do other numbers have both properties?)

The number of primes between 129 and 129^2 equals the number of primes between 129 and 2*129. (What's another number with the same property?)

The sum of the first 10^1 primes is 129.

129 is the smallest number that can be expressed as the sum of three squares in four different ways.

29th Day of the Year.

29^3 + 29 + 1 is prime.

"T is the first, fourth, eleventh..." has a 't' at the 29th letter.

29^2 + 30^2 is prime.

29 is of the form n^2 - n - 1 (n=6) and 29^2 - 29 - 1 is prime.

29^4 + 29^3 + 29^2 + 29^1 + 1 is prime.

90*29 + 37 and 90*29 + 73 are both prime.

29 = 2^2 + 3^2 + 4^2

The first 29 numbers don't have more than 2 prime factors (longest sequence of numbers).

Saturn makes one revolution around the Sun in over 29 years.

The NBA has not retired the number 29.

"Floccinaucinihilipilification" is the longest nontechnical word in the first edition of the Oxford English Dictionary. It is 29 letters long (Note: the letter e is not in this word--a rare ocassion).

If an odd perfect number exists, it must have at least 29 (not necessarily distinct) prime factors.

2n^2 + 29 is prime for n = 0,1,2,....28.

2^29 has all distinct digits (largest exponent with this property).

The 29th Fibonacci number, 514229 is a prime ending in 29.

29 + 92 = (2+9)^2.

TWENTY NINE can be written out with 29 toothpicks.

7^2 + 8^2 + ... + 29^2 = 92^2 (Note: 92 is the reverse of 29 and 9-2=7).

29^23 + 19^17 + 13^11 + 7^5 + 3^2 is prime.

29! + 111...111 (29 ones) and 29! - 111...111 (29 ones) are both prime.

2^9 + 9^2 is prime.

29 = (2*9) + (2+9)

1/3 + 1/5 + 1/7 + 1/11 + ... Once 1/29 is added, the sum is greater than 1.

January 30th (30th Day of the Year)

Jan 30th, 1/30.

130 = 103 + 30-1*3

130 = 301 - 13*(1+3+0) - (13-(3-1))^(3-1) + (3-1-0)

130 = 13*(1*3) + 13*(1+3) + 13*(1*3)

130 = 13*30/(1*3)

130 = 31*(3+1) + (3*1)!

130 = 31*(3-1) + 30 + (3-1)*(30-(13-(3-1)))

130^2 + 1 is prime.

130^2 + 131^2 is prime.

The sum of the first 130 primes is prime.

130^3 - 130 - 1 is prime.

1^2 + 2^2 + 5^2 + 10^2 = 130 (first four divisors of 130). This is the only number with this property.

130 written in bases 3, 4, 8, 12, and 25 are palindromes (11211, 2002, 202, AA, and 55 respectively).

30th Day of the Year.

3! + 4! = 5*6 (30)

30! - 1 is prime.

30^2 + 31^2 is prime.

30^4 + 30^3 + 30^2 + 30^1 + 1 is prime.

30^10 + 30^9 + 30^8 + 30^7 + 30^6 + 30^5 + 30^4 + 30^3 + 30^2 + 30^1 + 1 is prime.

There are 30 primes less than 11^2.

30 = 2*3*5 (first three primes).

30 = 1^2 + 2^2 + 3^2 + 4^2 (first four perfect squares).

30 = 1*1*2*3*5 (first six Fibonacci numbers).

(Note there are 6 Fibonacci numbers, last one being a 5. And 6*5 = 30.)

January 31st (31st Day of the Year)

Jan 31st, 1/31.

131 = 113 + 3*(1+3+1) + 1*3*1

131 = 311 - 3*(13+(3+1+(3-1))*3+(31-(3-1))

131 = (13+31) + (1+31) + (13+1) + (31+(13-1*3))

131 = (1*31) + (13*1) + (13*31) - 311 - (1+3+1)

131 = (1+3+1)*(31-(1+3+1)) + (3-1-1)

131 = (1*3*1)*(31+(3*(3+1))) + 1*(3-1)

131 = 1^2 + 3^2 + 11^2 (1,3,11 use digits only in 131).

131 is a palindromic prime with its beginning digits (13) and ending digits (31) prime.

131 is the first 3-digit palindromic prime.

131^2 + 131 +/- 1 are twin primes.

131^2 - 131 - 1 is prime.

131^3 + 131 + 1 are prime. (Do other palindromic primes have this property?)

"T is the first, fourth, eleventh, ..." is a self-writing sentence. There is a "t" at the 131 space (not included spaces).

131, 113, 311, 13, 31, and 11 are all prime.

131 = 41 + 43 + 47 (3 consecutive primes).

131 is the 32 prime (1+3+1 = 3+2).

The 131st prime number is the first Fibonacci number with all digits 0 through 9 (1066340417491710595814572169).

131 = (1^0+3^0+1^0) + (1^1+3^1+1^1) + (1^2+3^2+1^2) + (1^3+3^3+1^3) + (1^4+3^4+1^4)

The sum of the first 131 nonprimes is prime.

31st Day of the Year.

31 = 2^2 + 3^3 (first two primes)

31 = 1! + 3! + (1+3)!

31 is a Mersenne prime (2^5 - 1 = 31).

31 is the 11th prime. 11 is the 5th prime. 5 is the 3rd prime. 3 is the 2nd prime. 2 is the 1st prime.

There are 31 primes less than 2^7.

31 = 3^3 + 3 + 1 (three 3's and one 1).

31 = 2^4 + 2^3 + 2^2 + 2^1 + 1.

(13^31 - 3^31)/10 is prime.

31^6 + 31^5 + 31^4 + 31^3 + 31^2 +31^1 + 1 is prime.

31^2 - 31 - 1 is prime.

There are 31 primes less than 130.

31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime.

The first chapter of the Bible has 31 verses.

3 + 5 + 7 + 11 + ... + 89 = 31^2.

31 and the 31st prime are both Mersenne primes.

31111111111111111111111111111111/31 is prime (there are 31 1's on the numerator).

February 1st (32nd Day of the Year)

Feb 1st, 2/1.

21 = 1+2+3+4+5+6

21 written in base 3 is 120 (reverse of which is 21).

21 = 4^2 + 4^1 + 1.

21 is the smallest number not close to a power of 2 (for 2^n, you are "close" if you are within +/- n).

No NFL team has retired the number 21.

We are in 21st century.

Research determined that the average weight of the soul is 21 grams, but the weight is regarded as meaningless.

32nd Day of the Year.

32 = 2^5 (Note: 3+2=5).

32 = 1^1 + 2^2 + 3^3.

32 = 2!*(3*3 + 3!) + 2 (three 3's and two 2's).

3^2 and 2^3 differ by (3-2).

6*32 +/- 1 are twin primes.

32 = 23 + 3^2

2^31 and 2^32 do not contain a '0'.

32! - 1 is prime.

32^3 + 32 + 1 is prime.

32^2 + 33^2 is prime.

32^2 - 32 - 1 is prime.

90*32 + 37 and 90*32 + 73 are prime.

32 = 4^2 + 2^4

There are 32 teams in the National Football League.

February 2nd (33rd Day of the Year)

Feb 2nd, 2/2.

Perfect squares can only end in 22 different two-digit ends (00, 01, 04, 09, ...), thus ruling out 78% of all other numbers no matter how large.

Only using one digit endings, you can only rule out 40% of all numbers (numbers ending in 2,3,7,8).

22 written in base 3 and base 4 are reversals of each other (211 and 112, respectively).

There are 22 primes between 76^2 and 77^2.

1 + the sum of the first 22 primes is divisible by 22.

22 is the first two-digit Smith number. 22 = 11*2 and 2+2 = (1+1)+2.

22 is the only number that describes itself (two two).

33rd Day of the Year.

33 = 3^3 + (3+3/3)

33 = 3*(3*3+(3-3/3))

33 and 22 are both repdigits.

6*33 +/- 1 are twin primes.

33 = 4! + 3! + 2! + 1!

33^2 + 33 + 1 is prime.

33! - 1 is prime (32 and 33 are the last consecutive numbers with this property).

33, 34, and 35 all have 4 divisors (smallest run of 3 consecutive integers).

February 3rd (34th Day of the Year)

Feb 3rd, 2/3.

(23-1)/2 = 11 is prime. (11-1)/2 = 5 is prime. (5-1)/2 = 2 is prime.

23 divides the sum of the first 23 primes.

11111111111111111111111 is prime (23 ones).

23 is the first nontrivial prime with all prime digits.

There are 23 primes between 79^2 and 80^2.

The 23rd Fibonacci number is prime (as is 23).

23 is the smallest prime that has a gap of 6 between the next prime.

23 = 3*3*3 - 2*2 (Note: three 3's and two 2's).

23 is prime, an 2+3 = 5 is prime.

23^4 + 23^3 + 23^2 + 23^1 + 1 is prime.

23 is the smallest odd prime that is not a twin prime.

23 = 5 + 7 + 11 (three consecutive primes). Note the first 5 consecutive primes.

23 (along with one other number) cannot be expressed as the sum of fewer than 9 integer cubes.

If you have 23 people in a room, there is a 50% chance two share a birthday.

23! is 23 digits long (Only prime with this property).

Playing darts, 23 is the lowest score that cannot be gained by throwing a single dart.

Julius Caesar was stabbed 23 times.

The floor of e^pi is 23.

Hilbert's Problems are a list of 23 problems mathematician David Hilbert put forth in 1900.

Homo sapiens have 23 pairs of chromosomes.

11111*1111^11 + 11111111111 + 1 (23 ones) is prime.

23! is the smallest factorial where the digits 0,...,9 appear at least once.

If you would be able to fold a standard sheet of paper 23 times in half, it would become over a mile thick.

If 23 = n, n0123456789 is prime (Meaning, 230123456789 is prime).

23 = 0^5 + 1^4 + 2^3 + 3^2 + 4^1 + 5^0

123571113171923 and 231917131175321 are prime (concatenation of the first noncomposites up to 23).

If A = 1, B = 2, ... Z = 26. Then ODD = 15+4+4 = 23. And ODD + ODD = EVEN (46). Note the mathematical truth in this as well.

34th Day of the Year.

(34!!-3)/3 is prime (second largest number with this property).

34^4+1 is prime.

34^2+35^2 is prime.

There are 34 primes less than 12^2.
There are 34 semiprimes less than 100.

3^34 contains no digit 0 (second highest exponent with this property).

February 4th (35th Day of the Year)

Feb 4th, 2/4.

24 is divisible by 2+4, 2*4, and 2-4.

24 = 1*2*3*4 = 7+8+9

2^24 does not contain a 0.

24 divides the 24th Fibonacci number.

24 = 4*6 (first two composite numbers).

2^24 is the smallest power of 2 containing 3 of the same digits consecutively.

24 is the smallest number with 8 divisors (Note: 2*4 = 8).

1^2 + 2^2 + ... + 24^2 = 70^2.

There are 24 hours in a day.

The following are prime:

24^2 + 1.

24^2 + 24 + 1.

24^4 + 1  (24*4 + 1 is also prime).

24^2 + 25^2.

24^4 + 24^3 + 24^2 + 24^1 + 1.

35th Day of the Year.

35 = 1 + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) (Note: 35 is divisible by 5).

You could also say:

35 = 1*5+2*4+3*3+4*2+5*1

35 = 1^2 + 3^2 + 5^2 = 2^3 + 3^3

There are 35 twin prime pairs less than 1000.

35^2 + 36^2 is prime.

There are 35 primes less than 150.

35^3 - 35 - 1 is prime.

35 is the minimum age of a possible United States President.

February 5th (36th Day of the Year)

Feb 5th, 2/5.

There are 25 primes less than 100.

25 = 5^2 (Note the use of 2 and 5).

5/2 = 2.5 (Note the use of 2 and 5).

25^2 + 26^2 is prime (Note: 24^2 + 25^2 was also prime).

25^2 - 25 - 1 is prime (Also, 24^2 + 24 + 1 was prime).

25 = 3^2 + 4^2

5^n ends in 25 for all integers n > 2.

25^n ends in 625 for all integers n > 2.

625^n ends in 0625 for all integers n > 2.

36th Day of the Year.

Feb 5th (abbreviated 2/5) is the 36th Day of the Year. 25 and 36 are both perfect squares.

36 = 1+2+3+4+5+6+7+8 = 1^3 + 2^3 + 3^3 = (3!)^2

36^2 + 1 is prime.

36 is the concatenation of 3 and 3!.

36^2 - 36 - 1 is prime.

36 is a triangular number and the square root of 36 (6) is also a triangular number.

1+ 2 + 3 + 4 + 5 + ... + 36 = 666.

There are 36 inches in a yard.

A 36 is a perfect score on the ACTs.

February 6th (37th Day of the Year)

Feb 6th, 2/6.

26 is of the form 5^2 + 1 (5 is prime) and 26^2 + 1 is prime.

26 is the only number sandwiched between a perfect square and a perfect cube (5^2 and 3^3).

26!! - 1 is prime.

There are 26 letters in the English alphabet.

26^6 + 26^5 + 26^4 + 26^3 + 26^2 + 26^1 + 1 is prime.

