April 1st (91st Day of the Non-Leap Year)

Apr 1st, 4/1.

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!

91st Day of the Year.

91 = 1+2+3+4+5+6+7+8+9+10+11+12+13

91 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2.

90*91+1 is prime.

91^2 = 8281 (concatenation of consecutive numbers)

91 contains all odd numbers.
91^3 = 753571 has all odd numbers as well.

Of the first 100 primes, 91 do not contain a 0.

1+1/2+1/3+...+1/91 has a prime numerator.

There are 91 primes between 57000 and 58000.

91 in base 4 is 1123 (Note which type of sequence that is).

91 in base 8 is 133. 91 in base 5 is 331.

6^3-5^3 = 4^3+3^3 =91.

91 is the largest amount of money possible if you have one coin each less than a dollar (1+5+10+25+50 = 91).

April 2nd (92nd Day of the Non-Leap Year)

Apr 2nd, 4/2.

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.

92nd Day of the Year.

There are 92 ways to place 8 nonattacking queens on an 8 by 8 board.

90*92+37 and 90*92+73 are both prime.

There are 92 ways to place 2 nonattacking bishops on a 4 by 4 board.

There are 92 primes of the form 1+x^64 for x < 10000.

There are 92 primes between 16^3 and 17^3.

The Guinness Book of world record has a 92-character placename: Taumatawhakatangihangakoauauotamateaurehaeaturipukakapikimaungahoronukupokaiwhenuakitanatahu.

The average American child consumer 92 pounds of sugar a year.

April 3rd (93rd Day of the Non-Leap Year)

Apr 3rd, 4/3.

(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.

93rd Day of the Year.

93^6+93^5+93^4+93^3+93^2+93+1 is prime.

93^16+94^16 is prime.

There are 93 primes between 55000 and 56000.

9*10^93-1 is prime. That is 8999...999 with 93 9's is prime.

The digit '0' and '4' appear 93 times each in the first 1000 digits of pi.

United Airlines Flight 93 was one of the airplanes hijacked on September 11, 2001.

April 4th (94th Day of the Non-Leap Year)

Apr 4th, 4/4.

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.

94th Day of the Year.

94^2+1 is prime.
94! - 1 is prime.
94^16+1 is prime.
94^4+94^3+94^2+94+1 is prime.
94^2-94-1 is prime.

The 94th decimal digit of pi begins a string of two 1's.

There are 94 ways to place 6 nonattacking queens on a 6 by 7 board.

The length of an NBA court is 94 feet.

April 5th (95th Day of the Non-Leap Year)

Apr 5th, 4/5.

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.

95th Day of the Year.

95/19 = 5/1 = 5 (cancelling out the 9's works here).

95^3+95+1 is prime.

95^6+95^5+95^4+95^3+95^2+95+1 is prime.

There are 95 primes less than 500.

95^2-95-1 is prime.

The most assists in a 7-game NBA playoff series is 95, set by Magic Johnson in 1984.

April 6th (96th Day of the Non-Leap Year)

Apr 6th, 4/6.

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.

96th Day of the Year.

5! - 4! = 96.

90*96+37 and 90*96+73 are both prime.

96^32+1 is prime.

96^2 starts with a 9 and ends with a 6.

96^16+97^16 is prime.

April 7th (97th Day of the Non-Leap Year)

Apr 7th, 4/7.

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.

97th Day of the Year.

97 is the last prime below 100.

97 and 79 are both prime.

There are 97 primes less than 2^9.

97 is conjectured to be the last prime of the form 3^n+2^n (if there exists a higher one, it is larger than 10^16000000.

97^2+98^2 is prime.

97^2-97-1 is prime.

97, 907, 9007, 90007, and 900007 are all primes.
9000007, 90000007, 900000007, 9000000007, and 90000000007 are all composite.

There are 97 primes with exactly 3 distinct digits.

April 8th (98th Day of the Non-Leap Year)

Apr 8th, 4/8.

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.

98th Day of the Year.

10^98+49 is prime.

98^3-98-1 is prime.

98.6 degrees Fahrenheit is normal body temperature.

98 is the highest jersey number offered in the NHL (since 99 is retired by Wayne Gretzky).

April 9th (99th Day of the Non-Leap Year)

Apr 9th, 4/9.

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.

99th Day of the Year.

99^2+99+1 is prime.
99^4+99^3+99^2+99+1 is prime.

If 99 divides a four digit number ABCD, then 99 also divides BCDA, CDAB, and DABC.

There are 99 primes less than 23^2.

99^19+99^17+99^15+99^13+99^11+99^9+99^7+99^5+99^3+99+1 is prime.

There are 99 four digit left-truncatable primes.

10^27-99 is the largest prime less than 10^27.

99 = 2^3+3^3+4^3

"99" is a common price ending in psychological pricing.

99 Bottles of Beer is a famous folk song in the United States.

April 10th (100th Day of the Non-Leap Year)

Apr 10th, 4/10.

410 = 401 + (4-1)^(10/(4+1))
410 = 104 + 4*(10*4) + 140 + (10-4)
410 = (4+10)+(41+0)+(0+14) + (4+1)*41+ 140 + (10-4)-(1-0-4)
410 = 104+140+41+14+ (4-1)*(41-4*1)
410 = (4+1+0)*(41*((10-4)/(4-1)))
410 = (10-4)*(41+14+10) + 10*(4/(4-1-1))
410 = (10+4)*(4*(10-4)) + 41 + (4-1)*(10+(10-4)/(4^0+1^0))

410^16+411^16 is prime.

410 = 59+61+67+71+73+79 (6 consecutive primes).

100th Day of the Year.

Sum of the first 3 primes is 10. Sum of the first 3^2 is 10^2.

100 is also a square in bases 5, 8, and 16 (400, 144 and 64, respectively).

100 = 1^3+2^3+3^3+4^3
100 = (1+2+3+4)^2

100 degrees Celsius is the boiling temperature for water.

The United States Senate has 100 Senators.

Wilt Chamberlain holds the record for the most points scored in an NBA game; 100 points with the Philadelphia Warriors in 1962.

The Hundred Years' War lasted for 116 years.

April 11th (101st Day of the Non-Leap Year)

Apr 11th, 4/11.

411 = 114 + (4+1+1)*41 + (41+(14-4*1*1))
411 = 141 + (4+1+1)*(41-14) + (14-(4-1-1))*(11-(4-1-1))
411 = (41+1)+(4+11)+(1+14)+(11+4)+(1+1+4)+141+114+((4-1)^(4-1-1))*(4+(4-1))
411 = (41*1)+(4*11)+(1*14)+(11*4)+(4*1*1)+141+114+(4-1)^(4-1-1)
411 = (4+1+1)*(4^(4-1)) + (4-1)^(4-1)
411 = (41+1)*(11-(4-1-1)) + (4-1)*11
411 = (4+11)*((4+1)^(1+1)) + 4*(11-(1+1))
411 = (11-4)*(41+14) + (14+(4*(4-1)))

411 is a divisor of 99999999.

411!-410!-1 is prime.

101st Day of the Year.

101 = 10^(1+0+1) + 1

101 = (10-1)*(10+1) + (1+0+1)

101 = (10+1)*(11) - 10*(1+0+1)

101 = 110 - (10-1)

101 = 10*(10) + 1

101, 101+2, 101+6, 101+8, and 101+12 are all prime. (What's the next number with the same property?)

101 is the second palindromic prime (excluding one digit primes).

101 - (1+0+1) = 99 is a palindrome.

101 + (1+0+1) = 103 is a prime.

(What other numbers have these properties?)

101, 101^2, 101^3, and 101^4 are all palindromes. (Is there another number with this property?)

101*11 = 101*(10+1) = 1111 (repdigit)

101 is the first prime and the first palindrome with a 0 in it. (What is another number with both these properties?)

3^101 - 2^101 is prime. (What is the next number following this pattern?)

101 is the first prime with only 0s and 1s. (What is the next prime?)

101^2 + 101 + 1 is prime.

101^2 - 101 - 1 is prime. (What's the next number satisfying both these properties?)

101 is 5 in base 2 (5 is prime and 2 is prime). (Do other numbers share this property?)

101 is the smallest 3-digit prime. (What is the smallest 4-digit prime? 5-digit? 6?)

101 = 79 + 22 (22nd prime plus 22).

10^101 + 3 is prime. (What's the next number with this property?)

101^1 has a digit sum of (1+0+1)^1.

101^2 has a digit sum of (1+0+1)^2.

101^3 has a digit sum of (1+0+1)^3.

101^4 has a digit sum of (1+0+1)^4.

(Do other numbers have this same property?)

There are 101 primes less than 550.

101 = 10^2 - 1^2 (Note: 10 and 1 make up 101). (Are there other numbers with this property?)

101 = 13 + 17 + 19 + 23 + 29 (5 consecutive primes).

101 is the only known prime to exist such that its digit alternate between 1 and 0.

101 is the largest known prime of the form 10^n + 1. (Why?)

Room 101 is the torture chamber in George Orwell's book 1984.

101 is the generic term used for an intro course in college (Math 101, Art 101, Psych 101, etc.)

April 12th (102nd Day of the Non-Leap Year)

Apr 12th, 4/12.

412 = 124 + (4*1*2)*(41-(4+1))

412 = 142 + (12/4)*((4+1)*(14+1*4))

412 = 214 + (4*2+1)*(2*(14-(4-1)))

412 = 241 + (4-1)*(41+4^(1*2))

412 = 421 - (4*2+1)

412 = (4+12) + (41+2) + (2+14) + (21+4) + (4+1+2) + 241 + 4^(1+2)

412 = (4*12) + (41*2) + (2*14) + (21*4) + 142 + (4+1+2)*(4*(2-1))

412 = (4+1+2)*(41+4^2) + (12-(1-2))

412 = (4*1*2)*(41+(4*2+1)) + 4*(1+2)

412 = (41+2)*(4*2+1) + (4+1)^2

412 = (41-2)*(12-1*2) + (24+(2-4))

412 = (4+12)*((4+1)^2) + 2*(14-4*1*2)

412 = (4*12)*(4*1*2) + (21+(4+1+2))

412 = (41*2)*(4-1+2) +(4*1-2)

412^64+1 is prime.

412 is the maximum determinant of 3x3 matrix only using numbers 1,2,3,4...9.

There are 412 ways to place 4 nonattacking knights on a 4 by 4 board.

If 412 = n, n0123456789 is prime (Meaning, 4120123456789 is prime).

412 =  13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 (12 consecutive primes).

412 is the area code for Pittsburgh, Pennsylvania, USA.

102nd Day of the Year.

102 = (10+2)*(10-2) + 2*(1+0+2)

102 = 10 + 2 + 12 + 20 + 1 + 21 + (10/2 + 1)^2

102 = (20+1)*(20-1) - 201 - (10+2)*(10-2)

102 = 12 + 34 + 56

102 - (1+0+2) = 1 + 2 + 3 + 4 + 5 + 6 + 78

102*201 = 20502 (a palindrome). (What are other numbers with the same property?)

102 is the smallest 3-digit number to have 3 prime divisors.

102^2 + 103^2 is prime.

Numbers 102,103,104,105, when squared, have a DigitSum that is also a square. (100 and 101 also share this property. Is there another run of 6 numbers that share this property?)

There are 102 primes less than 560.

The sum of the first 102 primes is prime. (Does this work for other numbers?)

102^64 + 1 is prime. (What are other numbers that share this property?)

102!!!!!! + 1 is prime (six factorials). (What's another number with this property?)

There are 102 primes between 14000 and 15000.

There are 102 primes between 42000 and 43000.

102 = 19 + 23 + 29 + 31 (four consecutive primes)

The Empire State Building in New York City has 102 floors.

April 13th (103rd Day of the Non-Leap Year)

Apr 13th, 4/13.

413 = 314 + 3*(34-1)
413 = 431 - (4^(3-1)+(4-3+1))
413 = 341 + 3*(14+(4+1)*(3-1))
413 = 143 + (4*1*3)^(4+1-3) + 134 - (4+1+3)
413 = (41+3) + (4+13) + (3+14) + (31+4) + (4+1+3) + 14^(3-1) + (4*1*3)*(4-1+3)
413 = (4*13) + (41*3) + (3*14) + (31*4) + 4*(14+1*4)
413 = (4+1+3)*(4*13) - 3*(4/3)+1
413 = (41+3)*(13-4) + (4+13)
413 = (41-3)*(14-3) - (14-(3^(4+1-3)))
413 = (4+13)*((4-1)*(4+3+1)) - (4^(3-1)-(14-3))
413 = (13-4)*((4+1)*3^(4-3+1)) + (4+1+3)

413^413 contains a permutation of '0123456789'.

103rd Day of the Year.

103 = 10 + 13 + 3 + 30 + 31 + 1 + (10+3) - (1-0-3)

103 = (10+3)*(10-3) + (10+3) - 1

103 = (10-3)*(10-3) - (1-0-3)*(10+3) + 30 + (1-0-3)

103*301 = 31003 (Only 1,0,3 are used). (Are there other numbers with the same property?)

103*13 and 103*31 both have the same digits (in different orders). (Does this hold for other numbers?)

Inserting a 1 anywhere in 103 retains the prime property. (i.e. 1103, 1013, 1031 are all prime.) (What is the another number that shares this property?)

There are 103 primes between 11000 and 12000.

The world's largest tree, the General Sherman Tree, has a trunk that is roughly 103 feet in circumference.

103 + (10!)^3 is prime. (Are there other numbers with this property?)

Using a standard dartboard, 103 is the lowest prime number that cannot be scored with two darts.

103 is a strictly non-palindromic number (that is, it isn't a palindrome in bases 2 through 101). (What is the next number with the same property?)

When "and" is included, 103 is the smallest number requiring 18 letters when spelled out in English.

Moving the 3 to the front, 310 = 103*3 + 1.

April 14th (104th Day of the Non-Leap Year)

Apr 14th, 4/14.