26 = 2*(3^0) + 2*(3^1) + 2*(3^2)

There are 26 spacetime dimensions in bosonic string theory.

No NBA or NFL team has retired number 26.

There are roughly 26 miles in a marathon.

37th Day of the Year.

37 and 73 are both prime.

37 is the 12th prime and 73 is the 21st prime (Note: the reverse of 37 is 73 and the reverse of 12 is 21).

The sum of the first 37 primes squared is divisible by 37.

37! + 1 is prime.

37, 73, 3, and 7 are all prime.

37^1 + 37^1 + 37^1 = 111 (Note the exponents).

37 is the smallest power after the previous square and the previous power of 2.

37 and 38 are the first consecutive pair of integers not divisible by any of their digits.

Every natural number can be expressed as at most the sum of 37 fifth powers.

Normal human body temperature is around 37 degrees Celsius.

When asked for a random number between 0 and 100, most people say 37.

2^3 + 5^7 + 11^13 + 17^19 + 23^29 + 31^37 is prime.

10^(10^100) + 37 is the smallest number larger than a googolplex with no known factors.

2^37 + 3^31 + 5^29 + 7^23 + 11^19 + 13^17 + 17^13 + 19^11 + 23^7 + 29^5 + 31^3 + 37^2 is prime.

February 7th (38th Day of the Year)

Feb 7th, 2/7.

February 7th is known as Euler Day (for the number e = 2.718281828...)

27 is of the form x^x (for prime x). It is the only two-digit number with this property.

27! + 1 is prime.

27 = 3^3.
2+7 = 3^2.

27^2 + 27 + 1 is prime.
27^2 - 27 - 1 is prime.

27 is the 8th prime plus 8.

27^2 contains 2 and 7.

90*27 + 73 and 90*27 + 37 are both prime.

27 = 123b4 where b should be read "base".

27 is the first composite number not divisible by any of its digits.

27 makes up the 28th and 29th digit of pi (starting after the decimal place).

No NFL team has retired this number.

There are 27 bones in the human hand.

38th Day of the Year.

38 = 2^2 + 3^2 + 5^2

The average of the first 23 primes is 38 (first nontrivial average that is an integer).

38^2+38+1 and 38^2+38-1 are twin primes.

38! - 1 is prime (Note: 37! + 1 was prime).

38^6 + 38^5 + 38^4 + 38^3 + 38^2 + 38 + 1 is prime.

38^3-38-1 is prime.

The number made by the first 38 digits of pi is prime.

February 8th (39th Day of the Year)

Feb 8th, 2/8.

28 is the second perfect number (Note: the 2nd perfect number with 2 decimal digits).

28 = 1+2+3+4+5+6+7

28 divides 1 + the sum of the first 28 primes.

28^4 + 1 is prime.

28^4 + 28^3 + 28^2 + 28^1 + 1 is prime.

90*28 + 73 and 90*28 + 37 are both prime.

The number e is 2.18281828...

The revolution time on the surface of the sun is 28 days.

The shortest month is February, with 28 days.

In the NFL, the number 28 is retired for St. Louis Rams Marshall Faulk.

39th Day of the Year.

2^39 does not contain a 0.

39^3+39+1 is prime.

39^2 + 40^2 is prime.

39 and 93 are both semiprimes.

39^2-39-1 and 39^4-39-1 are prime.

There are 39 primes less than 170.

90*39 + 37 and 90*39 + 73 are both prime.

39 = 3^1 + 3^2 + 3^3

39 = 3 + 5 + 7 + 11 + 13 (5 consecutive primes).

February 9th (40th Day of the Year)

Feb 9th, 2/9.

29^3 + 29 + 1 is prime.

"T is the first, fourth, eleventh..." has a 't' at the 29th letter.

29^2 + 30^2 is prime.

29 is of the form n^2 - n - 1 (n=6) and 29^2 - 29 - 1 is prime.

29^4 + 29^3 + 29^2 + 29^1 + 1 is prime.

90*29 + 37 and 90*29 + 73 are both prime.

29 = 2^2 + 3^2 + 4^2

The first 29 numbers don't have more than 2 prime factors (longest sequence of numbers).

Saturn makes one revolution around the Sun in over 29 years.

The NBA has not retired the number 29.

"Floccinaucinihilipilification" is the longest nontechnical word in the first edition of the Oxford English Dictionary. It is 29 letters long (Note: the letter e is not in this word--a rare ocassion).

If an odd perfect number exists, it must have at least 29 (not necessarily distinct) prime factors.

2n^2 + 29 is prime for n = 0,1,2,....28.

2^29 has all distinct digits (largest exponent with this property).

The 29th Fibonacci number, 514229 is a prime ending in 29.

29 + 92 = (2+9)^2.

TWENTY NINE can be written out with 29 toothpicks.

7^2 + 8^2 + ... + 29^2 = 92^2 (Note: 92 is the reverse of 29 and 9-2=7).

29^23 + 19^17 + 13^11 + 7^5 + 3^2 is prime.

29! + 111...111 (29 ones) and 29! - 111...111 (29 ones) are both prime.

2^9 + 9^2 is prime.

29 = (2*9) + (2+9)

1/3 + 1/5 + 1/7 + 1/11 + ... Once 1/29 is added, the sum is greater than 1.

40th Day of the Year.

40^2 + 1 is prime.

There are 40 different ways to place 7 nonattacking queens on a 7 by 7 board.

40^6 + 40^5 + 40^4 + 40^3 + 40^2 + 40 + 1 is prime.

40^4 + 40^3 + 40^2 + 40 + 1 is prime.

40^2 - 40 - 1 is prime.

40 = 3^3 + 3^2 + 3 + 1 (3 is prime).

-40 degrees Fahrenheit equals -40 degrees Celsius.

In Christianity, Jesus is said to have walked 40 days and 40 nights through the desert without food or water.

February 10th (41st Day of the Year)

Feb 10th, 2/10.

210 = 201 + 10-(2-1-0)
210 = 102 + 12*(10-(1+0))
210 = 120 + (12-1*2)*(10-(1-0))
210 = (2+1+0)*(21*(2+1)+(10-(2+1+0)))
210 = 21*(2+2^(2+1+0))
210 = 12*(20-(2+1+0)) + 2*1*(2+1)

210 = 2*3*5*7 (first four primes) (Note: 2+3+5+7 is prime).

210 = 1 + 2 + 3 + ... + 20

210^2 + 1 is prime.
210^4 + 1 is prime.

There are 210 primes less than 36^2 or 6^4.

210^23 + 210^21 + 210^19 + 210^17 + 210^15 + 210^13 + 210^11 + 210^9 + 210^7 + 210^5 + 210^3 + 210 + 1 is prime.

210!!!!!! + 1 is prime.

210 = 13+17+19+23+29+31+37+41 (8 consecutive primes)

41st Day of the Year.

41 is the 13th prime (13 is also prime).

41! + 1 is prime.

41^2+41+1 and 41^2+41-1 are twin primes.

41^3+41+1 is prime.

x^2 + x + 41 is prime for x = -40,-39,-38,...-2,-1,0,1,2,...39.

41^2-41-1 is prime.
41^3-41-1 is prime.

DigitSum(41^2) is a square.

41 is the smallest number that 2^41 has four identical consecutive digits.

41 is the smallest number where [4100,4199] has 9 primes.

41 is a factor of 99999.

41 = 2+3+5+7+11+13 (Note: 41 is the 13th prime number).

41 = 11+13+17 (three consecutive primes)

41!+1, 41#-1, and 41!/41# -41 are prime.

41 = 1! + 2! + 3! + 1^1 + 2^2 + 3^3

11^41 doesn't contain a 0 (largest known exponent with this property).

A day on Mars is around 41 minutes longer than a day on Earth

41 is my favorite number!

February 11th (42nd Day of the Year)

Feb 11th, 2/11.

211 = 121 + 11*(11-(1+2)) + 2*1*1
211 = 112 + 11*(11-2)
211 = (2+1+1)*((11+2)*(2+1+1))
211 = (11+2)*(12+(2+1+1)) + 2*1+1
211 = (21-1)*(11-1*1) + (21-(11-1))
211 = (21+1)*(11-2) + (11+2)
211 = (11-2)*(21+2*1) + (2+1+1)

211 is the 47th prime (47 is prime).

211 = 1 + 2*3*5*7

211 is concatenation of two primes 2 and 11.

211 = 67+71+73 (three consecutive primes)

211 = 3^5-2^5 = 14^2+14+1

There are 211 prime lucky numbers less than 10^4 (Note: 211 itself is a prime lucky number and 4 = 2+1+1).

There are 211 primes that appear on a 24-hour digital clock 00:00-23:59.

211 has its own website: www.211.org

42nd Day of the Year.

42^3+42+1 is prime.

42^2 + 43^2 is prime.

42^2-42-1 is prime.

42 is said to be the answer to the Question of Life, the Universe, and Everything.

42 = 2^1 + 2^3 + 2^5

42 is the digit sum of the original Smith number (4937775 = 3*5*5*65837)

Jackie Robinson wore the number 42.

February 12th (43rd Day of the Year)

Feb 12th, 2/12.

212 = 122 + (1+2+2)*(21-(2+1))
212 = 221 - (2+1)^2
212 = 2*12 + 21*2 + 22*1 + (2+1+2)^(2-1+2) - (2+1-2)
212 = (2*1*2)*(21+2^(2+1+2))
212 = (2+1+2)*(21*2) + 12/(2*(1+2))
212 = (21+2)*((2+1)^2) + (2+1+2)
212 = (2+12)*(21-2*(1+2)) + (2-1)*2
212 = (2*12)*(12-(1+2)) - (2*1*2)
212 = (21-2)*(12-(2-1)) + 2-(1-2)
212 = (12-2)*21 - 2*(1-2)

212^3+212+1 is prime.

212^10+212^9+212^8+212^7+212^6+212^5+212^4+212^3+212^2+212+1is prime.

212 and 212^2 contain two different digits.

3^212 - 212^3 is prime.
11^212-212^11 is prime.

DigitSum(212^2) and DigitProd(212^2) are both squares.

There are 212 primes of the form x^16+1 less than 10^61.

There are 212 4-digit numbers that are multiples of their digit reversal.

212^2 + 213^2 + 214^2 + 215^2 + 216^2 + 217^2 is prime.

212^2//212^1//212^0 is prime (// denotes the concatenation function).

212,213,214,215,216,217,218,219 all have the same number of distinct prime divisors.

43rd Day of the Year.

(43!!-3)/3 is prime (largest known number with this property).

43^4+43^3+43^2+43+1 is prime.

m^43 == m (mod 43) for all m.

43 = 6^2+6^1+6^0

43 = 41+2 = 11+13+19 = 2+11+13+17 = 3+5+7+11+17 (2,3,4,5 consecutive primes).

A frown uses 43 muscles :-(

The world's oldest known captive goldfish died at the age of 43.

43^7 = 271818611107 = (2+7+1+8+1+8+6+1+1+1+0+7)^7

John F Kennedy was the youngest elected president at age 43.

February 13th (44th Day of the Year)

Feb 13th, 2/13.

213 = 231 - 2*(3^(2*1))
213 = 132 + (3^2)*(21/3-(2-1-3))
213 = 123 + 3*(21+3^2)
213 = 321 - 12*(2!+1!+3!)
213 = 312 - 3*(31+2)
213 = (2+1+3)*((21/3)*(2+1*3)) + (2-1)*3
213 = (21+3)*(2^3+1) - (21/(2^3-1))
213 = (21-3)*(2*3!) + 3*(1-2)
213 = (2+13)*(12+1*2) + 3!-2!-1!
213 = (13-2)*(21-2*1) + (2-1+3)

If 213 = n, 2n3n5n7n11n13 is prime (Meaning, 22133213521372131121313 is prime).

44th Day of the Year.

There are 44 primes less than 14^2.

44^16 + 1 is prime (Next highest prime of this form after 2^16+1).

44^4+44^3+44^2+44+1 is prime.

44 is the largest number for which Wolfram Alpha offers a visual representation.

Barack Obama is the 44th President of the United States.

February 14th (45th Day of the Year)

Feb 14th, 2/14.

214 = 241 - (2+1)^(4-1)
214 = 412 - 142 - ((2-1)*4)*14
214 = 421 - 241 + (21-4)*(4/2)
214 = 142 + (2*1*4)*((4-1)^(2*1))
214 = 124 + (2*4+1)*(2*(1+4))
214 = (2+14)+(21+4)+(4+12)+(41+2)+(42+1)+(1+24)+ 2*(24-1)
214 = 21*4 + 41*2 + 4*12
214 = (21+4)*(2*1*4) + 21-(2*4-1)
214 = (21-4)*((2+1)*4)
214 = (2+14)*(21-2*1*4)+((2*1)+4)
214 = (14-2)*(21-(2+1)) - (4/(1*2))
214 = (2*1*4)*((4-1)^(2+1)) - 24/(4*(1+2))
214 = (2+1+4)*(24+(2+4)) + (2-1)*4

214!! - 1 is prime.

The sum of the first 214 primes is prime.

If 214 = n, 2n3n5n7n11n13 is prime (Meaning, 22143214521472141121413 is prime).

214^2 + 215^2 + 216^2 + 217^2 + 218^2 + 219^2 is prime.

214 and 2^214 both end in a 4.

45th Day of the Year.

45 = 1+2+3+4+5+6+7+8+9

45 degrees is the largest angle that gives the maximum range of a fired projectile.

45 + (4+5) = reverse(45) (Only natural number with this property).

45^2-45-1 is prime.
45^3-45-1 is prime.

February 15th (46th Day of the Year)

Feb 15th, 2/15.

215 = 251 - (5+1)^2
215 = 152 + (5*2-1)*(2+5*1)
215 = 125 + 5*(21-(2+1))
215 = 512 - 152 - 125 - 5*(5-2+1)
215 = 521 - 251 - (5+2*1)*(15-2)
215 = (21+5) + (2+15) + (5+12) + (51+2) + (25+1) + (1+52) + (21+2*1)
215 = (2*15) + (21*5) + (5*12) + 5*(5-2+1)
215 = (2+1+5)*(25+1) + (2+5*1)
215 = (2*1*5)*21 + (2-1)*5
215 = (2+15)*((5-1)*(2+1)) + (15-(5-1))
215 = (21-5)*(15-2) + 21/(2+1)

215 = 5*43 (decreasing digits)

215^2+215+1 is prime.

215^16 + 216^16 is prime.

215^2 + 4 is prime.

215^3 is the largest number whose cube has 7 digits.

The 215th and 216th primes are twin primes.

215!! + 2^7 and 215!! + 2^8 are primes (Note the base of 2 and 7+8=15). This is the only known number with this property.

215^2 + 215 +/- 1 are twin primes.

215, 217, 219, 221 are semiprimes.

There are 215 solutions to 1 = 1/a + 1/b + 1/c + 1/d for a,b,c,d positive integers (rearrangements included).

215 is the largest known number with a 7 in its aliquot sequence.

46th Day of the Year.

46^4 + 1 is prime.

46^6 + 46^5 + 46^4 + 46^3 + 46^2 + 46 + 1 is prime.

There are 46 primes less than 200.

46^2-46-1 is prime.

There are 46 human chromosomes.

February 16th (47th Day of the Year)

Feb 16th, 2/16.

216 = 6^(1+2)
216 = 126 + 6*(21-6)
216 = 162 + 6*(2+1+6)
216 = 261 - (2+1+6)*(6-(2-1))
216 = 612 - 261 - (6-1)*(21+6)
216 = 621 - 162 - 126 - (2+1+6)*(2*6+1)
216 = 2*16 + 21*6 + 2*1*6 + 21*(6-1-2)
216 = 6*12 + 61*2 + (6+1+2) + (1+6*2)
216 = (2+16) + (21+6) + (6+12) + (61+2) + (26+1) + (1+62)
216 = (2+1+6)*(6*(2-1))*(6-2*1)
216 = (2*1*6)*(2+16)
216 = (21-6)*(16-2) + 6*(2-1)
216 = (21+6)*(2*1+6)
216 = (2+16)*(21-(2+1+6))

216 = (3!)^3

216 is the smallest number whose cube has 8 digits (Note: 216 and 8 are both cubes).

The sum of the first 216 primes is prime.

216 is divisible by 2*1*6, 2+1+6, and 2,1, and 6.

216 = 4*6*9 (first 3 semiprimes).

3^216 +/- 32 are primes.

3^2 + 4^2 = 5^2 = 25.
3^3 + 4^3 + 5^3 = 6^3 = 216.

47th Day of the Year.

47 is prime.
4+7 = 11 is prime.
1+1 = 2 is prime.

47^2 + 48^2 is prime.

3^3^3^3^3^3^3 has 47 different values depending on the parentheses (Note: there are 7 threes and 3,7, and 47 are all prime).

47 = 7^2-2 (7 is prime) and 47^2-2 is prime.

Tropic of Cancer and Tropic of Capricorn are 47 degrees of latitude apart.

47 appears 47 times in the first thousand primes.

A Tyrannosaurus Rex is 47 feet in length.

In the beginning of the movie Monster's Inc., the scream factory had gone 47 days without any accidents.

An AK-47 is the most widespread weapon in the world.

666^47 has a digit sum of 666.

4^3 + 0^3 + 7^3 = 407.

If an odd perfect number exists, then it must have at least 47 prime factors.

A modern concert harp has 47 strings.

The first 47 digits of prime numbers are zeroless.

47 is the largest prime whose square (2209) can be displayed on a 24-hour clock.

February 17th (48th Day of the Year)

Feb 17th, 2/17.

217 = 172 + (7+2)*(7-2)
217 = 127 + (1+2+7)*(12-(1+2))
217 = 271 - (21-(2+1))*(21/7)
217 = 721 - 271 - 21*7 - (72+7*2)
217 = 712 - 172 - 127 - (2*1*7)^(17-(2*7+1))
217 = 2*17 + 21*7 + (7-1)^2
217 = 71*2 + 7*12 - (7+1*2)
217 = (21+7) + (2+17) + (71+2) + (7+12) + (17-(7-2-1))*(7-2+1)
217 = (2+1+7)*(27-(7-2)) - (12/(7-2-1))
217 = (2*1*7)*(17-2) + (2-1)*7
217 = (21+7)*(7+2-1) - (17-(2+1+7))
217 = (2+17)*(12-(2-1)) + 2*(7-1-2)

217 = 7*31
217*(7+31) = 8246 (contains one of each nonzero even digit).

217^2+4 is prime.

There are 217 0's in all the four digit primes.

There are 217 squares with 5 digits.

48th Day of the Year.

48 is divisible by 4, 8, (4+8), and (4-8).

48^3 + 48 + 1 is prime.

48^4 + 1 is prime.

There are 48 primes less than 15^2.

48*48 = 2304.
48*84 = 4032.

48^3-48-1 is prime.

4800-4899 contains 9 primes (smallest interval of 100 to do so).

2*48 +/- 17 are both prime.

4^4^4^4^4^4^4 has 48 distinct values depending on placement of parentheses.
5^5^5^5^5^5^5 has 48 distinct values depending on placement of parentheses.
6^6^6^6^6^6^6 has 48 distinct values depending on placement of parentheses.
7^7^7^7^7^7^7 has 48 distinct values depending on placement of parentheses.
8^8^8^8^8^8^8 has 48 distinct values depending on placement of parentheses.
9^9^9^9^9^9^9 has 48 distinct values depending on placement of parentheses.
10^10^10^10^10^10^10 has 48 distinct values depending on placement of parentheses.

48 is the smallest number with 10 divisors.

There are 48 minutes in a full NBA game.

February 18th (49th Day of the Year)

Feb 18th, 2/18.

218 = 128 + (81+(8+1))
218 = 182 + (18+2) + 1*8*2
218 = 281 - (8+1)*(8-1)
218 = 812 - 281 - 21*8 - (1!+(8/2)!+(8-2-1)!)
218 = 821 - 128 - 182 - 81*2 - (2+1+8)^2 - (2*1+8)
218 = 21*8 + 2*18 + (21-(8-1))
218 = 8*12 + 81*2 - (8*(2-1))*(8-2-1)
218 = (2+18) + (21+8) + (8+12) + (81+2) + (8-2*1)*(8+2+1)
218 = (2+1+8)*((8/2)*(8-2-1)) - (28/(8*2-2*1))
218 = (2*1*8)*(2*(8-1)) - (8-1*2)
218 = (21+8)*(8-2+1) + (2+1)*(8/2+1)
218 = (21-8)*(28-(2+1+8)) - (8/2-1)

218^16 + 219^16 is prime.

218^2 + 218 +/- 1 are twin primes.

218^5 - 217^5 is prime.

218^5 - 218 - 1 is prime.

218^218 contains the digits '0123456789' consecutively in some order.

49th Day of the Year.

49^2 = 2401 and 24*2 + 01 = 49.
49^3 = 117649 and 1176*2 + 49 = 2401.

4, 9, and 49 are squares.

2^49 (15 digits) does not contain a 0.

49^2 - 49 - 1 is prime.

90*49 + 73 and 90*49 + 37 are prime.

49 is also square in base 5 (144) and base 6 (121).

The 49th parallel separates Canada from the US.

February 19th (50th Day of the Year)

Feb 19th, 2/19.

219 = 129 + (92-2*1)
219 = 192 + (2+1)*9
219 = 291 - (21-(2+1))*(12/(1+2))
219 = 912 - 291 - 129 - 192 - 9^(2*1)
219 = 921 - 192 - 291 - 129 - 9*(9+2-1)
219 = 2*19 + 21*9 - (9-2+1)
219 = 9*12 + 91*2 - (91-(29-(9*(2-1))))
219 = (2+19) + (21+9) + (9+12) + (91+2) + 9*(9-1-2)
219 = (2+1+9)*(2*1*9) + (9/(1+2))
219 = (2+19)*(9+2-1) + (2-1)*9
219 = (21+9)*(9-2*1) + (21-(2+1+9))
219 = (91+2)*(9/(2+1)) - (9-2-1)*(9+2-1)
219 = (91-2)*(21/(9-2)) - (21-9)*((9-1)/2)

219^3 has 3 consecutive numbers in its decimal representation.

219^3 + 219 + 1 is prime.

There are 219 primes less than 37^2 (Note: 37 is prime).

219^4 + 219 + 1 is prime.

2^219 - 219^2 is prime.

There are more primes between 219 and 2*219 than 219 and 219^2.

There are 219 3-dimensional space groups.

If 219 = n, 2n3n5n7n11 is prime (Meaning 221932195219721911 is prime).

219^32 + 220^32 is prime.

50th Day of the Year.

50^2+50+/-1 are twin primes.

50^2 + 51^2 is prime.

50^4 + 50^3 + 50^2 + 50 + 1 is prime.

There are 50 primes less than 230.

50 = 3^2 + 4^2 + 5^2

No NHL team has retired the number 50.

There are 50 states in the United States of America (50th being Hawaii).

In years of marriage, the 50th anniversary is the "golden" wedding anniversary.

50-50 usually means a probability that has 2 outcomes, 1/2 chance of either occurring.

Roads without speed limits in Australia have an implied speed limit of 50 km/h.

February 20th (51st Day of the Year)

Feb 20th, 2/20.

220 = 202 + (20-2)
220 = 22*(20/2)
220 = (20-2)*(20-(2^(2+2^0))) + 2*2+0
220 = (2+2+0)*(22+(20+(22-(2+2^0)^2)))
220 = (2*20)*(22/(2+2+0))

220 = 2*2*5*11
(2+2+5+11) = 20 (substring of 220)

220*202 = 44440

220 = 1 + (1+2) + (1+2+3) + ... + (1+2+3+4+5+6+7+8+9+10)

220^4 + 1 is prime.

220^6 + 220^5 + 220^4 + 220^3 + 220^2 + 220 + 1 is prime.

220^8 + 221^8 is prime.

The maximum difference between two consecutive primes less than 10^8 is 220 (Which primes?).

If 220 = n, n0123456789 is prime (Meaning 2200123456789 is prime).

The aliquot sequence for 220 does not terminate in 1.

220 = 47+53+59+61 (four consecutive primes).

51st Day of the Year.

2^51 (16 digits) does not contain a 0.

51^2-51-1 is prime.

There are 51 groups if order 2^5.

There are 51 primes of the form x^2 + 1 less than 10^5.

51 is a palindrome in base 2 (110011), base 4 (303), and base 16 (33).

51 in base 6 is 123, three consecutive digits (Note: 1+2+3 = 1*2*3 = 6).

51 in base 12 is 43 (Note the use of the first four natural numbers).

Area 51 in southern Nevada, USA is believed to contain secret aircraft testing.

February 21st (52nd Day of the Year)

Feb 21st, 2/21.

221 = 122 + ((2+1)^2)*(22/(2/2+1))
221 = 212 + (12-(1+2))
221 = (2*21) + (22*1) + (12*2) + 122 + (22/(2*1))
221 = (2+2+1)*(22*(2/2+1)) + (2/(2/1))
221 = (2*2*1)*(22+(2+1)*(12-(2-1))) + (2-2+1)
221 = (22-1)*(12-2) + (22/(2*1))
221 = (22+1)*((2+1)^2) + (12+2)
221 = (2+21) + (22+1) + (12+2) + (1+22) + 122 + (2+2)^(2/2+1)

221^3+221+1 is prime.

221^6 + 221^5 + 221^4 + 221^3 + 221^2 + 221 + 1 is prime.

221^8 + 222^8 is prime.

+/- 1 +/- 2 +/- 3 +/- ... +/- 13 = 1 has 221 solutions.

1111...11113 is prime (221 digits).

221^2 + 222^2 + 223^2 + 224^2 + 225^2 + 226^2 is prime.

There are 221 non-attacking knights on a  21 by 21 board.

If 221 = n, n0123456789 is prime (Meaning, 2210123456789 is prime).

221 = 37+41+43+47+53 (five consecutive primes).

221 = 11+13+17+19+23+29+31+37+41 (nine consecutive primes).

If you're dealt 2 cards from a single deck of 52 cards, you have a 1 in 221 chance that it's the same card (of a different suit).

52nd Day of the Year.