414 = 144 + 4*41 + 14*4 + (4/4+1)*(4+1)^(4/(4-1-1))
414 = 441 - (4-1)^(4-1)
414 = (4+14) + (41+4) + (4+1+4) + (4-1)*(144-(4+1)*(14-(4+4*1)))
414 = (4+14)*(4*(1+4)+(4-1))
414 = (41+4)*(4+1+4) + (4-1)^(4/4+1)

414 =2*3*3*23 (only uses 2 and 3, which are not in '414').

414^4+1 is prime.

414^10+414^9+414^8+414^7+414^6+414^5+414^4+414^3+414^2+414+1 is prime.

414^8+415^8 is prime.

If 414 = n, then 2n3n5n7n11n13 is prime (Meaning, 24143414541474141141413 is prime).

104th Day of the Year.

104 = 10 + 14 + 40 + 41 + (1+0+4) - (10-4)

104 = (10-4)*(10+4) + (10-4) + 14

104 - (1+0+4) = 9 + 8 + 7 + 6 + 5 + 43 + 21

104^3 and 104^4 do not contain zeroes. (Do other numbers N have this property given that N has at least one zero?)

104*401 has 1,0,4 (in order) in its decimal representation. (Are there others with the same property?)

104*(10+4) = 1456 (1 < 4 < 5 < 6) (Does the property hold for other numbers?)

104^2 + 105^2 is prime. (What are other numbers like this?)

There are 104 primes less than 570.

90*104 + 73 and 90*104 + 37 are both prime. (What other numbers have both these properties?)

104^23 + 104^21 + 104^19 + 104^17 + 104^15 + 104^13 + 104^11 + 104^9 + 104^7 + 104^5 + 104^3 + 104 + 1 is prime. (What's the next number with this property?)

There are 104 primes in [17000,18000], [19000,20000] and [21000,22000]. (Do other numbers share this property?)

The 104th and 105th primes are twin primes. (Are there other numbers like this?)

104 has 8 divisors (8 being one of them). (What's the next number with the same property?)

104 is a palindrome in base 5 (404), base 6 (252), and base 12 (88). (Are there other numbers that have this property?)

April 15th (105th Day of the Non-Leap Year)

Apr 15th, 4/15.

415 = 451 - (5+1)^(5-4+1)
415 = 514 - (4-1)*(41-(5+4-1))
415 = 541 - (5+1)*(15+(1+5))
415 = 145 + (5+4-1)*(15-(5+4-1)) + 154 + 15*4
415 = (4+15) + (41+5) + (5+14) + (51+4) + 154 + 145 + (4*1*5+(4-1))
415 = 4*15 + 41*5 + 5*14 + 51*4 - (15-4)^(5-4+1) - (15/(4+1))
415 = (4+1+5)*41 + (5*(5-4/1))
415 = (4*1*5)*(4*5+1) - (4+1)
415 = (4+15)*(14+(5+4-1)) - (15/(1+4))
415 = (41+5)*(4*1+5) + (5-1)/4
415 = (41-5)*(15+(4*(5-4+1)))/(5+1-4) + (4+1)/5

1 + 415*514 + 1 is a palindrome.

3^415, 3^416, and 3^417 have the same number of digits.

105th Day of the Year.

105 = 15 + 51 + (50-1) - 10

105 = (10+5)*(10-5) + (10+5)*(10/5)

105 = (1+0+5)*(10+5) + 15

105 = 3*5*7 (first three odd primes).

1 + 105 + 105^2 is prime.

10^105 + 3 is prime.

There are 105 primes less than 24^2.

There are 105 primes in [13000,14000].

105 is palindrome in base 4 (1221), base 8 (151), and base 20 (55).

105 = 7!! (7*5*3*1)

105 is in the middle of a prime quadruplet (101, 103, 107, 109).

"105" is a card game where the player loses if he or she has over 105 points.

The positive values of 105 - 2^k are all prime (for all k that make this positive).

105/pi^4 = (1+1/2^4)*(1+1/3^4)*(1+1/5^4)*(1+1/7^4)*(1+1/11^4)*...

April 16th (106th Day of the Non-Leap Year)

Apr 16th, 4/16.

416 = 614 - 6*41 + 4*(16-4)
416 = 641 - 164 - 61
416 = 461 - (4+1)*(6-1+4)
416 = 164 + 4*61 + 16/(6*1-4)
416 = 146 + 6*41 + 4*1*6
416 = (4+16) + (41+6) + (6+14) + (61+4) + 41*6 + (6+4-1)*(6-4*1)
416 = 4*16 + 41*6 + 146 - (4+16)*(14/(6+1))
416 = 6*14 + 61*4 + 164 + 4*(4+1+6)
416 = (4+1+6)*(41-6) + (46-(4-1)*(6-1))
416 = (4+16)*((4-1)*(6+1)) - 4*(6-4-1)
416 = (41+6)*(4-1+6) - 14/(6-4*1)
416 = (41-6)*(4*1*6/(6*1-4)) - 4*(6-(4+1))

416^16 + 417^16 is prime.

106th Day of the Year.

106 = 10 + 60 + 61 + 16 - (10+6)*(10-6) + (1+0+6) + (10+6)

106 = (10+6)*(10-6) + (1+0+6)*(10-6) + (10-6) + 10

106 = (10+6)*(1+0+6) - 6

106 - 61 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

106*106 = 11236 (1 ≤ 1 ≤ 2 ≤ 3 ≤ 6). (Are there other numbers with this property?)

106 = 83 + 23 (23rd prime plus 23).

106^4 + 1 is prime. (What's another number with this property?)

There are 106 primes less than 560.

3^106 - 10 is prime. (What's the next number with this property?)

106!!!!! + 1 is prime.

106!!!!!! + 1 is prime. (What other numbers have one or both of these properties?)

There are 106 primes in [10000,11000] and [32000,33000].

17^106 - 2 is prime.

21^106 - 2 is prime.

No other number has both these properties.

The number 9 appears 106 times in the first 1000 digits of pi.

106th prime plus 106 is a prime. (577+106 = 683)

April 17th (107th Day of the Non-Leap Year)

Apr 17th, 4/17.

417 = 471 - (7-4)^(7-4-1)*(7-1)
417 = 147 + 41*7 + (14+(7-4*1))
417 = 174 + 71*4 + 4*1*7 - (4-17)
417 = 741 - 7*41 - (41-4*1)
417 = 714 - 4*71 - (17-4)
417 = (4+17) + (41+7) + (7+14) + (71+4) + 174 + (74+(7-4+1))
417 = 4*17 + 41*7 + (71-(7-4)*(4-1))
417 = 7*14 + 71*4 + (4+1)*7
417 = (4+1+7)*(7*(4+1)) - (7-4*1)
417 = (41+7)*((4-1)^(14/7)) - (17-(14/7))
417 = (4+17)*(4*(7-(14/7))) - (7-4*1)
417 = (41-7)*(4+1+7) + (7-4)*(4-1)

417's aliquot sequence terminates in a perfect number.

417^4//417^3//417^2//417^1//417^0 is prime, where // represents the concatenation function.

417^3//417^2//417^1//417^0 is prime, where // represents the concatenation function.

There are 417 primes between 29^π and 30^π.

107th Day of the Year.

107 = 71 + (1-0-7)*(1-0-7)

107 = 17*(1+0+7) + (1+0+7)*(1-0-7) + (10-7)*(10-7) + 10

107 = (10+7)*(10-7) + 70 - (10+7) + (10-7)

107 = 10 + 17 + 70 + 71 - 17*(10-7) - 10

107 = 2 + 3*5*7 = 2*3*5 + 7*11

107^2 has digits that are all squares. (What are other numbers with this property?)

701*107 = 75007 (Note: 701 starts with a 7 and 107 ends with a 7). (What other numbers display this property?)

107*(10+7) = 107*17 = 1819 (concatenation of two consecutive numbers. Also note that 18 and 19 come right after 17). (Are there other numbers like this?)

107^3 only uses digits 0,1,2,3,4,5. (Do other numbers have this property?)

107 and 701 are both primes. (What's the next number like this?)

There are no primes between 1070 and 1079.

10^107 + 3 is prime. (What are other numbers with this property?)

There are 107 primes less than 580.

The 107% rule in Formula One racing decides which cars are qualified.

The polynomial n^2 - n + 67374467 is never divisible by any prime less than 107 (for integers n).

2^107 reversed and 2^107 - 1 are primes.

2^107 - 1 is the largest known Mersenne prime not containing all the individual digits.

There is no integer N such that N! has 107 zeroes.

107 = 1! in base 2 + 0! in base 2 + 7! in base 2. (This is the largest prime with such property. What's the next number less than 107 like this?)

107 ("One hundred and seven") is the smallest English number needing six syllables.

107 remains prime if 2 is added to any of its digits (307, 127, 109). (Do other numbers also share this property? Instead of a 2, what about 1? 3? 4? ...)

107 + 2!, 107 + 3!, ... 107 + 9! are all prime. (Note: There are (1+0+7) = 8 numbers here.) (Are there others with this property?)

Hyperpyrexia is a severe elevation of the body temperature (usually to 107 degrees Fahrenheit).

April 18th (108th Day of the Non-Leap Year)

Apr 18th, 4/18.

418 = 481 - (8+1)*(4-1)
418 = 814 - 81*4 - (81-(8+1))
418 = 841 - 8*41 - (4+1)*(18+(8/4-1))
418 = 184 + 18*(4+1+8)
418 = 148 + (8/4+1)^(8-4-1)*((4+1)*(8/4))
418 = 4*18 + 41*8 + (4-1)*(14-(8+4-1))
418 = 8*14 + 81*4 - (8+1)*(8/4)
418 = (4+18) + (41+8) + (8+14) + (81+4) + (8+4*1)*(14+(18/(8-4-1)))
418 = (4+18)*(4*(8/4+1)+(14/(8*1/4)))
418 = (41+8)*((8/4)^(8-4-1)) + (14+(8*1+4))
418 = (41-8)*(4+8) + (4+18)
418 = (4+1+8)*(4*8+1) - (8+4-1)

418 = 2*11*19.
2+11+19 = 32 = 4*1*8.

418^16 + 419^16 is prime.

108th Day of the Year.

108 = 10 + 18 + 80

108 = 81 + (10-8)*(1+0+8) + (1*8) + 1

108 = 10*8 + (10+8)(10-8) - 8

108 = (10+8)*(1+0+8) - (80-1) + (10+8) - (1-0-8)

108^2 = 11664 (concatenation of three squares--1//16//64). (Are there other numbers with the same property?)

108*810 ends in 810. (Do other numbers have this property?)

108 = 2*2*3*3*3 (two 2s and three 3s).

10^108 + 19 is prime. (What's the next number with the same property?)

The sum of the first 108 primes is prime. (For what other n does this property satisfy?)

There are 108 primes in [15000,16000].

108 = (1^1)*(2^2)*(3^3)

There are 108 nonzero palindromes less than 1000.

The number 108 is very sacred in many religions. The digits 1,0,8 mean one thing, nothing, and everything (infinity).

The prehistoric monument Stonehenge is around 108 feet in diameter.

In martial arts, there are 108 pressure points in the human body.

An official MLB baseball has 108 stitches.

There are 108 cards in a deck of UNO cards.

The volume expansion of freezing water is roughly 108%.

108 degrees Fahrenheit is when the human body's organs began to fail from overheating.

In the TV show "Lost", the main characters must enter the numbers 4 8 15 16 23 42 into a mysterious computer every 108 minutes. (Note: 4+8+15+16+23+42 = 108).

April 19th (109th Day of the Non-Leap Year)

Apr 19th, 4/19.

419 = 941 - 9*41 - 149 - (9-4-1)
419 = 914 - 91*4 - 4*19 - (4+1)*((9-1)/4+9)
419 = 491 - 4*(14+(9-4-1))
419 = 194 + 19*4 + 149
419 = 149 + 14*9 + (4*(9/(4-1)))^((1+9)/(1+4))
419 = 4*19 + 41*9 - (19-(9-4+1))*(9/(4-1)-1)
419 = 9*14 + 91*4 - (91-4*(9-4*1))
419 = (4+1+9)*(14+(9-4-1)^(9/(4-1)-1)) - (19-(4-1)*(9-4+1))
419 = (41+9)*((9-1)/4)^(9/(4-1)) + (14+(9-4*1))
419 = (41-9)*(9+1*4) + 9/(4-1)
419 = (4+19)*(9*(9-1)/4) + (9-4*1)

There are 419 primes less than 2900.

419^16 + 420^16 is prime.

419 is prime.
419^2-419-1 is prime.

When 419 is divided by 2, 3, 4, 5, 6, and 7, there is a remainder of 1, 2, 3, 4, 5, and 6, respectively.

109th Day of the Year.

109 = 91 + 19 + (10-9)

109 = 10 + 9*((10-9)+10)

109 = 10 + 19 - (1-0-9)*(1+0+9)

109 = 1+2+3+4+5+6+7+8+9 + (9-1)^(10-9+10-9)

109*91 = 9919 (only using 9 and 1, excl--0) (Do other numbers have this property?)

109 is the first number such that |first digit - second digit + third digit - fourth digit + ... | = 10. (What's the next number with this property?)

109^2 + 110^2 is prime. (What's another number with this property?)

There are 109 primes less than 600. (109 being one of them)

90*109 + 19 is prime. (Note: Only 1,0,9 are used in this expression.) (Are there other numbers with a similar property?)

109 is a prime formed by the concatenation of two consecutive numbers, 10 and 9. (What's the next prime like this?)

109 is the smallest number that is palindromic in base 5 (414) and base 9 (131).

Below 109 degrees Fahrenheit, carbon dioxide becomes a solid (dry ice).

109^2 = 11881 and 118-8-1 = 109.

109 = 1*2 + 3*4 + 5*6 + 7*8 + 9

The Sun's diameter is a bit over 109 times the diameter of the Earth.

109 = prime(prime(1+0+9)) where prime(n) denotes the nth prime number.

109 is the smallest number that has more distinct digits than its square. (What's the next number with the same property?)