52 = (5+5+5+5+5)*2+2 (5 fives and 2 twos).

There are 52 primes less than 240.

The 4th derivative of (x^x)^x at x=1 equals 52.

52!!!!! + 1 and 52!!!!!! + 1 is prime.

There are roughly 52 weeks in a year.

There are 52 white keys on a standard piano.

There are 52 playing cards in a deck of cards.

February 22nd (53rd Day of the Year)

Feb 22nd, 2/22.

222 = (2+2+2)*(22+(2+2/2)*(2+2+2/2))
222 = (2*2*2)*(22+(2+2+2)) - (2*(2/2))
222 = (22+2)*((2+2/2)^2) + (2+2+2)
222 = (22-2)*(22/2) + (2+2-2)
222 = (2*22) + (2*2*2) + (22*2) + (22+2) + (2+22) + (2+2+2) + ((2+2/2)^2)*(2^2*2)
222 = (2^2^2)*(22-2*2*2) - (22/(2*2^2+(2+2/2)))

222 = 2*3*37
222*(2+3+(3+7)) = 3330 (another rep digit, excluding the 0).

222^4 + 222^3 + 222^2 + 222 + 1 is prime.

10^222 + 7 is prime (Note: 1+0+2+2+2 = 7).

If 222 = n, 2n3n5n7n11n13 is prime (Meaning, 22223222522272221122213 is prime).

222 is 22020 in base 3 (only nonzero digits are 222).

53rd Day of the Year.

3^53 - 2^53 is prime (Note the use of prime numbers).

The sum of the first 53 primes is divisible by 53.

53^3 + 53 + 1 is prime.

53 is the largest prime less than e^4.

There are 53 primes less than 250.

53^10 + 53^9 + 53^8 + 53^7 + 53^6 + 53^5 + 53^4 + 53^3 + 53^2 + 53 + 1 is prime.

53 is the 16th prune and 53 written in base 16 is 35 (reverse of 53).

In How the Grinch Stole Christmas!, the Grinch says he has put up with the Who's Christmas cheer for 53 years.

53 is the maximum number of players on a National Football League roster.

Wilt Chamberlain in 1960 holds the record for the most points by a rookie in a NBA Playoff game (53 points).

If 53 = n, 1n1, 3n3, 7n7, and 9n9 are all prime (Meaning 1531, 3533, 7537, and 9539 are all prime. It's the smallest number with this property).

53 is the smallest prime factor of 1111111111111 (13 ones).

The chance that no pair of 53 people people in a room have the same birthday is around 1/53.

53 = 5+7+11+13+17 (five consecutive primes).

(53!/35!) + 1 is prime.

1000^53 - 53 is prime.

The average cow produces 53 pounds of milk per day.

2^53 is the smallest power of 2 with two consecutive zeros.

53^7 = 1174711139837 = (1+1+7+4+7+1+1+1+3+9+8+3+7)^7

The integer part of e^pi^phi = 53.

53 is a bisexual prime (the larger of two sexy primes and the smaller of two sexy primes).

February 23rd (54th Day of the Year)

Feb 23rd, 2/23.

223 = 232 - (2+3+2+(3-2/2))
223 = 322 - (22*(3^2/2))
223 = 2*23 + 22*3 + (32+(3+2))*(3*(2/2))
223 = 3*22 + 32*2 + 3*(32-2/2)
223 = (2+23) + (22+3) + (32+2) + (3+22) + 2*(23+(32+2))
223 = (2+2+3)*(2^(2+3)) - (2+2-3)
223 = (2*2*3)*(23-(2+3)) + (2+2+3)
223 = (2+2*3)*(22+2*3) + (3-2*2)
223 = (22-3)*(2*2*3) - (2^3-(3*(2/2)))
223 = (22+3)*(3^2) + 2*(2-3)
223 = (23-2)*(22/(3-2/2)) - (2+2*3)

223^2 = 49729 (concatenation of 7^2 and 27^2).

223^3 contains '567' and the numbers 5678901 only.

223^16 + 224^16 is prime.

223 = 71+73+79 (three consecutive primes).

223 = 19+23+29+31+37+41+43 (seven consecutive primes).

223 = -01+23+45+67+89

54th Day of the Year.

54 = 5*4+5*4+5*4-5-5+4 (5 fives and 4 fours).

54 = 2*3*3*3
54*(2+3+3+3) starts with a 5 and ends with a 4.

54^2+1 is prime.
54^4+1 is prime.
54^2-54-1 is prime.
54^3+54+1 is prime.

There are 54 primes less than 2^8.

54^2 + 54 +/- 1 are twin primes.

There are 54 primes less than the 100th prime (541) that do not contain a 1.

54^32 + 1 is prime.

54 is 312 base 4 (Note the use of four consecutive numbers 1,2,3,4).

54 is 36 base 16 (Note: 36 and 16 are both squares (6 and 4), and 64 is also a square).

2*sin(54) = phi (golden ratio).

54 is the fewest points in an NBA Playoff Game (1998--Chicago 96, Utah 54).

The New York Rangers won a Stanley Cup in 1994, 54 years after their previous win. This was the longest drought in the trophy's history.

There are 54 countries in Africa.

A Rubik's Cube has 54 colored squares.

There are 54 mg of caffeine in 12 ounces of Mountain Dew.

February 24th (55th Day of the Year)

Feb 24th, 2/24.

224 = 242 - (22-4)
224 = 422 - (4^2+2)*(2*2*4-(4+2/2))
224 = 2*24 + 22*4 + (42+2)*(4-2)
224 = 4*22 + 42*2 + (24+2)*(4-2)
224 = (2+24) + (22+4) + (4+22) + (42+2) + 2*(2*24+(4-2/2))
224 = (2+2+4)*(4*(2+(4+2/2)))
224 = (2*2*4)*(4+4*2+2)
224 = (22-4)*(4*(4-2/2)) + (2*2+4)
224 = (22+4)*(2+2+4) + 2*2*4
224 = (2+2*4)*(24-2) + 4*(2/2)

224 = 2*2*2*2*2*7
2+2+2+2+2+7 = 17 (also prime).

224^3 begins with the first four terms of the Fibonacci sequence (1123...)

224^2+1 is prime.

224^10 + 224^9 + 224^8 + 224^7 + 224^6 + 224^5 + 224^4 + 224^3 + 224^2 + 224 + 1 is prime.

2^224, 3^224, 5^224 all have even digit sums.

224^3 +/- 2 are both prime.

224^2 + 225^2 + 226^2 + 227^2 + 228^2 + 229^2 is prime.

4^224 - 2^224 - 1 is prime.

224 = 2^3 + 3^3 + 4^3 + 5^3

55th Day of the Year.

55 = 1+2+3+4+5+6+7+8+9+10

55 is the 10th Fibonacci number and 10th triangular number.

55 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2

There are 55 primes less than 260.

90*55 + 37 and 90*55 + 73 are prime.

55^2-55-1 is prime.
55^3-55-1 is prime.
55^4-55-1 is prime.

February 25th (56th Day of the Year)

Feb 25th, 2/25.

225 = 252 - (5-2)^(5-2)
225 = 522 - 252 - 5*(2+2+5)
225 = (2*25) + (22*5) + 5*(22-(2+2+5))
225 = 5*22 + 52*2 + (5*2+2/2)
225 = (2+25) + (22+5) + (52+2) + (5+22) + (5*2)*(5+2+2)
225 = (2+2+5)*25
225 = (2*2*5)*(2*5 + 2/2) + 5*(2/2)
225 = (2+25)*(5*2-2) + (5-2)^2
225 = (22-5)*(5*2+(5-2)) + (5-2/2)
225 = (25-2)*(22-(2+2*5)) - ((22+(5-2))/5)

225 = 15^2 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3

225 = 01+23+45+67+89

225^3+225+1 is prime.

225^16 + 226^16 is prime.

(6+225!)/6 is prime. (Second known largest number with property).

225 is the only three digit square with all prime digits.

A Scrabble board has 225 squares.

56th Day of the Year.

56 = 7*8 (Other number with this property: 12 = 3*4).

56^2+1 is prime.
56^4+1 is prime.

56^3+56+1 is prime.

10^56 + 3 and 10^56 + 9 are prime.

56^6 + 56^5 + 56^4 + 56^3 + 56^2 + 56 + 1 is prime.

56^2-56-1 is prime.

90*56 + 37 and 90*56 + 73 are primes.

56^16 + 57^16 is prime.

The numerator of 1/1 + 1/2 + 1/3 + ... + 1/56 is prime.

56 = 3+5+7+11+13+17 (6 consecutive primes).

56 = 1 + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) + (1+2+3+4+5+6)

There is a town in Arkansas named Fifty-Six, Arkansas.

According to Aristotle, the Universe has 56 layers.

February 26th (57th Day of the Year)

Feb 26th, 2/26.

226 = 262 - 6^(6-2-2)
226 = 622 - 262 - 2*(62+(6-2/2))
226 = (2+26) + (22+6) + (62+2) + (6+22) + 6*(26/2)
226 = 2*26 + 22*6 + 6*(6+2/2)
226 = 6*22 + 62*2 - 6*(6-2/2)
226 = (2+2+6)*((6+(6-2/2))*(6-2-2)) + 6*(2/2)
226 = (2*2*6)*((6/2)^2) + (2+2+6)
226 = (2+2*6)*(2^(6-2)) + (6-2-2)
226 = (22+6)*(2^(6/2)) + ((6-2)/2)
226 = (22-6)*(2+2*6 + (2/2)/(6+2)

226^5 - 225^5 is prime.

226^2 + 227^2 + 228^2 is prime.

57th Day of the Year.

57*(5+7) = 684 (odd numbers on left, even numbers on right).

57 = 7^2+7+1 (7 is prime) and 57^2+57+1 is prime.

57^2-57-1 is prime.

57^4-57-1 is prime.

57^2+4 is prime.

2^5 + 5^2 = 57.

The 57 in Heinz 57 represents the variety of foods produced by Heinz.

February 27th (58th Day of the Year)

Feb 27th, 2/27.

227 = 272 - (7-2)*(7+2)
227 = 722 - 272 - (22-7)^2 + (7-2-2-2/2)
227 = 2*27 + 22*7 + (7*2+(7-2))
227 = 7*22 + 72*2 - (72-2/2)
227 = (2+27) + (22+7) + (7+22) + (72+2) + 22*(7-2-2)
227 = (2+2+7)*(7*(7-2-2)) - (7+2/2)/2
227 = (2*2*7)*(2/2+7) + (7-2-2)
227 = (7-2-2)*(72+(7-2)) - (7-2-2/2)
227 = (7-2/2)*(22+2^(2+2)) - (7-(2*2*2))
227 = (22-7)*(7*2+2/2) + (7-(7*2-(7+2)))
227 = (22+7)*(2/2+7) - (7*2-(7+2))

227*227 contains all 6 different digits.

227^4 + 227^3 + 227^2 + 227 + 1 is prime.

22/7 approximates the famous value of pi (3.14).

227 = 2*3*5*7 + (2+3+5+7)

227 is the smallest three digit prime where 2^227 - 227^2 is prime.

227 is the smallest three digit prime where deleting a digit results in a composite.

The sum of the first composites up to 27 is 227.

There are 227 composite days in a non leap year.

58th Day of the Year.

58 = 2*29 and 5+8 = 2+2+9.

58^3-58-1 is prime.

58 = 2+3+5+7+11+13+17 (first 7 primes).

There are 58 counties in California, USA.

58 mph is the minimum wind speed needed to issue a Severe Thunderstorm Warning.

In the popular TV show Spongebob Squarepants, Patrick claims "58 is like the luckiest number ever."

February 28th (59th Day of the Year)

Feb 28th, 2/28.

228 = 282 - 2*(28-2/2)
228 = 822 - 282 - (8-2)*(2+2)*(8+(8/2+2/2))
228 = (2+28) + (22+8) + (82+2) + (8+22) + (8+2/2)*(8-2)
228 = 2*28 + 22*8 - (8-2-2)
228 = 8*22 + 82*2 - 2*(2*28)
228 = (22+8)*(8-2/2) + (8-2)*(8/2-2/2)
228 = (22-8)*(2*8) + (8-2-2)
228 = (2+2+8)*(8*2+(8-2)/2)
228 = (2*2*8)*(8-2/2) - (2+2-8)
228 = (2+2*8)*(8*2-(8-2)/2) - (22-2*8)

228^4+1 is prime.

There are 228 primes less than 38^2.

There are 228 ways to place 2 non attacking kings on a 5 by 5 board.

There are 228 primes between 39 and 39^2.

There are 228 composites less than or equal to 17^2.

228 = 29+31+37+41+43+47 (6 consecutive primes).
228 = 7+11+13+17+19+23+29+31+37+41 (10 consecutive primes).

59th Day of the Year.

59^2 = 3481 (3^4 = 81, it's a "factual" number).

5^59 - 4^59 is prime.
4^59 - 3^59 is prime.
3^59 - 2^59 is prime.

100^59 - 99^59 is prime.

59^2 + 59 +/- 1 are twin primes.

59 = 4^3-4-1 and 59^3-59-1 is prime.

There are 7 primes between 5900 and 5999 (smallest interval of 100 with 7 primes).