April 20th (110th Day of the Non-Leap Year)

Apr 20th, 4/20.

420 = 402 + (40/2-(4-2-0))
420 = 240 + 2*(20/4+40)*(4-2-0)
420 = 204 + 20*4 + 24*(4+2+0) - 2*4
420 = 24*40 - 240 - 2*40 - 204 - 4^2
420 = (42+20) + (24+40) + 240 + (4+2+0)*(4-2^0)^(4/2)
420 = (4+2+0)*(42+(20+4*2))
420 = (4+20)*(20-4) + (4+2+0)^(4-2-0)

420 is the smallest number divisible by 1,2,3,4,5,6,7. 420 is also divisible by 1+2+3+4+5+6+7.

If 420=n, then 30*n/(30+n) is an integer. This is the second highest number with this property.

420^5 + 420^3 + 420 + 1 is prime.

420^3 - 420^2 - 420 - 1 is prime.

420 is 120120b3 (bX means "base X")

420 = 101 + 103 + 107 + 109 (4 cons primes).

110th Day of the Year.

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.

April 21st (111th Day of the Non-Leap Year)

Apr 21st, 4/21.

421 = 412 + (4*2+1)
421 = 214 + 21*4 + 124 - (4-2-1)
421 = 241 + 2*41 + (4+2+1)*14
421 = 124 + 12*4 + 142 + 1*42 + (4+1)*(12+(4/2)-1)
421 = (4+21) + (42+1) + (1+24) + (12+4) + 241 + (4+2*1)*(4^2^1)
421 = 4*21 + 42*1 + 1*24 + 12*4 + 2*14 + 2*41 + (124-(14-(4-1)))
421 = (4+21)*(21-4) - 4*(2-1)
421 = (42+1)*(2*(4+1)) - (4*2+1)
421 = (42-1)*(12-(4/2)) + (14-(4-1))

421 is prime and 4+2+1 = 7 is prime.

There are 421 primes less than 54^2.

421 is prime and 421^2-421-1 is prime.

421 is the largest prime of the form (1+2+3+...+k)/210 for some k.

421 is a prime of the form n^2+n+1.

421 = 73+79+83+89+97 (five cons primes).

The Collatz conjecture says all integers (that undergo a piecewise function) will end with the sequence 4-2-1-4-2-1-4-2-1...

If A = 1st prime number, B = 2nd prime number, ... Z = 26th prime number, then "PRIME NUMBER" = 421, also a prime.

111th Day of the Year.

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.

April 22nd (112th Day of the Non-Leap Year)

Apr 22nd, 4/22.

422 = 242 + 2*42 + (4+2)*(4*2*2)
422 = 224 + 22*4 + 22*(4+2/2)
422 =  (4+22) + (42+2) + (2+24) + 242 + 42*2
422 = 4*22 + 42*2 + 2*24 + 242 - 4*(4*2+2)
422 = (4+22)*(4*2*2) + 24/(4*(2/2))
422 = (42+2)*(4*2+2) - (4+2)*(4-2/2)
422 = (42-2)*(4^2-(4+2/2)) - (22-(4*2-2))
422 = (4+2+2)*(42+22/(4-2)) - 24/((4+2)*2)

422^3 + 113 is a square (largest number with this property).

422^9 + 422^7 + 422^5 + 422^3 + 422 + 1 is prime.

112th Day of the Year.

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).

April 23rd (113th Day of the Non-Leap Year)

Apr 23rd, 4/23.

423 = 432 - (4+3+2)
423 = 342 + (4+2+3)^(3*2-4)
423 = 324 + (4*2+3)*(3^(4-2))
423 = 243 + 2*43 + 2*((4+3)^2-(4+2)/3)
423 = 234 + 23*4 + (42+(4*2-3)*(4*2+3))
423 = 4*23 + 42*3 + 234 - (23+2*3)
423 = 3*24 + 32*4 + 243 - 4*(2+3)
423 = (4+23) + (42+3) + (3+24) + (32+4) + 243 + (2+3)*(2+3+4)
423 = (4+2+3)*((4+3)^2+(4-2*3))
423 = (42+3)*(4+2+3) + (4+2)*3
423 = (4+23)*(42/3) + (42+3)
423 = (42-3)*(4*2+3) - ((4/2)-(4-2^3))

423^32 + 424^32 is prime.

423^3 does not contain a 4, 2, or 3.

113th Day of the Year.

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.

April 24th (114th Day of the Non-Leap Year)

Apr 24th, 4/24.

424 = 442 - (4*4+2)
424 = 244 + (4+2)*(24+(2+4))
424 = 4*24 + 42*4 + 2*44 + (24-(2+4))*(24/(2+4))
424 = (4+24) + (42+4) + (2+44) + 244 + 4*(4*2+(42/(4+2)))
424 = (4+2+4)*(4+2)*(4+(2+4/4)) + 2*(4-2)
424 = (42+4)*((4-2/(4-2))^(4-2)) + (4+2+4)
424 = (42-4)*(4*2+(2+4/4)) + 24/(2+4)
424 = (4*2*4)*(4^2-(24/(2*4))) + (4-2)*4

424*(4*2*4) = 13568 (strictly increasing number) and 424+(4*2*4) = 456.

26*424+1 and 27*424+1 are squares.

424 = 23+29+31+37+41+43+47+53+59+61(10 cons primes)

114th Day of the Year.

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?)

April 25th (115th Day of the Non-Leap Year)

Apr 25th, 4/25.

425 = 452 - (5-2)^(4*2-5)
425 = 254 + 25*4 + (42+(4+25))
425 = 245 + 24*5 + 4*(45/(5-2))
425 = 542 - 54*2 - (4^2-(2+5))
425 = 524 - (4+5)*(4+2+5)
425 = 4*25 + 42*5 + (4+2)*(24-5) + (4+2-5)
425 = 5*24 + 52*4 + (42+5*(4+2+5))
425 = (4+25) + (42+5) + (5+24) + (52+4) + 254 + 5*(4-2)
425 = (4+2+5)*(42-(5-2)) - 4*(4+2-5)
425 = (42+5)*((5-2)^(4-2)) + 2*(5-4)
425 = (42-5)*(4+2+5) - (5-2)*(4-2*5)
425 = (4+25)*(25-(2*5)) - (4^2-(4+2))

425^n does not contain a 4 until n = 6.

425 = 9^3-8^3+7^3-6^3+5^3-4^3+3^3-2^3+1^3

There are more primes between 425 and 2*425 than 425 and 425^2.

425^2//425^2//425^0 is prime, where // is the concatenation function.

115th Day of the Year.

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.

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.)

April 26th (116th Day of the Non-Leap Year)

Apr 26th, 4/26.

426 = 624 - (4^2-6)*(26-(2+4)) + (4*2-6)
426 = 642 - (4+2)^(6/2)
426 = 462 - 6^(4-2)
426 = 264 + 26*4 + (26+6/2)*(6-4)
426 = 246 + 24*6 + (24+2*6)
426 = 4*26 + 42*6 + (4+6)*(4+6/2)
426 = 6*24 + 62*4 + 2*(4^2+(6/(4+2)))
426 = (4+26) + (42+6) + (6+24) + (62+4) + 246 + 42/(4+6/2)
426 = (4+2+6)*(6^(4-2)) - 24/(6-2)
426 = (42+6)*((6/2)^(4-2)) - (26-4*(2+(2*6/4))
426 = (42-6)*(4*(6/2)) - 42/(4+2) + (4+2)/6

10^426+3 is prime (Meaning, 1000...0003 is prime, with 425 zeros).

The sum of the first 426 primes is prime.
The sum of the squares of the first 426 primes is prime.

426^8+1 is prime.

426^8 + 427^8 is prime.

426^1+426+1, 426^2+426+1, 426^3+426+1, and 426^4+426+1 are all prime.

The sum of the positive divisors of 426 is 864 (still uses all even digits).

116th Day of the Year.

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).

April 27th (117th Day of the Non-Leap Year)

Apr 27th, 4/27.

427 = 742 - (4^2-7)*(27+2^(7-4))
427 = 724 - (7+2)*(24+(7-4)^2)
427 = 472 - (47-2)
427 = 247 + 24*7 + (7-4)*(24/(2+4))
427 = 274 + 27*4 + (7^2-4)
427 = 4*27 + 42*7 + (7-2)^(4-2)
427 = 7*24 + 72*4 + (24+(7-2))
427 = (4+27) + (42+7) + (72+4) + (7+24) + 247 - 7*(7-2-4)
427 = (4+2+7)*(24+(7-4)^2) - (27-(2+7))/(4^2-7)
427 = (42+7)*(2+7) - (42/(7-4))
427 = (42-7)*(4*7-4^2) + 42/(4+2)
427 = (4+27)*(42/(7-4)) - 7*(4*2-7)
427 = (4*2*7)*((7-4)*(7-2)/2) + (27-(7-2)*4)

427!+1 is prime.

427^16 + 428^16 is prime.

There are 427 primes of the form x^16+1 for x < 10^67.

117th Day of the Year.

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.

April 28th (118th Day of the Non-Leap Year)

Apr 28th, 4/28.

428 = 482 - 2*(24+(4-8/(2*4)))
428 = 824 - 82*4 - (28+4*(2+8))
428 = 842 - 8*42 - 2*(24+(4^2-(8/(4*2))))
428 = 248 + 24*8 - 2*(8-4+2)
428 = 284 + 28*4 + (42-(2+8))
428 = 4*28 + 42*8 - (28-4*2)
428 = 8*24 + 82*4 - 2*(48-2)
428 = (4+28) + (42+8) + (8+24) + (82+4) + 2*(84+(8-2)*(4+8/(4*2)))
428 = (4+2+8)*(28+(8/4)) + (4^2-8)
428 = (4+28)*(4+(4-(4+2)/(8-2))^(8/4)) + 2*(8/4+(8-4))
428 = (42+8)*(48/(8-2)) + (24+(8-4))
428 = (42-8)*(4+8) + (4^2+(8/2))

428^2 = 183184 (concatenation of two consecutive numbers).

428^32+1 is prime.

428 concatenated with 428 1's is prime.

428^47 + 428^45 + 428^43 + ... + 428^5 + 428^3 + 428 + 1 is prime.

118th Day of the Year.

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?)

April 29th (119th Day of the Non-Leap Year)

Apr 29th, 4/29.

429 = 924 - 9*(42+(9+4))
429 = 942 - (24+(9-4-2))*(24-(9-4))
429 = 492 - (9-2)*(9-4-2)^(4-2)
429 = 249 + (9*2)*(2*(9-4))
429 = 294 + (9-4)*(42-(9-4-2)*(9-4))
429 = 4*29 + 42*9 - (9-4)*(9+4)
429 = 9*24 + 92*4 + (9-4)*(24+(9-2))
429 = (4+29) + (42+9) + (9+24) + (92+4) + (4^2-(2*(9-4)))^(9-4-2)
429 = (4+2+9)*(29+(4*2-9)) + (4^2-(9-2))
429 = (4+29)*(9+4)
429 = (42+9)*(4^2-4*2) + (9-4-2)*(9-2)

429 = 3*11*13 (only uses two digits--neither are 4, 2, or 9).

429*(3+11+13) = 11583 and 429*(3+(1+1)+(1+3)) = 3861 (does not contain 4, 2, 9 in either).

429^n does not contain a 2 until n=6 for n > 1.

429*924 = 396396 (396 concatenated with itself).

429+(4+2+9) (444) and 429-(4+2+9) (414) are both palindromes.

429*(4+2+9) uses 3,4,5,6 (unordered).

429 different resistance values can be made by rearranging 8 1-ohm resistors in series and parallel.

429^2+2 and 429^2-2 are both prime.

There are 429 primes less than e^8.

429 is a divisor of 111111.

119th Day of the Year.

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).

April 30th (120th Day of the Non-Leap Year)

Apr 30th, 4/30.

430 = 403 + 3^(4-3^0)
430 = 340 + 3*(4+3^0)*(3*(3-4^0))
430 = 304 + 3*(43-43^0)
430 = 4*30 + 43*(4+3+0) + 3^(3-4^0)
430 = (4+30) + (3+40) + 340 + (4+3^(3-4^0))
430 = (4+30)*(4*3+0) + (4*3-43^0)*(3-4^0)
430 = (30-4)*(4^(3-4^0)) + (4+3)*(4/(3-4^0))
430 = (40-3)*(4*3) - (30-4^(3-4^0))

430^32+1 is prime.

There are 430 primes less than 3000.

1^2 +- 2^2 +- 3^2 +- ... +- 20^2 = 0 has 430 different solutions.

430^1+1, 430^2+1, and 430^4+1 are prime.

There are 430 composite less than 23^2 (inclusively).

430^5 + 430^3 + 430 + 1 is prime.

120th Day of the Year.

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.

May 1st (121st Day of the Non-Leap Year)

May 1st, 5/1.

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.

121st Day of the Year.

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?)

May 2nd (122nd Day of the Non-Leap Year)

May 2nd, 5/2.

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.

122nd Day of the Year.

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.

May 3rd (123rd Day of the Non-Leap Year)

May 3rd, 5/3.

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 out 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).

123rd Day of the Year.

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 4 consecutive numbers satisfying this property?)

May 4th (124th Day of the Non-Leap Year)

May 4th, 5/4.

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.

124th Day of the Year.

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.

May 5th (125th Day of the Non-Leap Year)

May 5th, 5/5.

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.

125th Day of the Year.

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.

May 6th (126th Day of the Non-Leap Year)

May 6th, 5/6.

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.

126th Day of the Year.

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).

May 7th (127th Day of the Non-Leap Year)

May 7th, 5/7.

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.

127th Day of the Year.

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.

May 8th (128th Day of the Non-Leap Year)

May 8th, 5/8.

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."

128th Day of the Year.

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.

May 9th (129th Day of the Non-Leap Year)

May 9th, 5/9.

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

129th Day of the Year.

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.

May 10th (130th Day of the Non-Leap Year)

May 10th, 5/10.

510 = 501 + (10/5)^(5-1-51^0) + 5^(1*0)

510 = 150 + (5+10)*((10/5)*(10+10/5))

510 = 105 + 10*5 + 5*(51+10*(5^0+1^0))

510 = 15*51 - 5*10 - 5*(51-10)

510 = (5+10) + (51+0) + (1+50) + 150 + (5-10/5)^(5*1^0)

510 = (5+10)*(10+(5-10/5)*(10/5)^(10-5-10/5)

510^8 + 511^8 is prime.

510^8 + 1 is prime.

510^5 + 510^3 + 510 + 1 is prime.

510^9 + 510^7 + 510^5 + 510^3 + 510 + 1 is prime.

There are 510 primes between 16^2 and 16^3.

510 = 47+53+59+61+67+71+73+79 (8 cons primes)

510 = 31+37+41+43+47+53+59+61+67+71 (10 cons primes)

510 = 19+23+29+31+37+41+43+47+53+59+61+67 (12 cons primes)

130th Day of the Year.

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).

May 11th (131st Day of the Non-Leap Year)

May 11, 5/11.

511 = 151 + (5*1+1)*(51+(5-1-1)^((11-5)/(5-1-1)))

511 = 115 + (11-(1+1))*(51-(5+1+1))

511 = 15*51 - 5*11 - 51*1 - (151-(5-1-1))

511 = 5^(5-1) - (1+1)*(51+(5+1))

511 = 11^(5-1-1) - (5+1)! - 5*(15+5*1*1)

511 = (5+11)*(1+1)^5 - 1

511 = (11-5)*(51+(1+1)*(51/(5-1-1)))

511 = (51+1)*(5*(1+1)) - (5-1-1)^(1+1)

511^n does not have a 5 until n = 5 (n > 1).

511*115 does not contain any 1's whereas 511*511 contains 3 1's.

If 511 = n, then 2n3n5n7n11 is prime (Meaning 251135115511751111 is prime).

5^511 reversed is prime.

5-1-1 is a transportation and traffic information telephone hotline in some regions of the USA and Canada.

131st Day of the Year.

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.

May 12th (132nd Day of the Non-Leap Year)

May 12th, 5/12.

512 = 2^(5*2-1)

512 = 5^(5-(2-1)) - 125 + (5-2)*(5-1)

512 = 521 - (5*2-1)

512 = 125 + 12*25 + (51+(5+1)^2)

512 = 251 + 5*(25+1)*2+(12-(5*2+1))

512 = 215 + 21*15 - (5-2)*(5+1)

512 = 15*52 - 152 - 2*(51+(5+2))

512 = 51*12 - (5*1+2)^(5-1-2)

512 = 51*2 + 5*12 + (5*1*2)*(51-(5-1)^2)

512 = 2*15 + 21*5 + (5+1+2)*(51-(5-1)) + (1+2)/(5-1-2)

512 = (5+1+2)*(2^(5+1))

512 = (5*1*2)*(5+12)*(1+2) + (5-1-2)

512 = (5+12)*(12+5-(1-2)) + 52/(25+1)

512 = (51+2)*(5*2-1) + 5*(12-5)

512 = (51-2)*(5*1*2) + (5*2+1)*(5-1-2)

512 (2^9) and 5+1+2=8 (2^3) are both powers of 2.

5 and 12 are two sides of a 5-12-13 side right triangle.

3^512 - 512^3 is prime.

512 = 2^9 = 8^3 (Note that 2+9 = 8+3).

512 = (5+1+2)^(5-1-2)

132nd Day of the Year.

132 = 123 + (1+2^3)

132 = 213 - (13-(1+3))^2

132 = 231 - (13-2)*(3^2)

132 = (13-2)*(2*3!)

132 = 13*2 + 1*32 + 2*(32+(3+2))

132= 2*31 + 23*1 + (32+(13+2))

132 = 13*32 - 231 - (32+21)

132 = 12*23 - 213 - (3*(1+2))*(1+3*2)

132 = (1+32) + (13+2) + (2+31) + (23+1) + 3^(1+2)

132 = (1+3+2)*(23-1)

132 = (1*3+2)*(13*2) + (1+3-2)

132 = (1+3*2)*(21-2*1) - 1*(3-2)

132 = (13+2)*(3^2) - 3*(2-1)

132 = (1+32)*(3^2-(3+2))

132^3 contains 3 of the same digit in a row.

132 = 2*2*3*11 (only uses 1,3,2 in prime factorization).

132^4+1 is prime.

132^8+1 is prime.

132^32+1 is prime.

132^2-132-1 is prime.

The sum of the first 132 primes is prime.

2*132+13 is prime (Note the use of 1,2,3 in here: 2n+13 is prime with n = 132).

2*132-13 is prime (Note the use of 1,2,3 in here: 2n-13 is prime with n = 132).

132 is the highest number n such that 12n/(12+n) is an integer.

132^2+133^2+134^2 is prime.

12 + 13 + 21 + 23 + 31 + 32 = 132.

May 13th (133rd Day of the Non-Leap Year)

May 13th, 5/13.

513 = 135 + ((5+1)*3-(5-1-3))^(5-1*3)*(5*1-3)

513 = 153 - 5*(1-3)*(5+1)^(5-3)

513 = 351 + (5-3)*(3^(5-1))

513 = 315 + (5+1+3)*(13-(3-1))*(5*1-3)

513 = 531 - (5+1)*3

513 = (3-1)^(5+1+3) - (5-1-3)

513 = 5*13 + 51*3 + 5*(51+(5*1+3))

513 = 3*15 + 31*5 + (13-5)*(51-(5-1)*3) + (5-1-3)

513 = (5+13) + (51+3) + (3+15) + (31+5) + (5+1+3)*(53+5*(1-3))

513 = (5+1+3)*(51+(5+1))

513 = (5*1+3)*(51+13) + (13-(5-1)*3)

513 = (5+13)*(13+15) + (5+1+3)

513 = (51+3)*(5+1+3) + 3^(5+1-3)

513 = (51-3)*(13-1*3) + 3*(15-(5-1))

513*315 is a concatenation of two palindromes (161595).

513 = 2^n+1 (n=9) and 513 divides 2^513+1.

513^19 + 513^17 + 513^15 + 513^13 + 513^11 + 513^9 + 513^7 + 513^5 + 513^3 + 513 + 1 is prime.

If 513 = n, 2n3n5n7n11n13 is prime (Meaning, 25133513551375131151313 is prime).

133rd Day of the Year.

133 = 313 - (1*3*3)*(13+(1+3+3))

133 = 331 - 33*(1*3+3)

133 = (13-3)^(1+3/3) + 1*33

133 = (13-3/3)^(3-1) - (13-(3-1))

133 = 13*3 + 3*31 + 3/(3*1)

133 = 1*33 + 1*3*3 + (3^(3-1))^(1+3/3) + (1+3*3)

133 = (1+33) + (13+3) + (3+31) + (1+3+3)^(3-1)

133 = (1+3+3)*((1+3*3)+(1*3*3))

133 = (13+3)*((3-1)^3) + (3+3-1)

133 = (13-3)*((1+3)*3+1) + 3!/(3-1)

133 = (1+33)*(1+3) - 33/(13-(3-1))

133 = 7*19. 133*(7+19) = 3458 (3 < 4 < 5 < 8).

There are 133 squares less than 26^3.

If 133 = n, then 987654321n is prime (That is, 987654321133 is prime).

May 14th (134th Day of the Non-Leap Year)

May 14th, 5/14.

514 = 541 - (4-1)*(5*1+4)

514 = 451 + (5+1*4)*(14/(5-4+1))

514 = 415 + (15-4)*(14-5)

514 = 154 + (5*1*4)*(14+1*4)

514 = 145 + 14*5 + (4-1)*(5+1+4)^(5+1-4) - (5/(1+4))

514 = 5*14 + 51*4 + 4*15 + 41*5 - 5^(5-4+1)

514 = (5-4+1)^(5+4*1) + 54/((4-1)^(4-1))

514 = (51+4) + (5+14) + (4+15) + (41+5) + (5*14+5)*(1+4)

514 = (5+1+4)*51 + 14-(5+1+4)

514 = (5*1*4)*(15+(1+5+4)) + 15-(5/(4+1))

514 = (5+14)*(15+4*(15/(1+4))) + (45-(15-4)*(5-1))

514 = (51+4)*(5*1+4) + (5+14)

514 = (51-4)*(15-4) - (15/(1+4))

There are 514 pairs of primes differing by 18 less than 10^5.

If 514 = n, then n2357111317 is prime (Note 2357111317 is the concatenation of the first 7 primes).

514^7 + 514^5 + 514^3 + 514 + 1 is prime.

134th Day of the Year.

134 = 143 - ((4-1)^(3-1))

134 = 314 - (1*3*4)*(3*(1+4))

134 = 341 - 3*(4-1)*(31-4*(3-1))

134 = 413 - 31*(13-4)

134 = 431 - (14-3)*(3^(4-1))

134 = (14-3)^(3-1) + 13

134 = 13*4 + 1*34 + (1+3+4)*(4+3-1)

134 = 4*31 + 43*1 - 3*(14-3)

134 = (1+34) + (13+4) + (4+31) + (43+1) + (34-31)

134 = (1+3+4)*(13+4) - 14/(1*3+4)

134 = (1*3+4)*(31-1*3*4) - 1*(3-4)

134 = (1*3*4)*(14-3) + 34/(13+4)

134 = (1+34)*(13-3*(4-1)) - (14-4*(3-1))

134 = (13+4)*(1*3+4) + 3*(4+1)

134 = (13-4)*(3*(1+4)) + 1*(3-4)

134^2+1 is prime.

134^4+134^3+134^2+134+1 is prime.

There are 134 ways to make change for 75 coins of either 1, 5, 10, 25, 50, or 100 cents.

The world's tallest thermometer is 134 feet in Baker, California, USA.

The hottest temperature ever measured in the United States was 134 F in Death Valley, CA on July 10, 1913.

May 15th (135th Day of the Non-Leap Year)

May 15th, 5/15.

515 = 551 - (5+1)^(1+5/5)

515 = 155 + (5+15)*(5*1*5-(5+5/5+1))

515 = (1+5/5)^(5-1+5) + (5-5/5-1)

515 = 5*15 + 51*5 + (5+(5/5+1)^5)*5

515 = 1*55 + 15*5 + 5*(51+(5*5+1))

515 = (5+1+5)*(51-(5-1)) - (5/5+1)

515 = (5*1+5)*51 + 15/(5-(5/5+1))

515 = (5+15)*(5*5+1) - 5*(5/(5*1))

515 = (51+5)*(5-1+5) + (15-(5-1))

515 = (51-5)*(5+1+5) + (5-5/5-1)^(1+5/5)

If 515 = n, then n0123456789 is prime (Meaning, 5150123456789 is prime).

515^32 + 516^32 is prime.

515 =  41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 (9 cons primes).

135th Day of the Year.

135 = 153 - 3*(1+5)

135 = 315 - (1+3+5)*(5*(1+3))

135 = 351 - (5+1)^3

135 = 513 - 51*3 - 15^(3-1)

135 = 531 - 5*31 - 3^(5*1) + (15-13)

135 = 13*5 + 1*35 + 5*(13-(1+5))

135 = 5*31 - (1+3)*5

135 = 53*1 + 3*15 + (51-(5-3)*(5+3-1))

135 = (1+35) + (13+5) + (5+31) + (53+1) - (1+3+5)

135 = (1+3+5)*(1*3*5)

135 = (1*3+5)*(15+(3-1)) - (5-3-1)

135 = (1+3*5)*(13-5) + 1*3*5

135 = (13+5)*(15/(3-1))

135^3 contains 6 consecutive digits (out of the 7).

135^3+135+1 is prime.

135^2 + 136^2 is prime.

135^2-135-1 is prime.

The sum of the reciprocals of 11 certain odd numbers is exactly 1. The largest odd number used is 135.

Only two numbers > 1 equal their digit sum times their digit product. The lowest is 135.

135 = 6^3 - 5^3 + 4^3 - 3^3 + 2^3 - 1^3.

There are 135 primes between 1000 and 2000.

e^135 is closer to an integer than any other exponent < 135 and > 1.

135 = 1^1 + 3^2 + 5^3.

May 16th (136th Day of the Non-Leap Year)

May 16th, 5/16.

516 = 561 - (51-(5+1))

516 = 615 - (16-5)*(16-(1+6))

516 = 651 - 5*(6/(6-5+1))^(15/(6-1))

516 = 156 + (5+1+6)*(5*1*6)

516 = 165 + 16*5 + (5+16)*(5+16/(6-5+1)) - (6-5+1)

516 = (6-5+1)^(15-6) + (15-(16-5))

516 = 5*16 + 51*6 + 5*(56-5*1*6)

516 = 6*15 + 61*5 + (16-5)^(6-5+1)

516 = (5+16) + (51+6) + (6+15) + (61+5) + (15-(6-5+1))*(5*1*6-15/(6-1))

516 = (5+1+6)*(51-56/(6+1))

516 = (5*1+6)*(51-(5-1)) - 5/(6-1)

516 = (51+6)*(16-(1+6)) + 15/(6-1)

516 = (51-6)*(16-5) + (5+16)

516 = (5+16)*(6*(5-1)) + (16-(56/(15-1))

516 = 2*2*3*43 (prime factors don't contain a 5, 1, or 6 -- Also, Only 1,2,3,4,5,6 are used).

There are 516 primes less than 3700.

1 + 1/2 + 1/3 + ... + 1/516 has a prime numerator.

136th Day of the Year.