59! - 58! + 57! - 56! + ... + 1! is prime.

Only 59% of the Moon is directly visible from Earth.

The first 59 digits of 58^57 form a prime.

One day on Mercury is around 59 Earth days.

The largest record wave in the Atlantic Ocean was 59 feet.

59 = 17+19+23 (3 consecutive primes).

59, when divided by 1,2,3,4,5,6, leaves a remainder of 0,1,2,3,4,5 respectively (smallest number with such property).

The highest temperature recorded in Antarctica was 59 degrees Fahrenheit (January 5, 1974).

59 = 1*2*3*4+5+6+7+8+9

March 1st (60th Day of the Non-Leap Year)

Mar 1st, 3/1.

31 = 2^2 + 3^3 (first two primes)

31 = 1! + 3! + (1+3)!

31 is a Mersenne prime (2^5 - 1 = 32).

31 is the 11th prime. 11 is the 5th prime. 5 is the 3rd prime. 3 is the 2nd prime. 2 is the 1st prime.

There are 31 primes less than 2^7.

31 = 3^3 + 3 + 1 (three 3's and one 1).

31 = 2^4 + 2^3 + 2^2 + 2^1 + 1.

(13^31 - 3^31)/10 is prime.

31^6 + 31^5 + 31^4 + 31^3 + 31^2 +31^1 + 1 is prime.

2^31, 2^32, 2^33, ... 2^37 all do not contain a 0.

31^2 - 31 - 1 is prime.

There are 31 primes less than 130.

31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime.

The first chapter of the Bible has 31 verses.

3 + 5 + 7 + 11 + ... + 89 = 31^2.

31 and the 31st prime are both Mersenne primes.

31111111111111111111111111111111/31 is prime (There are 31 1's on the numerator).

60th Day of the Year.

60 is divisible by 1,2,3,4,5,6.

60 = (6*6)+(6*6)-(6+6) (6 six's).

60 = 2*2*3*5 and 60 is divisible by (2+2+3+5)

60^3-60-1 is prime.

60^2+61^2 is prime.

60^6+60^5+60^4+60^3+60^2+60+1 is prime (Note the exponents and that 60 is divisible by 6,5,4,3,2,1).

60^2-60-1 is prime.

The sum of the first 60 primes is prime.

60 = 29+31 (twin primes) and 60 is between twin primes 59 and 61.

60 = 11+13+17+19 (four consecutive primes).

There are 60 seconds in a minute and 60 minutes in an hour.

An equilateral triangle is composed of three 60 degree angles.

In years of marriage, the 60th anniversary is the diamond wedding anniversary.

There are at most 60 marbles in Chinese checkers.

There are 60 cards in the game Rack-O.

60 is the highest number of points that can be scored with a single dart.

March 2nd (61st Day of the Non-Leap Year)

Mar 2nd, 3/2.

32 = 2^5 (Note: 3+2=5).

32 = 1^1 + 2^2 + 3^3.

32 = 2!*(3*3 + 3!) + 2 (three 3's and two 2's).

3^2 and 2^3 differ by (3-2).

6*32 +/- 1 are twin primes.

32 = 23 + 3^2

2^31 and 2^32 do not contain a '0'.

32! - 1 is prime.

32^3 + 32 + 1 is prime.

32^2 + 33^2 is prime.

32^2 - 32 - 1 is prime.

90*32 + 37 and 90*32 + 73 are prime.

32 = 4^2 + 2^4

There are 32 teams in the National Football League.

61st Day of the Year.

2^61-1 is prime.

There are 61 primes less than 17^2.

61^6+61^5+61^4+61^3+61^2+61+1 is prime.

61^2-61-1 is prime.

90*61+37 and 90*61+73 are both prime.

If A = 1, B = 2, ... Z = 26, then the word PRIME is prime (16+18+9+13+5 = 61).

(2^61-1)/(2-1) and (2^61+1)/(2+1) are both prime.

61!-60!+59!-58!+...+1! is prime.

61 countries took part in World War II.

No Fibonacci number is divisible by 61.

March 3rd (62nd Day of the Non-Leap Year)

Mar 3rd, 3/3.

33 = 3^3 + (3+3/3)

33 = 3*(3*3+(3-3/3))

33 and 22 are both repdigits.

6*33 +/- 1 are twin primes.

33 = 4! + 3! + 2! + 1!

33^2 + 33 + 1 is prime.

33! - 1 is prime (32 and 33 are the last consecutive numbers with this property).

33, 34, and 35 all have 4 divisors (smallest run of 3 consecutive integers).

62nd Day of the Year.

62^2+62+1 is prime.

There is no prime between 620 and 629.

62^4+62^3+62^2+62+1 is prime.

There are 62 primes less than 300.

62^3 = 238328 (only number whose cube has 3 digits occurring twice).

March 4th (63rd Day of the Non-Leap Year)

Mar 4th, 3/4.

34 = 3*3*3+(4+4-(4/4)) (three 3's and four 4's).

(34!!-3)/3 is prime (second largest number with this property).

34^4+1 is prime.

34^2+35^2 is prime.

There are 34 primes less than 12^2.
There are 34 semiprimes less than 100.

3^34 contains no digit 0 (second highest exponent with this property).

63rd Day of the Year.

63*(6+3) = 567 (three consecutive digits).

63^4+63^3+63^2+63+1 is prime.

63 = 2^5+2^4+2^3+2^2+2+1

Michael Jordan scored a record 63 points in a double-overtime NBA Playoff game on April 20, 1986.

March 5th (64th Day of the Non-Leap Year)

Mar 5th, 3/5.

35 = 1 + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) (Note: 35 is divisible by 5).

You could also say:

35 = 1*5+2*4+3*3+4*2+5*1

35 = 1^2 + 3^2 + 5^2 = 2^3 + 3^3

There are 35 twin prime pairs less than 1000.

35^2 + 36^2 is prime.

There are 35 primes less than 150.

35^3 - 35 - 1 is prime.

35 is the minimum age of a possible United States President.

64th Day of the Year.

64*64 begins with a 4 and ends with a 6.

64 = 2*2*2*2*2*2
64*222222 still contains 4 consecutive twos.

64 = 2^6 = 4^3 = 8^2

64^3-64-1 is prime.

A chessboard has 64 squares.

64 is the maximum number of strokes in any Chinese character.

There are 64 sex positions in the Kama Sutra.

March 6th (65th Day of the Non-Leap Year)

Mar 6th, 3/6.

36 = 1+2+3+4+5+6+7+8 = 1^3 + 2^3 + 3^3 = (3!)^2

36^2 + 1 is prime.

36 is the concatenation of 3 and 3!.

36^2 - 36 - 1 is prime.

36 is a triangular number and the square root of 36 (6) is also a triangular number.

1+ 2 + 3 + 4 + 5 + ... + 36 = 666.

There are 36 inches in a yard.

A 36 is a perfect score on the ACTs.

65th Day of the Year.

65^2 + 66^2 is prime.

65^2-65-1 is prime.

(65!)^2 + 1 is prime (second highest number with this property).

65^2+4 is prime.

10^65+49, 10^66+49 and 10^67+49 are all primes.

65 = 1^5+2^4+3^3+4^2+5^1

65 is usually the minimum grade to pass an exam.

March 7th (66th Day of the Non-Leap Year)

Mar 7th, 3/7.

37 and 73 are both prime.

37 is the 12th prime and 73 is the 21st prime (Note: the reverse of 37 is 73 and the reverse of 12 is 21).

The sum of the first 37 primes squared is divisible by 37.

37! + 1 is prime.

37, 73, 3, and 7 are all prime.

37^1 + 37^1 + 37^1 = 111 (Note the exponents).

37 is the smallest power after the previous square and the previous power of 2.

37 and 38 are the first consecutive pair of integers not divisible by any of their digits.

Every natural number can be expressed as at most the sum of 37 fifth powers.

Normal human body temperature is around 37 degrees Celsius.

When asked for a random number between 0 and 100, most people say 37.

2^3 + 5^7 + 11^13 + 17^19 + 23^29 + 31^37 is prime.

10^(10^100) + 37 is the smallest number larger than a googolplex with no known factors.

2^37 + 3^31 + 5^29 + 7^23 + 11^19 + 13^17 + 17^13 + 19^11 + 23^7 + 29^5 + 31^3 + 37^2 is prime.

66th Day of the Year.

66 = 1+2+3+4+5+6+7+8+9+10+11

66^1+1 and 66^2+1 are primes.

66^2+66+1 is prime.

There are 66 primes less than 18^2.

66^6+66^5+66^4+66^3+66^2+66+1 is prime.

66^2-66-1 is prime.

66^16+67^16 is prime.

66^8+67^8 is prime.

66 = 3^4 - 2^4 + 1^4.

66^2 + 66 +/- 1 are twin primes.

In the NHL, the number 66 was retired by Pittsburgh Penguins' Mario Lemieux.

Route 66 is a historic route passing through New Mexico.

The most hot dogs eaten in 15 minutes is 66, a World record in Hot Dog Eating a Championships in 2007.

March 8th (67th Day of the Non-Leap Year)

Mar 8th, 3/8.

38 = 2^2 + 3^2 + 5^2

The average of the first 23 primes is 38 (first nontrivial average that is an integer).

38^2+38+1 and 38^2+38-1 are twin primes.

38! - 1 is prime (Note: 37! + 1 was prime).

38^6 + 38^5 + 38^4 + 38^3 + 38^2 + 38 + 1 is prime.

38^3-38-1 is prime.

The number made by the first 38 digits of pi is prime.

67th Day of the Year.

67 is prime but, when squared, the digits are all composite.

67 is a bisexual prime: 67 +/- 6 are both prime.

2^67 (21 digits) contains no 0.

67^2-67-1 is prime.

67^2+4 is prime.

67 = 7+11+13+17+19 (5 consecutive primes).

There are 67 counties in Pennsylvania, Alabama, and Florida.

Typing "*67" into your phone before a call blocks your caller-ID information from the other caller.

67^10 contains all 10 digits (smallest prime with this property).

2^6+2^1+2^0 = 26+21+20 = 67.

Fresh milk has a pH of 6.7 and is slightly acidic.

67^2 and 67^3 contain different digits.

March 9th (68th Day of the Non-Leap Year)

Mar 9th, 3/9.

2^39 does not contain a 0.

39^3+39+1 is prime.

39^2 + 40^2 is prime.

39 and 93 are both semiprimes.

39^2-39-1 and 39^4-39-1 are prime.

There are 39 primes less than 170.

90*39 + 37 and 90*39 + 73 are both prime.

39 = 3^1 + 3^2 + 3^3

39 = 3 + 5 + 7 + 11 + 13 (5 consecutive primes).

68th Day of the Year.

68^4+68^3+68^2+68+1 is prime.

68^6+68^5+68^4+68^3+68^2+68+1 is prime.

3^68 (33 digits) does not contain a 0. It is conjectured to be the highest exponent of 3 with this property.

68^4-68-1 is prime.

68 = 7+61 = 31+37 (largest number to be sum of two primes in two different ways).

March 10th (69th Day of the Non-Leap Year)

Mar 10th, 3/10.

310 = 31*10

310 = (10/(3-1-0))*31*(3-1)

310 = 31 + 10 + 30 + 13 + (3+1+0) + (30/(3-1-0))^(3-1-0) - 3

310 = 103 + 130 + 31 + 30 + 13 + 10 + (3-10)

310 = 130 + 10*(10+3+(10/(3-1-0)))

310 = 301 + 3^(3-1-0)

310 = 103*(3+1+0) - 31 - 13 - 30 - 10 - (3+1+0) - (10+(3+1+0))

310*103 and 310*301 use the same numbers (31930 and 93310, respectively). (What other numbers have this property?)

3^310 + 10 is prime (Note: 3 and 10 concatenated give the number 310). (Do other numbers have a similar property?)

(1!)^2 + (2!)^2 + (3!)^2 + ... + (310!)^2 is prime. (What's the next number with this property?)

310 written in base 6 is 1234.

69th Day of the Year.

69^2-69-1 is prime.
69^2+69+1 is prime.

69^3-69-1 is prime.
69^3+69+1 is prime.

69^2 + 70^2 is prime.

69 of the first 100 primes do not contain a 9.

3^69 - 16 and 3^69 - 32 are both prime.

The numerator of 1+1/2+1/3+...+1/69 is a prime number.

69^23+69^21+69^19+69^17+69^15+69^13+69^11+69^9+69^7+69^5+69^3+69+1 is prime.

69^4+69+1 is prime.

March 11th (70th Day of the Non-Leap Year)

Mar 11th, 3/11.

311 = 131 + 113 + 31 + 3*11 + 3*1*1

311 = 113*(3*1*1) - (31-3*1)

311 = 31*11 - (31-1)

311 = (31+1)*(3^(1+1)) + (31-(1+1)^3)

311 = 131 + 3*11*(3+1+1) + (3*1*1)*(3+1+1)

311 = (3*1*1)*(11-3)*(11+3) - (3+1+1)^(3-1*1)

Every permutation of 311 is a prime (31, 13, 11, 113, 131, 311).

311^8 + 312^8 is prime. (What's another number like this?)