136 = 163 - 3^(6/(3-1))

136 = 316 - 31*6 + 36/(6*1)

136 = 361 - 3*61 - 6*(13-6)

136 = 613 - 6*13 - 61*3 - 6^(3*1)

136 = 631 - 6*31 - 63*1 - 6*(36+(6-1))

136 = (6*(3-1))^(6/3) - (16/(3-1))

136 = 13*6 + 1*36 + (6/3)*(16-(6-1))

136 = 6*31 - (3-1)*(6-1)^(6/3)

136 = 3*61 - (63-(1+3)^(3-1))

136 = 16*3 + 1*63 + (6-1)^(3-1)

136 = (13+6) + (1+36) + (6+31) + (63+1) - 3*(6+1)

136 = (1+3+6)*(16-3) + (16-(1+3+6))

136 = (1*3+6)*(3*(6-1)) + (6/3-1)

136 = (1+3*6)*(13-6) + 6/(3-1)

136 = (1+36)*(6-(3-1)) + (1-3)*6

136 = (1*3*6)*(63/(6+3)) + (1+3+6)

136 = 17*8 and 1+7 = 8.

136 = 17*2*2*2 and 17+2+2+2 = 23 is also prime.

136 = 1+2+3+...+16.

136^3 - 136 - 1 is prime.

There are 136 primes less than 1000 that do not contain a 4.

There are 136 primes less than 1000 that do not contain a 5.

There are 136 primes less than 1000 that do not contain a 6.

There are more primes between [136,2*136] than [136^2,137^2].

1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.

The hottest temperature ever recorded was 136 F in 'Azizya, Libya but the reading is questioned.

May 17th (137th Day of the Non-Leap Year)

May 17th, 5/17.

517 = 571 - (5+1)*(17-(1+7))

517 = 751 - 75*1 - (7-5+1)*(51+(7-5*1))

517 = 715 - (1+5*7)*((7+5-1)/(7*1-5))

517 = 175 + 17*5 + 7*(1+5*7) + 15/(7-5+1)

517 = 157 + 15*7 + 1*57 + (7+5-1)*(17+(7-5-1))

517 = 5*17 + 51*7 + 75*1

517 = 7*15 + 71*5 + 57*1

517 = (5+17) + (51+7) + (7+15) + (71+5) + (7-5+1)*(5*(5+17)+15/(1*5))

517 = (5+1+7)*(5*(1+7)) - (7-5+1)

517 = (51+7)*(15-(1+5)) - 15/(7-5+1)

517 = (51-7)*(5*1+7) - (5-1+7)

517 = (5+17)*((5-1)*(7-1)) - (17-(7-1))

517 = 11*47 and 5+1+7 = 1+1+4+7.

517^3 + 518^3 is prime.

517 = 97 + 101 + 103 + 107 + 109 (5 cons prime).

137th Day of the Year.

137 = 173 - (7-1)^(3-1)

137 = 317 + (1-3*7)*(3^((7-1)/3))

137 = 371 - (7-1)*(37+(7-1)/3)

137 = 713 - 71*3 - 3*(1+3+7)^(3-1)

137 = 731 - 7*31 - 13*((1+3+7)+3*(7-1))

137 = (1+3+7)^((7-1)/3) + (7-3)^(3-1)

137 = 1*37 + 13*7 + 3^((7-1)/3)

137 = 7*31 - 73*1 - 7*(7-3!)

137 = (13+7) + (1+37) + (7+31) + (73+1) - (7-3-1)(1+3+7)

137 = (1+3+7)*(17-(7+1)/(3-1)) - (13-7)

137 = (1+37)*((1+7)/(3-1)) - 3*(7-3+1)

137 = (13+7)*(13-7) + 17

137 = (13-7)*(1+3*7) + (13-(7+1))

137 = (1*3+7)*(7*(3-1)) - (7-3-1)

137^2+138^2 is prime.

There are 137 primes less than 28^2.

137^10+137^9+137^8+137^7+137^6+137^5+137^4+137^3+137^2+137+1 is prime.

137^4-137-1 is prime.

137 is prime. 13, 37, and 17 are all prime, too.

The fine structure constant is approximately 1/137; it characterizes the strength of electromagnetic interaction.

137 is the largest factor of 123456787654321.

137 is a prime factor of 11111111.

Of the primes less than 10^10 the most common digits are 1, 3, then 7 in that order.

Hawaii is comprised of 137 islands, islets, and shoals.

One molecule of chlorophyll contains 137 atoms.

The first seven digits of pi squared is 137 (3^2+1^2+4^2+1^2+5^2+9^2+2^2=137).

May 18th (138th Day of the Non-Leap Year)

May 18th, 5/18.

518 = 581 - (8-1)*(8+1)

518 = 815 - 81*5 + (1+8)*(8+5-1)

518 = 851- 8*51 + 5*(18-(8-5*1))

518 = 185 + 18*5 + (8-5)^5

518 = 158 + 15*8 + 15*((8-5-1)^(5-1))

518 = 5*18 + 51*8 + 5*(8-5+1)

518 = 8*15 + 81*5 + (15-8)

518 = (5+18) + (51+8) + (8+15) + (81+5) + 158 + 185 - 8*(15-(5*1+8))

518 = (5+1+8)*(5*(8-1)+(8-5-1))

518 = (5*1*8)*(5*1+8) - (8-5-1)

518 = (51-8)*((5-1)*(8-5)) + (8-5-1)

518 = (51+8)*(15-(1+5)) + (5*1+8)

518 = (5+18)^(8-5-1) + (18-(8-1))

518^5 is the next time a power of 518 contains a 5 (besides 518^1).

518!! + 1 is prime (next number with this property is > 30000).

518 = 5^1 + 1^2 + 8^3.

518^9 + 518^7 + 518^5 + 518^3 + 518 + 1 is prime.

138th Day of the Year.

138 = 183 - (8+1)*(8-3)

138 = 318 - 31*8 + (1+3)*(13+(1+3))

138 = 381 - 3*81

138 = 831 - 8*31 - 381 - 8^(3-1)

138 = 813 - 81*3 - 318 - 183 - 3*(8*3-1)

138 = 1*38 + 13*8 + (8-3-1)

138 = 8*31 - 83*1 - 3^(13-8-(3-1))

138 = (1+38) + (13+8) + (8+31) + (83+1) - (1+8)*(8-3)

138 = (1+3+8)*(1*3+8) + 18/3

138 = (1*3*8)*(8-3+1) - 18/3

138 = (13+8)*(8-(3-1)) + 3*(8-3-1)

138 = (13-8)*(3*(1+8)) + 81/(31-(8-3-1))

138 = (1+38)*(8-3-1) - (31-13)

138^4 contains no 0's and 138^5 contains 4 0's.

138*831 = 114678 (a nondecreasing order of digits).

138 = 2*3*23 (2 and 3 are the digits of 23).

138^2+138 +/- 1 are twin primes.

138^23+138^21+138^19+138^17+138^15+138^13+138^11+138^9+138^7+138^5+138^3+138+1 is prime.

138 is the smallest number > 100 without any zeros but its square has at least one zero.

138 and the 138th prime both contain an 8 (138 is the smallest number with this property).

There are 138 numbers < 10^5 with 11 prime factors (counted with multiplicity).

138 = 29+31+37+41 (four cons primes).

The Universe is said to be 13.8 billion years old.

The TV show The Simpsons did a "138th Episode Spectacular" for their 138th episode.

May 19th (139th Day of the Non-Leap Year)

May 19th, 5/19.

519 = 591 - (9-1)*(15-(1+5))

519 = 915 - 91*5 + 59*1

519 = 951 - 9*51 + (9-5-1)^(9-1-5)

519 = 195 + 19*5 + 15^(9/(9-5-1)-1) + (19-15)

519 = 159 + 15*9 + 9*(19+(5+1))

519 = 5*19 + 51*9 - 5*(15-(9-1))

519 = 9*15 + 91*5 - (59+(5-1)*(9-5-1))

519 = (5+19) + (51+9) + (91+5) + (9+15) + 15*(15+(1+5))

519 = (5+1+9)*(15+19) + (19-(1+9))

519 = (5+19)*(19+9/(9-5-1)) - (15-(1+5))

519 = (51+9)*(15-(1+5)) - (15+(1+5))

519 = (51-9)*((5-1)*(9-1-5)) + 15

139th Day of the Year.

139 = 193 - 9*(9-3*1)

139 = 319 - 3*19 - 3*(39+(9/3-1))

139 = 391 - 39*1 - 3*(91-(1+3)*(9-3-1))

139 = 913 - 91*3 - 319 - 91*(9/3-1)

139 = 931 - 9*31 - 391 - (91-3*(9+1))*(13-(9+3-1))

139 = 1*39 + 13*9 - (19-(9/3-1))

139 = 9*31 - 93*1 - (39+(9-1))

139 = (13+9) + (1+39) + (9+31) + (93+1) - 3*19

139 = (1+3+9)*(9+3-1) - (9/3+1)

139 = (13+9)*(9-3*1) + (9-3+1)

139 = (13-9)*((9-3+1)*(9-3-1)) + ((9-3-1)-(13-9))

139 = (1+39)*(13-9) - (19+(3-1))

139^2 contains a 1,3,9.

139 is the largest prime less than e^5.

139^2+140^2 is prime.

139^2-139-1 is prime.

139^4-139-1 is prime.

There are 139 primes less than 800.

If 139=n, then (30^n+1)/31 is prime (139 is the smallest number with this property).

139 = 19+23+29+31+37 (5 cons primes).

139 and 149 are the first consecutive primes differing by 10.

139 is the largest prime (less than a googol) formed by the concatenation of powers of 3.

139 = 9*8+7*6+5*4+3*2-1.

May 20th (140th Day of the Non-Leap Year)

May 20th, 5/20.

520 = 502 + (5-2)*(5+2^0)

520 = 205 + 20*5 + 5*(50-(5+2+0))

520 = 250 + 2*50 + (5*2)*(20-(5-2))

520 = 5*20 + 2*50 + 250 + (5*2)*(5+2)

520 = (5+20) + (50+2) + 205 + 5*20 + 2*50 + 2*(20-2^0)

520 = (5+2+0)*(25*(5-2)) - (5-2*0)

520 = (5+20)*(20+2^0) - 5*(2^0)

520 = 52*(5*2)

520 = 2*2*2*5*13 and 520*(2+2+2+5+13) = 12480 (concatenation of consecutive powers of 2 --excl the 0).

520^1 contains a 5. The next power of 520 that contains a 5 is 520^7.

There are 520 ways to place 2 nonattacking kings on a 6 by 6 board.

There are 520 ways to place 2 nonattacking bishops on a 6 by 6 board.

140th Day of the Year.

140 = 104 + (40-4*1)

140 = 401 - 40*1 - (14+14^0)^(4-1-1^0)

140 = 410 - 4*10 - 41*1^0 - (14+(4-1))^(1+4^0) + 10^(1+4^0)

140 = 1*40 + 14 + (40+1) + (1+4)*(10-1^0)

140 = 14*41 - 3*(4*(4-1))^(1+4^0) - (1+4^0)

140 = (1+4+0)*(40-4*(4-1))

140 = (1+40)*(4-1) + (14+(4-1))

140 = 14*(40/(4*1-0))

1^2+2^2+3^2+4^2+5^2+6^2+7^2 = 140.

140^4+1 is prime.

140^8+1 is prime.

140^3-140-1 is prime.

The maximum number of characters allowed in a tweet on Twitter is 140.

May 21st (141st Day of the Non-Leap Year)

May 21st, 5/21.

521 = 512 + (5*2-1)

521 = 125 + 12*5 + (5+2+1)*(52-5*2)

521 = 152 + 1*52 + (5-2*1)*(5*21) + (5-2-1)

521 = 251 + 2*51 + (5+2+1)*21

521 = 215 + 21*5 + (5-2-1)*(5*2)^(52/(5+21)) + 15-2*(5+2*1)

521 = 5*21+ 52*1 + 215 + 125 + (25-1)

521 = 1*25 + 12*5 + 251 + 152 + (5*2+1)*(5-2*1)

521 = (5+21) + (52+1) + (1+25) + (12+5) + (5-(2-1))*(5*2)^(5-2-1) - (12-(5*2+1))

521 = (5+2+1)*(5*(15-2)) + ((5-2-1)*(5*2+1)-21)

521 = (5+21)*(5*(5-(2-1))) + (25-(5-1)*(5+1))

521 = (52+1)*(5*2*1) - (5*2-1)

521 = (52-1)*(12-(5-2-1)) + (5*2+1)

521^7 is the next power of 521 (after 521^1) that contains a 5.

2^521-1 is prime (Meaning 512*2^512-1 is prime).

4^521-3^521 is prime (Note that 521 is missing a 4 and a 3 to make it a full string of consecutive numbers).

521 is the only prime of the form n^9+9 for prime n (n=2).

521 = 5^4-5^3+5^2-5^1+1.

521 is the smallest prime whose reversal is a cube.

521 is the reversal of 5^(2+1).

141st Day of the Year.

141 = 114 + (4-1)^(4-1)

141 = 411- 4*11 - 41*1 - 114 - (41+(4-1)*(14-4*1))

141 = 1*41 + 14*1 + 11*4 + (1+41)

141 = (1+41) + (14+1) + (11+4) + (4-1)*(11+4*(4-1))

141 = 11^(4-1-1) + 4*(11-(4+1+1))

141 = (1+4+1)*(4*(4+1+1)) - (11-(1+1)*4)

141 = (14+1)*(14-(1+4)) + (1+4+1)

141 = (14-1)*11 - (4-1-1)

141 = (1+41)*(4-1) + (14+1)

141^2+141 +/- 1 are twin primes.

141^2-141-1 is prime.

141*2^141+1 is prime (141 is the smallest number > 1 with this property).

There are 141 primes < 1000 that do not contain an 8.

There are 141 squares less than 27^3.

141, 142, 143, ... 148 all have 2 distinct prime factors.

May 22nd (142nd Day of the Non-Leap Year)

May 22nd, 5/22.

522 = 252 + (5+2+2)*(22+2^(5-2))

522 = 225 + (22+5*2+2/2)*(5+2+2)

522 = 5*22 + 52*2 + 252 + (5+2)*(2^(5-2))

522 = 2*25 + 22*5 + 225 + 9*(25-2*5) + 22/(5+2*(5-2))

522 = (5+22) + (52+2) + (2+25) + (22+5) + (5+2+2)*(52-(5-2)^2)

522 = (5+2+2)*(52+(2*(5-2)))

522 = (5+22)*(22-(5-2)) + (5+2+2)

522 = (52+2)*(22-(5*2+2)) - (22+2/2-5)

522 = (52-2)*(5*2) + (52-(5*(2*(5-2))))

522*522 = 272484 (concatenation of two palindromes).

522 = 2*3*3*29 and 2+3+3+29 = 37 is also prime.

522 = 73+79+83+89+97+101 (6 cons primes).

142nd Day of the Year.

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

142 = 214 - 4*(14+1*4)

142 = 241 - (1+4*2)*(14-(4-1))

142 = 412 - 41*2 - 4*(41+(1*4+2))

142 = 421 - 4*21 - (41-2)*(4+2-1)

142 = 1*42 + 14*2 + (1*4*2)*(1+4*2)

142 = 2*41 + 24*1 + (4+2)^(4-2*1)

142 = (1+42) + (14+2) + (41+42)

142 = (2+41) + (24+1) + 2*(41-4*1)

142 = (1+4+2)*(12+1*4*2) + (1*4-2)

142 = (1+42)*(12/4) + (12+(2-1))

142 = (14+2)*(1+4*2) - 14/(1+4+2)

142 = (14-2)^(12/4-1) - 24/(14-2)

142 = (1*4*2)*(24-(2+4)) - (1*4-2)

142^4+1 is prime.

142^2-142-1 is prime.

142^16+143^16 is prime.

142 = 1 + 2*(3) + 3*(3)^2 + 4*(3)^3.

There are 142 staircases at Hogwarts School of Witchcraft and Wizardry.

May 23rd (143rd Day of the Non-Leap Year)

May 23rd, 5/23.

523 = 532 - 3*(5-2)

523 = 352 + (25-2*3)*(2^3+(3+2)/5)

523 = 325 + (25-3)*(5*3-(5+3-2))

523 = 253 + (5+2+3)*(3^(5-2))

523 = 235 + 2^(3^2-5)*(23-5)

523 = 5*23 + 52*3 + (5*2-3)*(2*3)^(5-3)

523 = 3*25 + 32*5 + 32*(5*2-(3-2))

523 = (5+23) + (52+3) + (3+25) + (32+5) + 25*(5^2-5*2)

523 = (5+2+3)*((5*2+3)*(3^2-5)) + (5-2)*(3-2)

523 = (52+3)*(3^2) + (5+23)

523 = (52-3)*(5+2*3) - 2^(5-(3-2))

523 = (5+23)*(23-5) + (5^2-2*3)

523^2 contains 5, 2, 3.

523 is prime and all of its digits are prime (the first 3 prime numbers, to be specific).

523 = 61+67+71+73+79+83+89 (7 cons primes).

541 is the next prime, 18 after 523. Further, 523 and 541 are the smallest pair of consecutive primes with the same digit sum.

143rd Day of the Year.

143 = 134 + 3*(4-1)

143 = 341 - 3*41 - (1+4)*(13+(3-1))

143 = 314 - 31*4 - ((34+1)+1*4*3)

143 = 413 - 41*3 - 134 - (1+4*3)

143 = 431 - 134 - 4*31 - (3-1)*(3*(4+1))

143 = 1*43 + 14*3 + (3-1)*(31-(3-1))

143 = 3*41 + 34*1 - (1*4+3)*(3-1)

143 = (1+43) + (14+3) + (3+41) + (34+1) + (14-(4*3-1))

143 = (1+4+3)*(14+1*4) - 1*(4-3)

143 = (14+3)*(1+4+3) + (1*4+3)

143 = (14-3)*(1+4*3)

143 = (1+43)*(4-1) + (4*3-1)

143^2+143+1 is prime.

143^3+143+1 is prime.

143^4+143^3+143^2+143+1 is prime.

1+1/2+1/3+...+1/143 has a prime numerator.

There are more numbers in [143,2*143] than in [143,143^2].

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

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

3^4+4^4+5^4+6^4 = 7^4 (- 143).

May 24th (144th Day of the Non-Leap Year)

May 24th, 5/24.

524 = 542 - 2*(5+4)

524 = 452 + (5+4)*(2*4)

524 = 425 + (42-(5+4))*(24/(2*4))

524 = 245 + 24*5 + (5-2)*(54-(5-4))

524 = 254 + 2*54 + (52/(24+(4-2)))(5-2)^4

524 = 5*24 + 52*4 + (5*2+4)^(4-2)

524 = 4*25 + 42*5 + 245 - (5*(2+4)-(5-2-4))

524 = (5+2+4)*(42+5) + (5*2-(5-2))

524 = (5+24)*(4^2+(2*(5-4))) + 2^(5-4)

524 = (52+4)*(5*4-(5+2+4)) + (5*4)

524 = (52-4)*(5+2+4) + 4*(5-2-4)

524 = (5*2+4)*(2^5+(5*2-4)) - 2^(5+2-4)

524 = (5+2*4)*(5*2*4) + 4*(25-24)

3^524, 3^525, and 3^526 all contain the same number of digits.

144th Day of the Year.

144 = (4*(4-1))^(1+4/4)

144 = 414 - 41*4 - (1+4/4)*(41+4*(4-1))

144 = 441 - 4*41 - (4+4-1)*(14+4+4/4)

144 = (1+4+4)*(1*4*4)

144 = 1*44 + 14*4 + 44*1

144 = 4*41 + 44*1 - 4^(4-1)

144 = (1+44) + (14+4) + (4+41) + (44+1) - (1+4+4)

144 = (14+4)*(1*4+4)

144 = (14-4)*14 + 44/(1+4+4+(1+4/4))

144 = (1+44)*(4-1) + (1+4+4)

144= (1*4*4)*(1+4+4) (Only other number > 1 with this property is 135).

144 = 12^2 and 441 = 21^2.

144, (1+4+4), and (1*4*4) are all perfect squares.

144^3+144+1 is prime.

144^2+145^2 is prime.

144 = (3!^2)*(2!^2)*(1!^2)*(0!^2).

144 is the 12th Fibonacci number (and 144 = 12^2).

144 is the largest Fibonacci number that is also a square.

144 is the smallest number with exactly 15 divisors.

144 is the smallest number whose fifth power is the sum of four smaller fifth powers.

The maximum determinant in a 9 by 9 matrix of 0's and 1's is 144.

2^144 is the smallest power of 2 that contains the first 5 digits of pi consecutively (including the 3).

May 25th (145th Day of the Non-Leap Year)

May 25th, 5/25.

525 = 552 - (5-2)*(5*2-5/5)

525 = 5^(5-2) + 25*(2^(5-5/5))

525 = 5^(5-2+5/5) - (5+5)^2

525 = 5*25 + 52*5 + (5+5)*(5*2+5-5/5)

525 = (5+25) + (52+5) + (55+2) + 255 + (5+2)*(25-(2+5))

525 = (5+2+5)*(52-(5+5-2)) - (5-2)

525 = (5+25)*(25-(2+5)) + 5*(2+5/5)

525^3 - 525^2 +/- 1 are twin primes.

145th Day of the Year.

145 = 154 - (1*5+4)

145 = 415 - 41*5 - 5*(14-(5-4))

145 = 451 - 4*51 - (1+5)*(14+(4-1))

145 = 514 - 51*4 - 5*14 - 5*(14+5)

145 = 541 - 5*41 - 54*1 - (154 - (5*4-(4-1)))

145 = 1*45 + 14*5 + 5*(4-1)!

145 = 5*41 - 54*1 - (54/(5+4))

145 = (1+45) + (14+5) + (5+41) + (54+1) - (15+(1+5))

145 = (1+4+5)*(15-(5-4)) + 45/(4+5)

145 = (1+4*5)*(14/(5-4+1)) - (5-(4-1))

145 = (1*4+5)*((5-4+1)^4) + 1*(5-4)

145 = (14+5)*(14-(1+5)) - (14/(5-(4-1)))

145 = (1+45)*(4-1) + ((4-1)!+(5-4))

145 = 1!+4!+5! (These are called "factorions". 145 is the first nontrivial factorion -- only one other higher than it.)

145^4+145^3+145^2+145+1 is prime.

145^2-145-1 is prime.

145 = 3^4 + 4^3.

May 26th (146th Day of the Non-Leap Year)

May 26th, 5/26.

526 = 562 - (26+5*2)

526 = 625 - (6+5-2)*(25-(2*5+6))

526 = 652 - 65*2 + (5*2-6)

526 = 256 + 25*6 + (26-(6-2)!)*(5*2*6)

526 = 265 + 26*5 + (5*2*6) + (56+5*6/2)

526 = 5*26 + 52*6 + (6-2)*(26-5)

526 = 6*25 + 62*5 + (65+(6-5))

526 = (5+26) + (52+6) + (6+25) + (62+5) + 265 + (62+6*2)

526 = (5+2+6)*(52-2*6) + (5-2)!

526 = (5+26)*(5+2*6) - (2-(6-5))

526 = (52+6)*(5+6-2) + (26-2*(5+6))

526 = (52-6)*(5+6) + 5*(6-2)

526 = 263*2 and 263+2 = 265 (re-ordering of 526 -- Thus it is a Smith number).

526^5+526^3+526+1 is prime.

146th Day of the Year.

146 = 164 - 6*(4-1)

146 = 461 - 4*61 - (61+(6*1+4))

146 = 416 - 41*6 - 1*4*6

146 = 614 - 61*4 - 6*14 - 14*(4+6)

146 = 641 - 6*41 - 64*1 - (1+4)*(41-4*1)

146 = 1*46 + 14*6 - (1+4+6)*(6-4*1)

146 = 6*41 - 64*1 - (46-(4+6))

146 = (1+46) + (14+6) + (6+41) + (64+1) - (6-(4-1))*(6+4+1)

146 = (1+4+6)*(16-(4-1)) + (6-(4-1))

146 = (1+4*6)*((6-(4-1))!) - 16/4

146 = (1*4+6)*(16-(6-4)) + (16-(4+6))

146 = (14+6)*(14/(6-4)) + (14-(6-4)^(4-1))

146 = (14-6)*(14+1*4) + (6-4*1)

146 = (1+46)*(6-4+1) + (41-6^(6-4))

146^2 and 146^3 contain the same digits.

146^2+1 is prime.

146^3+146+1 is prime.

146^4+146+1 is prime.

There are 146 primes less than 29^2.

146^6+146^5+146^4+146^3+146^2+146+1 is prime.

146^2-146-1 is prime.

The sum of the first 146 primes is prime.

146^23 + 146^21 + 146^19 + ... + 146^3 + 146 + 1 is prime.

There are 146 primes of the form 1+x^32 for 1 < x < 10^4.

There are 146 different values (depending on the parenthesis placement) of the third derivative of x^x^x^...^x with 21 x's evaluated at x=1.

May 27th (147th Day of the Non-Leap Year)

May 27th, 5/27.

527 = 572 - 5*(2+7)

527 = 725 - (2+7)*(27-5)

527 = 752 - (5*2+(7-2))^(7-5)

527 = 257 + 25*7 + 5*(5+2*7)

527 = 275 + 27*5 + (2+7)*(5*2+(5-2))

527 = 5*27 + 52*7 + 7*(7+2-5)

527 = 7*25 + 72*5 - (5*2-(7-5))

527 = (5+27) + (52+7) + (72+5) + (7+25) + 275 + 52

527 = (5+2+7)*(27+2*5) + 27/(5-2)

527 = (5+27)*(2^(7-5+2)) + (7*2+5/(7-2))

527 = (52+7)*(2+7) - 2*(7-5)

527 = (52-7)*(5+7) - (5^2-(5+7))

527^5 is the next power of 527 to contain a 5.

527^3 does not contain a 5, 2, or 7.

If 527=n, then n7n and 7n7 are both prime (Meaning, 5277527 and 75277 are both prime).

The concatenation of 527^4, 527^3, 527^2, 527, and 1 is prime.

147th Day of the Year.

147 = 174 - (7-4)^(4-1)

147 = 417 - 41*7 + (14+(7-4))

147 = 471 - 4*71 - 4*(7+4-1)

147 = 741 - 471 - 41*(7-4)

147 = 714 - 417 - (1+4)*(7*4+(7-4-1))

147 = 1*47 + 14*7 + (7-4-1)

147 = 7*41 - 74*1 - (7-1)*(7+4)

147 = (1+47) + (14+7) + (7-1)*(17-4)

147 = (7+41) + (74+1) + 4*(7-1)

147 = (1+4+7)*(17-4) - (14-(1+4))

147 = (1+4*7)*(1+4) + (7-4-1)

147 = (1*4+7)*(17-4) + (1+7)/(7-4-1)

147 = (1+47)*(7-4*1) + (7*1-4)

147^2+147+1 is prime.

147^4-147-1 is prime.

1 = 1/a + 1/b + 1/c + 1/d + 1/e has 147 solutions for 0 <= a <= b <= c <= d <= e.

1999...999 is prime (with 147 9's).

May 28th (148th Day of the Non-Leap Year)

May 28, 5/28.

528 = 825 - (2^(8-5)+(8-5-2))*(5+28)

528 = 852 - (5*2+8)^(5*2-8)

528 = 582 - (8-2)*(8*2-(5+2))

528 = 285 + 28*5 + 2*(58-2) - (8-5)^2

528 = 258 + 25*8 + 5*(5+(8-5)^2)

528 = 5*28 + 52*8 - (5+2)*(8/2)

528 = 8*25 + 82*5 - 82*(5-8/2)

528 = (5+28) + (52+8) + (8+25) + (82+5) + (5+2+8)*(25-8/2)

528 = (5+2+8)*(28+(5+2)) + (8-5)

528 = (5+2*8)*(2^(8-5)+2*8) + (8*(5-2)-(5+2*8))

528 = (5*2+8)*(28+(5-8/2)) + 2*(8-5)

528 = (52+8)*(2^(8-5)) - (8*2-8/2)

528 = (52-8)*(28-2*8)

528 = 2*2*2*2*3*11 and 2+2+2+2+3=11.