311 is a reflective prime (113 is also prime). (What's the next number satisfying this property?)

The digit sum and digit product of 311 are primes (5 and 3, respectively). (What's another number with this property?)

DigitSum(311^1) = 5^1

DigitSum(311^2) = 5^2

(What's the next number with the same property?)

311 is prime. 3 and 11 are primes (concatenation of primes form a new prime). (What's the next number with this property?)

311 = 101 + 103 + 107 (3 consecutive primes).

311 = 53 + 59 + 61 + 67 + 71 (5 consecutive primes).

311 = 31 + 37 + 41 + 43 + 47 + 53 + 59 (7 consecutive primes).

311 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (11 consecutive primes).

(Note: the number of primes added are prime...--3,5,7,11)

70th Day of the Year.

+/- 1 +/- 2 +/- 3 +/- 4 +/- 5 +/- 6 +/- 7 +/- 8 +/- 9 +/- 10 +/- 11 = 0 has 70 solutions.

70^2+71^2 is prime.

90*70+37 and 90*70+73 are both prime.

70^3-70-1 is prime.

1^2+2^2+3^2+...+24^2 = 70^2.

Clemson University gave up 70 points to WVU in the Orange Bowl in 2012, this is the most points ever given up in the history of all bowl games.

The national speed limit in the UK is 70 mph.

The 70th wedding anniversary is known as the platinum wedding anniversary.

The French do not have a word for 70, instead the say "sixty plus ten" which is "sioxante-dix".

March 12th (71st Day of the Non-Leap Year)

Mar 12th, 3/12.

312 = 213 + 123 - (1+23)

312 = 123 + (23-2*3)^(3+1-2)

312 = 132 + 123 + 3*(23-(3+1-2))

312 = 231 + (2^3+1)^(3+1-2)

312 = 31*12 - 31*2 + (3+1-2)

312 = 3*12 + 31*2 + 2*13 + 21*3 + (3+1*2)^3

312 = (3+12) + (31+2) + (2+13) + (21+3) + (3+12)^(3+1-2)

312 = 32*1 + (32+1) + 23*1 + (23+1) + 123 + (2^3-1)*(13-2)

312^4 uses all numbers 3 to 9. (Do other numbers have this or a similar property?)

312 = 2*2*2*3*13 (only uses 1,2,3 in prime factorization). (What's another number like this?)

312^4 + 1 is prime. (What's the next number with the same property?)

312 = 0!*5! + 1!*4! + 2!*3! + 3!*2! + 4!*1! + 5!*0!

1 + 2*312 + 3*312^2 + 4*312^3 is prime (Note: If 312 = n, 1 + 2n + 3n^2 + 4n^3 is prime). (What's the next number with this property?)

There are 312 ways to place 7 nonattacking queens on a 7 by 8 board.

312 written in base 5 is 2222. (What's another number with a similar property?)

312 written in base 7 and 11 have the same digits (624 and 264, respectively). (What other numbers have similar properties?)

312 written in bases 18, 19, 20, ... 36 use at least one letter (except one of the bases). (Which base uses only numbers?)

71st Day of the Year.

71 and 17 are both prime.

71^2 = 7!+1!

71^3 = 357911 (concatenation of odd numbers)

71^2-71-1 is prime.
71^2+71+1 is prime.

71^3-71-1 is prime.
71^3+71+1 is prime.

2^39 has a digit sum of 71. This isn't surpassed until 2^48 (73).

71^4-71-1 is prime.

3^71 +/- 20 are primes.

There are 71 different characters that can be used with a standard English keyboard (uppercase included).

71 divides 2+3+5+7+11+...+61+67+71.

The Earth is approximately 71% of Earth's surface.

2^71 does not contain a 9 (largest known prime exponent with this property).

Clint Eastwood is Inspector 71 in the movie Dirty Harry (which came out in 1971).

71π is the closest to a prime than any multiple of π below it.

March 13th (72nd Day of the Non-Leap Year)

Mar 13th, 3/13.

313 = 133 + 3*(31*(3-1)) - (3*1+3)

313 = (31-13)^(3-1) - (13+(1-3))

313 = (31+13)*(3+1+3) + (3-1+3)

313 = (31+3)*(3*1*3) + (3+1+3)

313 = (31*(13-3)) + 3

313 = (13-1)^(3-1) + 13^(3-1)

313 = (3+13)^(3-1) + 31 + (31-(3-1+3))

313 is a prime of the form n^2 + (n+1)^2 (Here, n = 12). (What's another prime of this form?)

313^16 + 314^16 is prime. (What's the next number with the same property?)

313^2 + 4 is prime. (What's the next number with this property?)

313 is prime. 13 is prime. 3 is prime.

313 is prime. 31 is prime. 3 is prime.

(What other numbers have one or both of these properties?)

You need 313 people to ensure a 50% chance that 5 people share the same birthday.

313 and 119 both have a digit product of 9. (Does this happen with other dates?)

313 is the smallest palindromic prime with only one 1 and with two 3s.

313 written in bases 2 and 13 (and 10) are palindromic (100111001 and 1B1, respectively).

72nd Day of the Year.

72 = 2*2*2*3*3
72*(2+2+2+3+3) = 864.
72*(7+2) = 648.

2^72 (22 digits) does not contain a 0.

72 = 2^3*3^2.

72^2+73^2 is prime.

72^6+72^5+72^4+72^3+72^2+72+1 is prime.

72^4+72+1 is prime.

72 = 13+17+19+23 (four consecutive primes).
72 = 5+7+11+13+17+19 (six consecutive primes).

72 degrees Fahrenheit in considered room temperature.

There are 72 average heartbeats per minute for a resting adult.

The human body is composed 72% of water.

The axis of the Earth moves one degree every 72 years compared to the stars.

72 is usually par score for an 18 hole golf course.

March 14th (73rd Day of the Non-Leap Year)

Mar 14th, 3/14.

314 = 143 + 134 + (31+(3-1+4))

314 = 431 - 134 + (3+14)

314 = 341 - (13-4)*3

314 = 3*14 + 31*4 + 4*13 + 41*3 + (1-4)^3

314 = 413 - (3+1+4)*(14-3) - (14-3)

314 = 34*(4-1)^(3-1) + (3+1+4)

314 = (3*1*4)*(31-4) - (41-31)

314 = 431 - 143 + (31-4) + 1

Happy Pi Day!

314^2 + 1 is prime. (What's the next number with this property?)

There are only 4 primes between 31400 and 31499. (Can you name them?)

There are 314 primes less than 10000 with at least one 8 (Note: 3+1+4 = 8).

314^2 + 314 + 1 is prime. (What's another number like this?)

73rd Day of the Year.

73^2 = 5329 (concatenation of two primes).

73 is the 21st (7*3) prime and 37 is the 12th prime (Note the reversal of digits).

Sheldon Cooper on the Big Bang Theory claims 73 is the best number.

73! + 1 is prime.

(19^73-3^73)/16 is prime (73 is the smallest number with this property).

73^4+73^3+73^2+73+1 is prime.

73^6+73^5+73^4+73^3+73^2+73+1 is prime.

73^2+4 is prime.

73 in the smallest integer with 12 letters in its English name.

73 is the only prime repunit in base 8 (111b8).

73 is the 21st prime. 73 is 1001001 base 2. 21 is 10101 base 2.

It took 73 seconds for the tragic explosion of the Challenger Space shuttle.

In international curling competitions, each side is given 73 minutes to complete all of its throws.

The Philadelphia 76ers lost in the 1972-73 season (9-73), it was the most losses in NBA history.

In the 1940 NFL championship game, the Bears beat the Redskins 73-0, the most points scored ever in an NFL game.

March 15th (74th Day of the Non-Leap Year)

Mar 15th, 3/15.

315 = 31*5 + 3*15 + (13+(3-1)*5)*5

315 = 51*3 + 5*13 + 53 + (3+15)

315 = 153 + (15-3) + 3*1*5 + 135

315 = 351 - (35+1)

315 = 531 - 351 + 135

315 = 35*(3+1+5)

315 = 5!*(5-3+1) - 3*15

315 = 5^3 + 3^(5-1) + 135 - (31-5)

315 = (3*1*5)*(3-1+5)*(5-3+1)

315*513 = 161595 (concatenation of two palindromes). (What's another number with this property?)

315 = 3*3*5*7 (3 ≤ 3 ≤ 5 ≤ 7)

315 = 3*3*5*7

315*(3+3+5+7) begins with '567' (three consecutive numbers).

315 is divisible by its digit sum and digit product. (What's the next number with this property?)

There are 315 primes between 47 and 47^2 (inclusive).

74th Day of the Year.

74^2+1 is prime (and a twin prime, as well).

74^4+1 is prime.

74^16+1 is prime.

74^3+74+1 is prime.

74^4+74+1 is prime.

74^4+74^3+74^2+74+1 is prime.

2^74 (23 digits) does not contain the digit 2.

A hurricane or typhoon is a system with sustained winds of at least 74 mph.

March 16th (75th Day of the Non-Leap Year)

Mar 16th, 3/16.

316 = 136 + 163 + (3*6-1)

316 = 361 - 3*16

316 = 3*16 + 31*6 + 6*13 + 61*3 + (163+16)

316 = (631 + (6/3-1))/(6-3-1)

316 = 613 - (3*1*6)*16 - (3+6)

316 = (3+1+6)^(6-1-3) + 6^(3*1)

316 = (31+6) + (3+16) + (6+13) + (61+3) + 163 + (6+1)*(3-1)

316 = (16+63)*(6+1-3)

316 = (6^(3-1))*(3+6-1) + (6+1)*(3+1)

316 = 2*2*79

2+2+79 = 83 (prime factors added is a prime). (What's another number with the same property?)

There are 316 primes of the form x^2 + 1 less than 10^7.

316^23 + 316^21 + 316^19 + 316^17 + 316^15 + 316^13 + 316^11 + 316^9 + 316^7 + 316^5 + 316^3 + 316^1 + 1 is prime. (What's another number with this property?)

316^8 + 317^8 is prime. (What's the next number with this property?)

316 is the largest number such that its square has 5 digits.

316 written in bases 16 through 34 include at least one number. (Do other numbers have bigger gaps?)

316 written in base 7 is 631 (uses 3,1,6). (Do other numbers have this property? With other bases?)

75th Day of the Year.

75^2+75+1 is prime.

75^16+76^16 is prime.

75!! + 2 is prime.

75*2^75 + 1 is prime.

2^75+75 is prime.

The oldest a Canadian senator can be is 75.

March 17th (76th Day of the Non-Leap Year)

Mar 17th, 3/17.

317 = 371 - (7+3-1)*(13-7)

317 = 137 + 13*7 + (73+(7-3)^(3-1))

317 = 173 + 1*73 + 71

317 = 731 - 7*31 - ((7+3)^(3-1)+73+3*(7+1))

317 = 713 - 71*3 - (7-3-1)*(71-(7+3*1))

317 = 3*17 + 31*7 + 7^(3-1)

317 = 7*13 + 71*3 + (17-(7-3*1))

317 = (3+17) + (31+7) + (7+13) + (71+3) + (3+1+7)*(13+(3-1))

317 = (3+1+7)*(31-(3-1)) - (7-1)/3

317 = (3*1+7)*31 + (31-3*(1+7))

317 = (3+17)*(3-1)^(7-3) - (7-3-1)

317 = (31+7)*((7-3)/(3-1))^3 + 13

317 = (31-7)*13 + (17-(7-1)*(3-1))

317 = 137 + (3+7)*(3*1*7-(7-3-1))

317 = 173 + (3*1*7-(3+7-1))^((7-1)/3)

317 = 713 - 371 - (7-(3-1))^((17-3)/7)

317 = (7+1)*13 + 71*3

317 = 37*1 + 73*1 + (17-3)^(3-1) + (3+1+7)

317 = (3*1*7)^(3-1) - (3+1+7)^((7-1)/3) - (7-3-1)

317 = (-3)^3 + 1^3 + 7^3

317^5 is the next time 317^n has a 7.

317^2 contains 2 zeros.

111...111 (with 317 ones) is prime.

There are 317 primes less than 2100 (Note that 3*1*7 = 21).

2*3*5*7*11*13*17*...*317 - 1 is prime.

317 is prime.

31, 17 and 37 are also prime.

317 has 317 pages on the OEIS as of Nov 13, 2013. (Is there another number like this?)

317 is the concatenation of 3 and 17 (two primes) or 31 and 7 (also two primes).

317 is prime. (Are there other numbers like this?)

317 is prime.

317^2 + 4 is prime.

(Any other primes with this property?)

76th Day of the Year.

2^76 (23 digits) does not contain a 0.

(76!)^2+1 is prime (76 is the largest number with this property).

76^n ends in 76 for any n > 0.

17th prime + 17 = 59 + 17 = 76.

76^16+1 is prime.

76^3-76-1 is prime.

There are 76 ways to place 3 nonattacking queens on a 3 by 7 board.

There are 76 numbers <= 1000 with 5 prime factors.

76^8 + 77^8 is prime.

There are 76 primes between 14^3 and 15^3.

March 18th (77th Day of the Non-Leap Year)

Mar 18th, 3/18.