1+2+3+...+32 = 528.

(528!-3)/3 is prime (Only one known number > 528 also has this property).

There are 528 primes less than 3800.

528^9+528^7+528^5+528^3+528^1+1 is prime.

148th Day of the Year.

148 = 184 - (14-8)^(8/4)

148 = 418 - (8+1)*(48-18)

148 = 481 - (4-1)^(8/4)*(41-4*1)

148 = 814 - 81*4 - 18*(14+(1+4))

148 = 841 - 8*41 - (1+4)*(81-8*1)

148 = (1+48) + (14+8) + (8+41) + (84+1) - (8-4-1)*(18+(8/4-1))

148 = 1*48 + 14*8 - (1*4+8)

148 = 8*41 - 84*1 - (14-8)*(8/4)^(4+1)*(8-4-1)

148 = (1+4+8)*(8+4-1) + (8-4+1)

148 = (1+4*8)*(8-4*1) + 8^(14-(4+8))

148 = (1*4+8)*(14-(8/4)) + (8-4*1)

148 = (1+48)*(8-4-1) + (8/4-1)

148 = (14+8)*(8-(8/4-1)) - (14-8)

148*841 = 124468 (nondecreasing integers).

148 = 2*2*37.

2+2+37 = 41.

2+2+(3+7) = 14.

1481, 1483, 1487 and 1489 are all prime.

It is theorized that one can only maintain a stable social relationship with at most 148 people.

May 29th (149th Day of the Non-Leap Year)

May 29th, 5/29.

529 = (5+2*9)^(9-5-2)

529 = 592 - 9*(5+2)

529 = 295 + 9*(5*(9-2)-9)

529 = 259 + (5*2)*9*(5-2)

529 = 952 - 9*52 + (29+2^(9-5))

529 = 925 - 92*5 + 2^(9-5+2)

529 = 5*29 + 52*9 - (9-5)*(29-2^(5-2))

529 = 9*25 + 92*5 - (9*2-5)*(9+5-2)

529 = (5+29) + (52+9) + (9+25) + (92+5) + 259 + (9-5)*(9+2)

529 = (5+2+9)*(29+(9-5)) + (29-(5+2)*(9-5))

529 = (5+29)*(25-2*5) + (5*2+9)

529 = (52-9)*(9+5-2) + (9*2-5)

529 = (52+9)*((5-2)^(9-5-2)) - (2*9+(9-5-2))

529 = (5*2+9)*(29-(9-5-2)) + 2^(9-5)

529 = 23^2 and 23 = 5+2*9 or 2^5-9.

If 529 = n, 987654321n is prime (Meaning 987654321529 is prime).

If 529 = n, n0123456789 is prime (Meaning 5290123456789 is prime).

3456789012345678901234.... (529 digits) is prime.

149th Day of the Year.

149 = 194 - 9*(4+1)

149 = 491 - 19*((4-1)*(9-(4-1)))

149 = 419 - (9+1)*(9*(4-1))

149 = 941 - 9*41 - 419 - (9-4-1)

149 = 914 - 91*4 - (19-1*9)*(41+14)

149 = 1*49 + 14*9 - ((9/(4-1))*(9+1)-(9-4-1))

149 = 9*41 - 94*1 - 14*9

149 = (14+9) + (1+49) + (9+41) + (94+1) - (9/(4-1))*(14+9)

149 = (1+4+9)*(19-(9-1)) - (9-4*1)

149 = (1+49)*(9/(4-1)) - (14-9-1*4)

149 = (14+9)*(9-(4-1)) + (14-(4-1))

149 = (1*4+9)*(19-(9-1)) + (9-(4-1))

149 = (1+4*9)*(9-4-1) + ((9-4-1)-(9/(4-1)))

149 = 6^2+7^2+8^2 and 1+4+9 = 14 = 1^2+2^2+3^2.

149^2+150^2 is prime.

149^16+150^16 is prime.

149^6 + 149^5 + 149^4 + 149^3 + 149^2 + 149 + 1 is prime.

149^2-149-1 is prime.

1/149 repeats after 148 terms (the most possible for any integer).

149 and 941 are prime (Note how both don't have any prime digits).

14444999999999 is prime (one 1, four 4's, nine 9's).

149 is prime but 1149, 2149, ... 9149 are all composite (The smaller numbers below 149 that have this property are 2 and 5).

For \$149 dollars, Atlas Sports Genetics will test your child's DNA and send you a report listing the sports your child is most likely to conquer.

May 30th (150th Day of the Non-Leap Year)

May 30th, 5/30.

530 = 503 + 3^(5-3+53^0)

530 = 305 + 30*5 + 5*(30/(5-3))

530 = 350 + 3*50 + 5*(5+3^0)

530 = 53*35 - 350 - 503 - 3*50 - 305 - (5*3+(5-3))

530 = (5+3+0)*(53+5*3) - (5*3-5^0)

530 = (5+30) + (53+0) + (50+3) + (5*(5-3))^(5-3) + (5*3+(5-3))^(3-5^0)

530 = (5+30)*(5*3) + 30/(5+3^0)

530^5 is the next power of 530 to contain a 5 or a 3.

530 = 16^2+17^2+18^2.

530*6^530 - 1 is prime (322 digits).

530*4^530 - 1 is prime (416 digits).

530 = 6 + 28 + 496 (first three perfect numbers).

150th Day of the Year.

150 = 105 + 5*(10-1^0)

150 = 510 - 5*10 - 105 - 5*(51-10)

150 = 501 - 105 - 50*1 - (5-1)*(50-1)

150 = 51*15 - 501 - 105 - (15-(1+5))

150 = 50*15 - 105 - 510 + 15

150 = (1+50) + (15+0) + (50+1) + (10+5^0)*(15/5)

150 = (1+5+0)*(5^(1+5^0))

150 = (1+50)*(5-1^0-51^0) - (5-10/5)

150 = 15*(5*(1^0+5^0))

150^6 is the first power of 150 (after 150^1) to have a 1 in it.

150^2+1 is prime.

150^2+150+1 is prime.

150^3-150-1 is prime.

Dunbar's number is the maximum number of people one can maintain a social relationship with. It is believed to be between 100 and 250 and is usually deemed 150.

150 =  7+11+13+17+19+23+29+31 (8 cons primes).

A Professor's Cube is a 5x5x5 version of the Rubik's cube, with 150 squares.

May 31st (151st Day of the Non-Leap Year)

May 31st, 5/31.

531 = 513 + (15+3)

531 = 315 + (5+1)^3

531 = 351 + (15+3)*(5*(3-1))

531 = 135 + (5+3+1)*((5-1)*(13-(3-1)))

531 = 153 + 3*(5-3+1)*(35+(5+3-1))

531 = 5*31 + 53*1 + 315 + (5+3*1)

531 = 1*35 + 13*5 + 351 + (5*(3-1))*(5*1+3)

531 = (5+31) + (53+1) + (1+35) + (13+5) + (5+3+1)*(35+(3+5))

531 = (5+3+1)*(51+(5-3*1)^3)

531 = (5+3*1)*(51+5*3*1) + (5-3+1)

531 = (5*3+1)*(31+(3-1)) + (13-5*(3-1))

531 = (53+1)*(5+3+1) + 5*(3^(3-1))

531 = (53-1)*(5*(3-1)) + (15-(5-1))

531^4 is the first time a power of 531 > 1 has a 5.

531^5 is the first time a power of 531 > 1 has a 3.

151st Day of the Year.

151 = 115 + (5+1)^(1+1)

151 = 511 - 51*1 - 5*11 - (1+5+1)*(51-15) - (15/5-1)

151 = 1*51 + 15*1 + 5*(15+1+1)

151 = (1+51) + (15+1) + (11+5) + (51+(15+1))

151 = (1+5+1)*(15+(1+5)) + 1*(5-1)

151 = (1+5*1)*(5^(1+1)) + 1^51

151 = (1+51)*(5-1-1) - 1*5*1

151^3-151-1 is prime.

(14^151-5^151)/9 is prime (The second smallest number with this property. Smallest is (14^2-5^2)/9 is prime).

The total number of Pokemon in the original set (including Mew and Mewtwo) is 151.

The Statue of Liberty from base to top of torch is 151 feet tall.

If A = 1, B = 2, ... Z = 26, then "JESUS CHRIST" is 151.

June 1st (152nd Day of the Non-Leap Year)

Jun 1, 6/1.

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.

152nd Day of the Year.

152 = 125 + (2+1)^(5-2)
152 = 215 - (5*2-1)*(1*5*2)
152 = 251 - (5*2+1)*(5*2-1)
152 = 512 - 5*12 - (1*5-2)*(25*(5-1))
152 = 521 - 5*21 - (1+5+2)*(21+12)
152 = 5^(1+2)+(25+(5-2-1))
152 = 1*52 + 15*2 + (1*5*2)*(1*5+2)
152 = 2*51 + 25*1 + 1*5^2
152 = (1+52) + (15+2) + (2+51) + (25+1) + (5-2*1)
152 = (1+5+2)*(21-2*1)
152 = (1+5*2)*(12+1*2) - (5-2-1)
152 = (15+2)*(5*2-1) - (12-(1+5*2))
152 = (15-2)*((1+5)*2) - 12/(5-2)
152 = (1+52)*(5-2*1) - (1*5+2)

152^2 contains 0, 1, 2, 3, 4 only once.

152^3+152+1 is prime.

152^8+1 is prime.

152^8+153^8 is prime.

June 2nd (153rd Day of the Non-Leap Year)

Jun 2nd, 6/2.

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).

153rd Day of the Year.

153 = 3*51
153 = 135 + 3*(5+1)
153 = 315 - (5-3)*(3^(5-1))
153 = 351 - (5+3+1)*(53-31)
153 = 531 - 5*31 - 15^(3-1) + (5-3*1)
153 = 513 - 51*3 - (1+5+3)*(13+5*(3-1))
153 = 1*53 + 15*3 + 5*(13-(3-1))
153 = 35*1 + 5*13 + 1*53
153 = (1+53) + (15+3) + (3+51) + (35+1) - (1+5+3)
153 = (1+5+3)*(13+(1+3))
153 = (15-3)*13 - (5-3+1)
153 = (15+3)*(1+5+3) - (15-(1+5))
153 = (1+53)*(5-3+1) - (1+5+3)
153 = (1+5*3)*(1+5+3) + (3^(3-1))
153 = (1*5+3)*(5*(3+1)-(5-3-1)) + (5-3-1)

153 = 1^3 + 5^3 + 3^3.

153 = 1+2+3+...+17.

153 = 1! + 2! + 3! + 4! + 5!

153^2+153+1 is prime.
153^3+153+1 is prime.

There are 153 less than 10^3 that do not contain a 0.

153^4-153-1 is prime.

Take any multiple of three and add the cubes of its digits. Keep doing this. You'll reach 153.

1 + 153^2 + 153^4 + 153^6 + 153^7 is prime (Note that the digits of 153 are the only digits < 8 that aren't one of the exponents).

153^2+153 +/- 1 are twin primes.

153 in base 2 is 10011001 (concatenation of the same number with itself).
153 in base 4 is 2121 (concatenation of the same number with itself).

June 3rd (154th Day of the Non-Leap Year)

Jun 3rd, 6/3.

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.

154th Day of the Year.

154 = 145 + (1*5+4)
154 = 415 - 41*5 - (5+4-1)*(14/(5-4+1))
154 = 451 - 4*51 - (4-1)*(41-(5+4+1))
154 = 541 - 5*41 - 14*(15-(5-4+1))
154 = 514 - 51*4 - (1+5+4)*(15+(5-4+1)^4)
154 = 1*54 + 15*4 + 4*(15-1*5)
154 = 4*51 - 45*1 - 15/(4-1)
154 = (1+54) + (15+4) + 4*(1*5*4)
154 = (45+1) + (4+51) + (54-1)
154 = (1+5+4)*(5*(4-1)) + (5!/4!-1)
154 = (1+5*4)*(14/(1^5+1^4)) + (15-(5-4+1)^(4-1))
154 = (1*5+4)*(14+(4-1)) + 1*(5-4)
154 = (15+4)*(5+4-1) + (5-(4-1))
154 = (15-4)*14
154 = (1+54)*(4-1) - (15-4)

154!+1 is prime.

154^4+1 is prime.

154^2+155^2 is prime.

154^4+154^3+154^2+154+1 is prime.

There 154 primes less than 900.

154^4-154-1 is prime.

The first run of 3 identical digits in the decimal expansion of pi occurs at the 154th digit.

154 = 0!+1!+2!+3!+4!+5!

June 4th (155th Day of the Non-Leap Year)

Jun 4th, 6/4.

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.

155th Day of the Year.

155 = 515 - 51*5 - 5*(15+(1+5))
155 = 15*5 + 1*55 + 5^(1+5/5)
155 = 5*51 - 55*1 - (55-(5+5))
155 = (1+55) + (15+5) + (1*5*5+(55-1))
155 = (5+51) + (55+1) + (51-(1+5/5)^(5-1-5/5))
155 = (1+5+5)*(15-5/5) + 1*(5/5)
155 = (15+5)*(15/5+5) - 55/(1+5+5)
155 = (15-5)*15 + 15/(5-1-5/5)
155 = (1+55)*(5-1-5/5) - (15-(1+5/5))

155^5 is the next power of 155 that contains a 1.

155^2+155 +/- 1 are twin primes.

155^3+155+1 is prime.
155^3-155-1 is prime.

The maximum coefficient in the polynomial (1+x+x^2+x^3)^5 is 155.

155 = 5*31 and 5+7+11+13+...+31 = 155.

June 5th (156th Day of the Non-Leap Year)

Jun 5th, 6/5.

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.

156th Day of the Year.