318 = 138 + 183 - 3

318 = 381 - 3*(3+18)

318 = 31*8 + 3*18 + (3-1)*8

318 = 8*13 + 81*3 - 3*1*8 - (8-3*1)

318 = 1*83 + 38*1 + 183 + (3-1)*(8-1)

318 = (3+1+8)*(3*1*8) + (3+18) + (8+1-3)

318 = 138 + 18*(8-1+3)

318 = 183 + (8-1*3)*(3*(1+8))

318 = 31*18 - (8-1+3)*(3*1*8)

318 = 2*3*53 (all prime digits--just like 1114). (What other dates have this property--both day and date satisfying it?)

318*(3*1*8) = 7632 (7 > 6 > 3 > 2). (Do other numbers have this property?)

318^16 + 1 is prime. (What's another number with this property?)

If 318 = n, 2n3n5n7n11 is prime (Meaning, 231833185318731811 is prime). (What's the next number with this property?)

According to the The Simpsons, 318 is the Police code for waking an officer.

The mass of Jupiter is approximately 318 times the Earth.

77th Day of the Year.

77!+1 is prime.

77^2-77-1 is prime.

77^2+77+1 is prime.

77^4+77^3+77^2+77+1 is prime.

2^77 (24 digits) does not contain a '0'.

77= 3^4-3-1 (3 is prime) and 77^4-77-1 is prime.

77^4+77+1 is prime.

There are 77 inequivalent ways to cut a 5 by 5 square into squares with integer sides.

77 is a palindrome and the 77th triangular number is a palindrome.

There are more primes between [77,2*77] than [77,77^2].

There are 77 numbers less than 4^5 with 5 not necessarily distinct prime factors.

2^77 reversed is prime.

77 is the smallest positive integer requiring 5 syllables.

March 19th (78th Day of the Non-Leap Year)

Mar 19th, 3/19.

319 = 31*9 + 3*19 - (13 + (9/3+1))

319 = 91*3 + 9*13 - 93 + (3+19)

319 = 93 + 39 + 193 + (3*1-9)

319 = 31*19 - (3*1*9)*(13-9/3)

319 = (31+9) + (3+19) + (91+3) + (9+13) + 139 + (9/3-1)

319 = 193 + 139 - 13

319 = 391 - (9*(3-1+9) - (3*1*9))

319 = (3+1+9)*(3+19) + (9/3*1)*(3-1+9)

319 = (3*1*9)*(3*1+9) - (9-3-1)

319 = (3-1+9)*(3*1*9+(9/3-1))

319^3 = 32461759 (all different digits). (This is the largest number with this property. What's the second to last number with this property?)

319 = 11*29 (11 < 29 and 1 ≤ 1 ≤ 2 ≤ 9).

10^29 + 319 is the first prime after 10^29.

319^10 + 319^9 + 319^8 + 319^7 + 319^6 + 319^5 + 319^4 + 319^3 + 319^2 + 319^1 + 1 is prime. (What's another number with this property?)

There are 319 primes less than 46^2.

319 is a song by Prince.

319 = 103 + 107 + 109 (three consecutive primes). (Note: these primes were used above for 1115.)

319 contains 6 consecutive 1s in binary.

78th Day of the Year.

78 = 1+2+3+4+5+6+7+8+9+10+11+12

56 = 7*8 (Note: 5,6,7,8 are consecutive).

78^2+78+1 is prime.

There are 78 primes less than 400.

There are 78 different values for 2^2^2^2^2^2^2^2^2 (depending on the placement of parentheses).

There are 78 ways to place 2 nonattacking kings on a 4 by 4 board.

78^8+79^8 is prime.

The digit 6 appears 78 times in the first 1000 Catalan numbers.

The digit 1 appears 78 times in the first 1000 prime numbers.

2*78! + 1 is prime.

9*10^78+1 is prime (That is, 9000...0001 is prime with 77 zeros).

There are 78 total gifts in the song Twelve Days of Christmas.

March 20th (79th Day of the Non-Leap Year)

Mar 20th, 3/20.

320 = 203 + 23*(3+2+0) + 2

320 = 230 + 3*20 + 30

320 = 3*20 + 32 + 23 + 30*2 + 230 - (3+2+0)*(30/2) - (3^2+2^0)

320 = (3^2)*32 + (30+2)

320 = (2^3)*(32+2^3)

320 = 23*(30/2) - (3+2)^2

320 = (20-3)^2 + (32-(3-2))

320 = (30-2)*(3*2+(3+2)) + (20-3) - (3+2+0)

320 = (3+2+0)*(2^(3*2))

Every nonzero digit and every sum of any number of digits of 320 is prime (i.e. 3, 2, 3+2, 3+2+0, 3+0, 2+0, ...etc are all prime).

320! + 1 is prime. (What's the next number with the same property?)

320^4 + 1 is prime. (What's another number like this?)

320^6 + 320^5 + 320^4 + 320^3 + 320^2 + 320 + 1 is prime. (What's the next number satisfying this property?)

There are 320 possible moves a queen could make on a 5 by 5 chessboard.

There are 320 primes between 33^3 and 34^3.

320 is the largest determinant that can be obtained from a 10 by 10 matrix of zeros and ones.

79th Day of the Year.

79^2+80^2 is prime.

79^4+79^3+79^2+79+1 is prime.

79^4-79-1 is prime.

There are 79 ways to place 4 nonattacking kings on a 4 by 4 board.

2^79 is the smallest power of 2 greater than Avogadro's Numbers (6.022e23).

79 = 2^7 - 7^2 (Note: 2+7 = 9).

The square root of 79 begins with four 8's.

In Illinois, USA, riding in the left hand lane for over half a mile is a \$79 fine.

1 = one --> 15+14+5 = 34

2 = two --> 20+23+15 = 58

...

Numbers 1-79 when written out in English and added up the letters, the letters are more than the number itself. It is not until 80 that the letters are less than 80.

79 = 11 + 31 + 37

97 = 11 + 13 + 73

March 21st (80th Day of the Non-Leap Year)

Mar 21st, 3/21.

321 = 123 + 231 - 3*(32-21)

321 = 213 + 123 - (12+3)

321 = 132 + 213 + (3+2-1)*(3*2*1)

321 = 231 + 132 - (2^3-1)*(3+2+1)

321 = 32*21 - 231 - 123 + (3*(2-1))

321 = 12*23 + (3+2)*(3^2)

321 = 3*21 + 32*1 + 12*3 + 1*23 + 132 + (2^3-1)*(3+2)

321 = (32+21)*(3+2+1) + (3*(2-1))

321 = (32+1) + (3+21) + (12+3) + (1+23) + (12+3)^(3-2+1)

321 = 21*(12+3) + (3*2*1)

321 = (32+1) + (12+3) + (31+2) + (13+2) + (1+23) + (3+21) + 132 + (3^2)*(3+2)

321 = 13*(3+21) + 3^2

321 = (21-3)^(3-2+1) - 3*(2-1)

321 = (13-2)*(31-2) + (3-2+1)

321 = (12-3)*((3+2+1)^(3-2+1)) + 3*(1-2)

321 = (21/3)*((3^2)*(3+2)) + (3*2*1)

321^16 + 322^16 is prime. (What's the next number with this property?)

321^19 + 321^17 + 321^15 + 321^13 + 321^11 + 321^9 + 321^7 + 321^5 + 321^3 + 321 + 1 is prime. (What other numbers have this property?)

The digit 8 appears 321 times in all the four-digit primes.

The sum of divisors of 321 is 432 (similar format as 321).

There are 321 zeros between numbers 1 and 1111.

80th Day of the Year.

80^2+80+1 is prime.

80^4+1 is prime.

80^6+80^5+80^4+80^3+80^2+80+1 is prime.

Green Day released a song called "80", a nickname for the lead singer's wife, Adrienne or Adie.

March 22nd (81st Day of the Non-Leap Year)

Mar 22nd, 3/22.

322 = 223 + 3*(22+(3^2+2))

322 = 232 + (2+3+2)*(2*(3+2) + 3*(2/2)) + (3-2-2)

322 = 3*22 + 32*2 + 2*23 + 22*3 + ((3+2)*2)*(3*2+2)

322 = (32+2) + (3+22) + (2+23) + (22+3) + 3*(3^(2+2) - (3+2)*2)

322 = (3*2*2)*(3+22) + (32-2*(3+2))

322 = (3+2+2)*(2*23)

322 = 2^(2^3) + 22*3

322 = (3^(2+2))*((2^3)/2) - (3-2/2)

322 = 2*7*23 (uses only prime digits and uses 3,2,2 in prime factorization). (Do other numbers have both of these properties?)

322 is composite but both 233 and 223 are prime. (What other numbers have the same property?)

322 is the 12th Lucas number (Note: 12 = 3*2*2). (Do other Lucas numbers share this property?)

322 is the smallest number whose square has 6 distinct digits (103684).

There are 322 different ways to rearrange 1,2,3,4,5,6,7 so no consecutive numbers are next to each other.

323^11 - 322^11 is prime. (What's the next number with this property?)

322^2 + 323^2 + 324^2 is prime. (What's another number like this?)

There are 322 composites less than 20^2 (including 20^2).

322 is a composite number consisting of all prime digits. (What's a composite number with this property that doesn't use the number 2?)

If 322 = n, 2n3n5n7n11 is prime (Meaning, 232233225322732211 is prime). (What's the next number with the same property?)

81st Day of the Year.

81 = (8+1)^2

81 = 8*8+(8^(8/8)+8^(8/8))+1 (Eight 8's and One 1).

2^81 (25 digits) does not contain a 0.

81 is the smallest number of the form (k!+9)/9 (k = 6).

81^3-81-1 is prime.

81 divides 2^81+1.

2^81-81^2 is prime.

1/81 = .012345679012345679012... (missing the number 8).

March 23rd (82nd Day of the Non-Leap Year)

Mar 23rd, 3/23.

323 = 233 + (2+3+3)*(2^3+3) - (3-2-3)

323 = 332 - (3*2+3)

323 = (3*2*3)^(3+2-3) - (2-3/3)

323 = 3*23 + 32*3 + 33*2 + (23*(3-2+3))

323 = (3+23) + (32+3) + (33+2) + ((3+2)*3)^(3+2-3) + 2*(3/3)

323 = 23*(23-(3+2+3)) - (23+(2-3))

323 = 32*(3*2*3 - (3+2+3)) + 3^(3-2)

323 = (3+23)*(3^2+3) + (3+2^3)

323 = (32+3)*(3*2+3) + (3+2+3)

323 = 17*19

(1+7) + (1+9) = 18 (18 = 3*2*3). (Does this happen with other numbers?)

Inserting a 9 between adjacent digits in 323 results in a prime (i.e. 3923 and 3293 are prime). (What's the next number with this property?)

323 is the smallest natural number that uses 26 letters in its English spelling, including the "and" ("three hundred and twenty three").

There are 323 perfect squares less than 47^3.

323 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (nine consecutive primes).

23^323 + 2 is prime. (Note this is of the form 23^n + 2. 23 and 2 are both in 323). (What's another number with this property?)

323 is also palindrome if it's written in bases 14 and 18 (191 and HH, respectively). (What other palindromes in base-10 are palindromes in other bases? Three other bases? Four?)

323 is the smallest palindrome that is the product of two twin primes (17*19).

82nd Day of the Year.

821, 823, 827, and 829 are all prime.

82 = 3^4+1 (3 is prime) and 82^4+1 is prime.

Nuclei with either 82 protons or neutrons are more stable against nuclear decay.

82^2+83^2 is prime.

82^4-82-1 is prime.

There are 82 ways to place 4 nonattacking queens on a 5 by 5 board.

The code *82 unblocks your caller ID for phones that block anonymous calls.

March 24th (83rd Day of the Non-Leap Year)

Mar 24th, 3/24.

324 = 432 - (4+3+2)*((24-3)-(3+2+4))

324 = 243 + (3+2+4)^(2*(4-3))

324 = 234 + (4+2+3)*(4+2*3)

324 = (32/4+(4+2*3))^((4+2)/3)

324 = 3*24 + 32*4 + 4*23 + (2*(4-3))^(4+3-2)

324 = 43*2 + 2*34 + 42*3 + (3+2*4)*((3-2)*4)

324 = (32+4) + (3+24) + (4+23) + (42+3) + (34+2) + (43+2) + (4+2^3)*(3+2+4)

324 = (3+2+4)*((3*(4-2))^(3*2-4))

324 = (3*2*4)*(3^2+4) + (3+2+4)

324 = (3+24)*(3*2+4)

324^3 has digits no higher than 4. (Note: 4 is the highest number in 324. Do other numbers have this property or a similar property? Fourth power?)

324*423 has each non-composite digit (137052). (Are there other numbers like this?)

324 = (2^2)*(3^4) (uses only the digits in 324). (What other numbers satisfy this property?)

324! - 1 is prime. (What's another number with this property?)

There are 324 primes less than 10000 with at least one 5.

The concatenation of 324^2, 324, and 1 is prime (that is, 1049763241 is prime). (What's the next number with this property?)

324 = 73 + 79 + 83 + 89 (four consecutive primes).

Besides base-10, 324 is also a square if written in base 9, 15, 16, 17, and 18 (400, 169, 144, 121, 100). (Is there a number that is a square is more than 6 bases?)

324 is 169 base 15 (13^2).

324 is 144 base 16 (12^2).

324 is 121 base 17 (11^2).

324 is 100 base 18 (10^2).

(Do other numbers have this property?)

83rd Day of the Year.

83^3+83+1 is prime.

83^4+83^3+83^2+83+1 is prime.

83 is the 23rd prime number (Note: 23 is also prime).

83 = 23+29+31 (three consecutive primes).

83 = 11+13+17+19+23 (5 consecutive primes).

(Note that both equations have the 23 and 83 is the 23rd prime).

When a man turns 83 years old, he may celebrate a second bar mitzvah.

TI-83 is a type of calculator.

The smallest prime with a digit sum of 83 is 3999998999.

There are 83 9-digit squares with all 9 digits being different.

83^2 = 6889 is a strobogrammatic number.

83 is the only prime of the form p^4+2 for prime p.

The average of all primes up to 83 is 38.

2^83 (25 digits) does not contain a '2' (83 is the largest known prime exponent with this property).

March 25th (84th Day of the Non-Leap Year)

Mar 25th, 3/25.

325 = 235 + (2*5)*((5-2)*3)

325 = 253 + (5-(3-2))*(23-5)

325 = 352 - 3^(5-2)

325 = (32+5) + (3+25) + 253 + (2*5-3)

325 = (5+23) + (52+3) + 253 - (3*2+5)

325 = (53+2) + (35+2) + 235 - (2^3-5)

325 = 3*25 + 32*5 + (2*3*5)*(5-2)

325 = 5*23 + 52*3 + (5-2)*(23-5)

325 = 35*2 + 2*53 + 5^3 + (5-2)*(2^3)

325 = (3*2*5)*(3*2+5) - 25/(3+2)

325 = (3+2+5)*(2^5) + 5^(3-2)

325 = 25*(5*3-2)

325 = (32+5)*(3^2) - 2^3

325 = (3+25)*(3*2+5) + (3*5+2)

325 = ((5-2)*(2*3))^(5-3) + (5-3)/2

3251, 3253, 3257, and 3259 are all prime. (What's the next number with the same property?)

325^19 + 325^17 + 325^15 + 325^13 +325^11 + 325^9 + 325^7 + 325^5 + 325^3 + 325 + 1 is prime. (What's another number with this property?)

12^325 - 325^12 is prime. (What's the next number with this property?)

325 divides (5^325 - 3^325 - 2^325). (Are there other numbers with this property?)

325 written in bases 2, 4, 8, 18, and 24 are palindromes. (What other base-10 non-palindrome has a similar property?)

84th Day of the Year.

84 = 1 + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) + (1+2+3+4+5+6) + (1+2+3+4+5+6+7)

84*84 = 7056

84*48 = 4032 (Note the similarities between these equations...)

84^2+1 is prime.

84 = 1^2+3^2+5^2+7^2

There is no prime between 840 and 849.

84^2+85^2 is prime.

84^2-84-1 is prime.

Los Angeles Lakers Magic Johnson holds the record for most assists (84) in a 6-game NBA final series in 1985.

There's a town in Pennsylvania, USA called Eighty Four.

It takes 84 years for Uranus to orbit the sun once.

March 26th (85th Day of the Non-Leap Year)

Mar 26th, 3/26.

326 = 263 + (3-2+6)*(6*3/2)

326 = 236 + (3+2)*((3^2)*(6/3))

326 = 362 - (3*2)^(6/3)

326 = (32+6) + (3+26) + 263 - (6*2/3)

326 = (6+23) + (62+3) + 236 - ((6/3)+2)

326 = 3*26 + 32*6 + (2^3+6)*(6*2/3)

326 = 6*23 + 62*3 + (2^3-6)

326 = 36*2 + 2*63 + 2^(3-2+6)

326 = (3+2+6)*(3+26) + (3-2+6)

326 = (3*2*6)*(6*3/2) + (2^3-6)

326 = (32+6)*(3*(6/2)) - (6-2)^(6/3)

326 + 3*2*6 = 362

326^2 + 1 is prime. (What's another number with the same property?)

326^16 + 327^16 is prime. (What's the next number with this property?)

Of all the four digit primes, there are 326 4's.

There are 326 primes less than 10000 with at least one 4 (Note: this and the statement above are different).

326 = 251 + 75 (54th prime plus 54th composite)

326 prefixed or followed by any digit still remains composite. (What's another number with this property?)

85th Day of the Year.

85^2+86^2 is prime.

There are 85 primes less than 21^2.

85^4+85^3+85^2+85+1 is prime.

85 and 58 both have 2 prime factors.

85 = 17*5 and 8+5 = 1+7+5.

85 = 4^3+4^2+4+1.

90*85+37 and 90*85+73 are both prime.

There are 85 primes between 43000 and 44000 (This is the lowest number of primes between n*1000 and (n+1)*1000 until n = 64).

85 = 125 base 8 (Note: 125 is 5^3 and 8 is 2^3. Further 5+3 = 8 and 2+3 = 5).

March 27th (86th Day of the Non-Leap Year)

Mar 27th, 3/27.

327 = 273 + (2+7)*(3*2)

327 = 237 + (3^2)*(7+3)

327 = 372 - (27+3) + 3*(2-7)

327 = (3*2*7)*(3-2+7)

327 = (3+2+7)*27 + (7+2)/3

327 = 32*7 + 3*27 + (2*7-3)*((7-3)/2)

327 = 7*23 + 72*3 - ((7-3)/2)*((7-2)^(3^2-7))

327 = (32+7) + (3+27) + (72+3) + 7+23) + 2^7 + (7-2)^((7-3)/2)

327 = (32+7)*((7-3)*2) - 3*(2-7)

327 = (3+27)*(7*2-3) - (7+2)/3

There are 327 primes less than 2200.

The first prime after 10^52 is 10^52 + 327.

327!! + 32 is prime (Only one known number higher). (What is that number?)

There are 327 primes less than 3^7.

86th Day of the Year.

2^86 (26 digits) contains no '0' (This is conjectured to be the highest exponent with such property).

86^2-86-1 is prime.

86^3-86-1 is prime.

86^10+86^9+86^8+86^7+86^6+86^5+86^4+86^3+86^2+86+1 is prime.

86^23+86^21+86^19+86^17+86^15+86^13+86^11+86^9+86^7+86^5+86^3+86+1 is prime.

There are 86 primes between 45000 and 46000.

There are 86 metals in the periodic table.

March 28th (87th Day of the Non-Leap Year)

Mar 28th, 3/28.

328 = 283 + (3^2)*(8-3)

328 = 238 + (2+8)*(8-2+3)

328 = 382 - (8-2)*(8+3-2)

328 = 3*2*8 + 283 - (8-2-3)

328 = 3*28 + 32*8 - 3*(8/2)

328 = 8*23 + 82*3 + (23-(8-2))*(3*2)

328 = 38*2 + 2*83 + (83+(8-3-2))

328 = (3*2*8)*(8/2+3) - (2^3)

328 = (3+2+8)*(28-3) + (8-3-2)

328 = (3+28)*((8-3)*2) + (8-2)*3

328 = (32+8)*((3-2)*8) + (2^3)

328 = (32+8) + (3+28) + (8+23) + (82+3) + ((3*8)/2)^(8-3*2) - (8-3-2)

The sum of the first 15 primes is 328 (2+3+5+7+11+13+17+19+23+29+31+37+41+43+47 = 328).

328^4 + 1 is prime. (What's the next number with the same property?)

The sum of the first 328 primes is prime. (When will this happen next?)

If 328 = n, n0123456789 is prime (Meaning 3280123456789 is prime). (What's the next number with this property?)

87th Day of the Year.

87^3+87+1 is prime.

87^2+88^2 is prime.

87^6+87^5+87^4+87^3+87^2+87+1 is prime.

87^2-87-1 is prime.

1/5+2/4+3/3+4/2+5/1 has 87 on the numerator.

87^2+4 is prime.

87 is 322 in base 5 and 223 in base 6.

In the National Hockey League, Wayne Gretzky scored 87 goals with the Edmonton Oilers in 1983-84.

There were 87 years between the signing of the Declaration of Independence and the Battle of Gettysburg (Thus, Abraham Lincoln's famous words were "Four score and seven years ago...").

March 29th (88th Day of the Non-Leap Year)

Mar 29th, 3/29.

329 = 293 + (9-3)^2

329 = 239 + (9-3)*(9*2-3)

329 = 392 - (3^2)*(9-2)

329 = 3*29 + 32*9 - 9*(3+2) - (9/3-2)

329 = 9*23 + 92*3 - 239 + (3+2)*(9+2^3)

329 = 2*39 + 93*2 + 3*2*9 + (2+9)*(3-2)

329 = (3*2*9)*((9/3)*2) + (9/3+2)

329 = 23*(3+2+9) + (2^3-(9/3-2))

329 = (32+9)*(9-3+2) + (9-2^3)

329 = (29-3)*((9-3)*2) + (9+2^3)

329 = (3+29) + (32+9) + (9+23) + (92+3) + 3*2*9 + ((3+2)*(9*2-3))

329 + (3+2+9) = 343

329 + (3*2*9) = 383 (both palindromes)

(What's another number with this property?)

329 = 7*47

7+47 = 54 = 3*2*9

(Are there other numbers with this property?)

329 = 7*47

747*329 uses 2,3,4,5,6,7 once (245763). (Do other numbers have a similar property?)

There are 329 primes less than 47^2 (Note: 47 is a prime factor of 329). (Do other numbers satisfy both these properties?)

329 is not divisible by 3,2, or 9. (What's another composite number with this property?)

329^2 + 329 + 1 is prime. (What's the next number with this property?)

There are 329 primes of the form x^16 + 1 less than 10^65.

1331329 and 3291331 are both prime.

329 = 107 + 109 + 113 (3 consecutive primes).

88th Day of the Year.

88^4+1 is prime.

88^2 only contains 2 different digits.

You need 88 people in a room for a 50% chance that 3 people have the same birthday.

It takes around 88 days for Mercury to complete an orbit around the Sun.

A standard playing card is 88 mm.

There are 88 keys on a standard piano.

March 30th (89th Day of the Non-Leap Year)

Mar 30th, 3/30.

330 = 303 + 3^3

330 = 33*(3*3+3^0)

330 = (3+3^0)*(3*30) - (3+3)*(3+(3+3^0))

330 = (3*3)*(3+3)^(3-3^0) + (3+3+0)

330 = (3+3+0)*((30-3)*(3-3^0)) + (30/3-(3+3^0))

330 = (30-3)*(3*(30/3-(3+3+0))) + (3+3+0)

330^16 + 1 is prime. (What's another number divisible by 10 with this property?)

330 = 43 + 47 + 53 + 59 + 61 + 67 (six consecutive primes).

There are 330 dimples on a British golf ball.

89th Day of the Year.

2^89-1 is prime.

89 = (8+9)+(8*9)

89^2+89+1 is prime.

There is no prime between 890 and 899.

89^6+89^5+89^4+89^3+89^2+89+1 is prime.

89^16+90^16 is prime.

2*3*5*7*11*...*83*89 - 1 is prime.

89+98 = 187
187+781 = 968
...
After 24 iterations, the result will be a palindrome. No number < 10000 has this many iterations.

March 31st (90th Day of the Non-Leap Year)

Mar 31st, 3/31.

331 = 313 + (3/3+1)*(3*3*1)

331 = 133 + (33/(3*1))*((3*3-1)+(13-3))

331 = (3*3*1)*((3+3)^(3-1)) + (3+3+1)

331 = (3+3+1)*(33+13) + (3*3*1)

331 = 33*1 + 3*31 + 1*33 + 13*3 + 133

331 = (3+31)*(3*3+1) - (3*3*1)

331 = (3+31) + (33+1) + (1+33) + (13+3) + 133 + (3+3-1)*((3-1)^(3+1))

331 = (13+3)*(3*(3+3+1)) - (3+3-1)

331 is the 67th prime (67 is prime). 67 is the 19th prime (19 is prime). (What's another prime like this?)

331 is prime and (3+3+1) is prime. (What's another prime with this property?)

10^28 + 331 is the first prime after 10^28.

331^2 - 331 - 1 is prime. (What's the next prime with this property?)

The sum of the first 15 semiprimes is 331.

331 = 59 + 61 + 67 + 71 + 73 (five consecutive primes).

Sound travels just over 331 meters per second in dry air at 0 degrees Celsius.

331, 3331, 33331, 333331, 3333331, 33333331 are all prime.

133, 1333, 13333, 133333, 1333333, 13333333 are all composite.

(Do other primes satisfy this interesting property?)

83^331 - 82^331 is the only known exponent for this number to be a prime (further, this is only a probable prime).

331 is the smallest prime that is Cuban, good, lucky, and happy.

90th Day of the Year.

90^2+1 is prime.
90^4+1 is prime.

90^2+90+1 is prime.
90^2-90-1 is prime.

90^2+91^2 is prime.

A right triangle is a triangle with a 90 degree angle.

Major League Baseball bases are 90 feet away in distance.
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