156 = 165 - (15-6)
156 = 615 - 61*5 - (1*5*6+1*(5-6))*5
156 = 651 - 6*(51 - (1*5*6))
156 = 516 - 51*6 - 15*(15-6*(6-5+1))
156 = 561 - 5*61 - (16-1*6)^(6-5+1)
156 = 15*6 + 1*56 + (6+5-1)
156 = 6*51 - 65*1 - (5-1)*(6*5*1-(6+5*1))
156 = (1+56) + (15+6) + 6*(15-(6-(5-1)))
156 = (6+51) + (65+1) + (51-(1*5*6-(1+5+6)))
156 = (1+5+6)*(15-(6-(5-1)))
156 = (1*5+6)*(15-(6-5)*1) + (6-(5-1))
156 = (1+5*6)*(16-(1*5+6)) - 1*(5-6)
156 = (15+6)*(1+6) + (15-(1+5))
156 = (15-6)*(1*5*6-(1+5+6)) - (16-(6+5-1))

156*651 has only 1, 5, and 6 as nonzero digits.

156^2+1 is prime.

156^16+1 is prime.

156^6+156^5+156^4+156^3+156^2+156+1 is prime.

156 = 5^3+5^2+5+1.

156^32+1 is prime.

156^4-156-1 is prime.

156^4 + 157^4 is prime.

June 6th (157th Day of the Non-Leap Year)

Jun 6th, 6/6.

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.

157th Day of the Year.

157 = 175 - (7-1)*(7-(5-1))
157 = 517 - 51*7 - (7-(5-1))
157 = 571 - 5*71 - (51+(7-5)^(7-(5-1)))
157 = 715 - 7*15 - 71*5 - (7-5)*(57-(7+1))
157 = 751 - 7*51 - 75*1 - (7-5)*(7-(5-1))^(5-1)
157 = 1*57 + 15*7 - 5*(7-5-1)
157 = 7*51 - 75*1 - 5^(7-(5-1))
157 = (1+57) + (15+7) + 7*(15-(5-1))
157 = (7+51) + (75+1) + (17+(7-1))
157 = (1+5+7)*(1*5+7) + (7-5-1)
157 = (15+7)*(15-7) - (15+(5-1))
157 = (15-7)*(5*(5-1)) - (7-(5-1))
157 = (1+57)*(7-(5-1)) - 17
157 = (1+5*7)*(5-1) + (1+5+7)

157 = 12^2 + 12 + 1.

157^2+158^2 is prime.

151 is the prime before 157 and 163 is the prime after 157. This this is a sexy prime triplet. 157 can be called a "bisexual" prime meaning a prime p such that p+6 and p-6 are primes.

157^2 and 158^2 use the same digits.

(157^157+1)/(157+1) is prime.

2^157 contains '666', it is the smallest apocalyptic number.

June 7th (158th Day of the Non-Leap Year)

Jun 7th, 6/7.

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.

158th Day of the Year.

158 = 185 + (5-8)^(8-5*1)
158 = 518 - 51*8 + (1+5)*8
158 = 581 - 5*81 - (1+5)*8
158 = 851 - 8*51 - 85*1 - (18-1*8)^(8-5-1)
158 = 815 - 8*15 - 81*5 - (8-5)*(51-(15-8))
158 = 1*58 + 15*8 - 5*(8-(5-1))
158 = 8*51 - 85*1 - 5*(58-5^(8/(5-1)))
158 = (1+58) + (15+8) + (5-1)*(15-(5-1))
158 = (8+51) + (85+1) + (18-5)
158 = (1+5+8)*((5+1)*8/(5-1)) - 5*(8/(5-1))
158 = (1+5*8)*(8-(5-1)) - 18/(8-5)
158 = (1*5+8)*(8+5-1) + (8-5-1)
158 = (15-8)*(15+8) - (8-5*1)
158 = (1+58)*(8-5*1) - (15+(5-1))

158^2 does not contain 1, 5, or 8.

158^16+1 is prime.

158^6+158^5+158^4+158^3+158^2+158+1 is prime.

158^2+159^2+160^2+161^2+162^2+163^2 is prime.

June 8th (159th Day of the Non-Leap Year)

Jun 8th, 6/8.

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).

159th Day of the Year.

159 = 195 - (5+1)^((9-1)/(5-1))
159 = 519 - 51*9 + 9*(15-(5-1))
159 = 591 - 5*91 + (19+(5-1))
159 = 915 - 91*5 - 9*15 - ((9-1)/(5-1))*(91-(9-1))
159 = 951 - 9*51 - 95*1 - (19-5)*(5+(5+1)*(9-1)/(5-1))
159 = 1*59 + 15*9 - (9*(5-1)-1)
159 = 9*51 - 95*1 - 5*(1*5*9-(9-5*1))
159 = (1+59) + (15+9) + 5^((9-1)/(5-1))*(9-5-1)
159 = (9+51) + (95+1) + (9-5-1)
159 = (1+5+9)*(19-1*9) + (9-5-1)^((9-1)/(5-1))
159 = (1*5+9)*(15-(5-1)) + (9-(5-1))
159 = (1+59)*(9-5-1) - (9-5-1)*(15-(9-1))
159 = (15+9)*(15-9) + 5*(9-5-1)
159 = (15-9)*(9-5-1)^(9-5-1) - (9-5-1)

159^4+159+1 is prime.

159*2^159 - 1 is prime.

June 9th (160th Day of the Non-Leap Year)

Jun 9th, 6/9.

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.

160th Day of the Year.

160 = 106 + 6*(10-6^0)
160 = (601 - 60*1 - 1*(6^0))/(10-6) + (6-1)^(6^0+1^0)
160 = (1*60) + (1+60) + (10-(6+1^0))*(16-(6/(1+1^0)))
160 = (60-1)*(6/(1+1^0)) - (16+16^0)
160 = 16*(10-6) + 10^(1^6+6^0) - 16/(10-6)
160 = (1+60) + (16+0) + (0+61) + (10+6*(1^6+6^0))

Sum of the first 11 primes is 160.

160^2+1 is prime.
160^4+1 is prime.

160^2+161^2 is prime.

160^6+160^5+160^4+160^3+160^2+160+1 is prime.

160 = 2^3 + 3^3 + 5^3.

June 10th (161st Day of the Non-Leap Year)

Jun 10th, 6/10.

610 = 601 + (10-6^0)
610 = 160 + 106 +(16/(6^0+1^0))*(61-6*(10-(6+1^0)))
610 = (6*10 + 61*1^0)*(10-6) + 6*((10-6-1^0)*(6+1^0))
610 = (6+10) + (61+0) + (0+16) + (10+1^0)*(61-(10+(10-6)))
610 = (61+16)*(10-6) + 2*(160-(10-(1+0)))
610 = (61-16)*(10+6) - 10*(16-(6-1))

610 = 2*5*61 and 610*2561 only contains those digits.

There are 610 primes less than 4500.

160^8+1 is prime.

610111...111 (610 1's after 610) is prime.

3^610, 3^611, and 3^612 all have the sum number of digits.

161st Day of the Year.

161 = 116 + (6-1)*(11-(1+1))
161 = 611 - 61*1 - 6*11 - (16+6*1)^(6/(1+1+1))
161 = (1+61) + (16+1) + (1+1)*(61-(6-1)*(6-1-1))
161 = 1*61 + 16*1 + 11*6 + 6*(6/(1+1))
161 = (1+6+1)*(16+(6-1-1)) + 1*(1^6)
161 = (16+1)*(11-(1+1)) + (1+6+1)
161 = (16-1)*11 - (6-1-1)
161 = (1+61)*(6/(1+1)) - (6-1)^(1+1)
161 = (1+6*1)*(16+(1+6))

161^2+161+1 is prime.

June 11th (162nd Day of the Non-Leap Year)

Jun 11th, 6/11.

611 = 161 + 1*61 + 16*1 + (6/(1+1))*(61+(1+1)^(6-1)) + (1+1)*(61-(1+1)*(6+1)
611 = 16*61 - (11-6)*(61+6*(1+1))
611 = 61*11 - (61-1)
611 = 6*11 + 61*1 + 16*1 + (6*(1+1))*(11+(6-1-1)*(6+1))
611 = (6+1+1)*(61+16) - (11-6)
611 = (6-1-1)*(116+6^(1+1)) + 6/(1+1)
611 = (61+1)*((6-1)*(1+1)) - (6/(1+1))^(1+1)
611 = (6+11)*(6^(1+1)) - ((11-6)-(6-1-1))

611 = 47*13 and 611*4713 contains all different digits (7 digits total).

611*(6*1*1) ends in three 6's.
611*(6+1+1) ends in three 8's.

If 611 = n, then 987654321n is prime (Meaning, 987654321611 is prime).

162nd Day of the Year.

162 = 126 + 6^2*1
162 = 216 - 6*(6+2+1)
162 = 261 - 26*1 - (61+12)
162 = 612 - 61*2 - 6*12 - 16^2
162 = 621 - 6*21 - 62*1 - (261+2*(6-1))
162 = 1*62 + 16*2 + (6-2)*(2+(6-1)*(6+1))
162 = 2*61 + 26*1 + (1+6)*2
162 = (1+62) + (16+2) + (6/2)^(6-2)
162 = (2+61) + (26+1) + (1*6+2)*(1+6+2)
162 = (1*6+2)*(26-6*1) + 6/(2+1)
162 = (16+2)*(1+6+2)
162 = (16-2)*(16-(6-1)) + (1*6+2)
162 = (1+62)*(6-2-1) - (6-2-1)^(6*1/2)
162 = (1*6*2)*(16-2) - (12/(1*2))

162^3+162+1 is prime.
162^4+162+1 is prime.

162^2+163^2 is prime.

162^4+162^3+162^2+162+1 is prime.

The sum of the first 162 primes is prime.

162^64+1 is prime.

162^16+163^16 is prime.

Each baseball team plays a total number of 162 games in the regular season of MLB.

June 12th (163rd Day of the Non-Leap Year)

Jun 12th, 6/12.

612 = 621 - (6+2+1)
612 = 126 + 12*6 + 1*26 + (6-1*2)*(61+6^2)
612 = 162 + 1*62 + 16*2 + (12/(1+2))*(62+(6-1-2)^(6/(1*2))
612 = 216 + 2*16 + 21*6 + (2*(1+6))*((6-1)^2-16/2)
612 = 261 + 2*61 + 26*1 + (6+1)*(26+6/2)
612 = 6*12 + 61*2 + (26-(6-2))*(21-2*1)
612 = 2*16 + 21*6 + 2*(216+(2+1+6))
612 = (6+12) + (61+2) + (2+16) + (21+6) + 2*(1+2)^(6-1)
612 = (6+1+2)*(61+(6+1))
612 = (6*1+2)*(61+16) - (6-1*2)
612 = (6-1*2)*(26+(6-1)^2)*(6/(1*2))
612 = (61+2)*(6+1+2) - (61-16)
612 = (61-2)*((6-1)*2) + (26-(6-2))
612 = (6+12)*(26+(2+6))

612^2 does not contain a 6, 1, or 2.

612 is the second largest number such that 36*612/(36+612) is an integer.

612^2+613^2+614^2 is prime.

The concatenation 612^5//612^4//612^3//612^2//612^1//612^0 is prime.

The concatenation 612^4//612^3//612^2//612^1//612^0 is prime.

163rd Day of the Year.

163 = 136 + 3^(6/(3-1))
163 = 316 - 31*6 + (36-(6-3))
163 = 361 - 3*61 - 3*(6-1)
163 = 613 - 6*13 - 61*3 - (6*(3-1))^(6/3) - (36+(3+6))
163 = 631 - 6*31 - 63*1 - (6^3+(6/3+1))
163 = 1*63 + 16*3 + 13*(36/(3+6))
163 = 3*61 - 36*1 + (3+1)^(6-3-1)
163 = (1+63) + (16+3) + 16*(6-1)
163 = (3+61) + (36+1) + (63-1)
163 = (1+6+3)*16 + (6-3*1)
163 = (16+3)*(16/(3-1)) + (13-(3-1))
163 = (16-3)*13 - (36/(1*6))
163 = (1+63)*(6-3*1) - (31-(3-1))
163 = (1*6+3)*(1*6*3) + (6/3-1)

163^6+163^5+163^4+163^3+163^2+163+1 is prime.

163^3-163-1 is prime.

The number e^(π*√163) has 12 9's after the decimal place. (e^(π*√163) = 262537412640768743.999999999999250072597 ....)

163 = 1123 in base 5 (Note Fibonacci numbers: 1,1,2,3,5,...)

163 is the smallest number that cannot be strained using only three darts on the dart board.

If A = 1, B = 2, ... Z = 26, then IS A PRIME NUMBER = 163.

163 = 1+2*3^4 (note all different binary operations).

According to Cam McLeman, 163 is the coolest number in existence.

June 13th (164th Day of the Non-Leap Year)

Jun 13th, 6/13.

613 = 631 - 6*3*1
613 = 136 + 13*6 + 1*36 + 3*(6*(3-1)-1)^(6-1-3)
613 = 163 + 16*3 + 1*63 + (361-(16+1*6))
613 = 316 + 3*16 + 31*6 + 63*1
613 = 361 + 3*61 + 36*1 + 3*(16-(6-1))
613 = 6*13 + 61*3 + (13-(3-1))*(6/3)^(6-1)
613 = 3*16 + 31*6 + (361+3*6*1)
613 = (6+13) + (61+3) + (3+16) + (31+6) + (6*3-1)*(31-3*1)
613 = (6+1+3)*61 + (6/3+1)
613 = (6*1+3)*(61+(6+1)) + (6/3-1)
613 = (6+13)*(36-(3+1)) + (6-6/3+1)
613 = (61+3)*(6+1*3) + (36+1)
613 = (61-3)*(6+1+3) + (36-(6-3))

5999...999 (with 613 9's) is prime.

The Beatles mentioned the word "love" 613 times in their songs.

613 is three special numbers if you rotate the digits and keep them in their order. 613 is prime. 136 is triangular. 361 is a square.

164th Day of the Year.

164 = 146 + 6*(4-1)
164 = 416 - 4*16 - 41*6 + (61-(6-(4-1)))
164 = 461 - 4*61 - 46*1 - (14/(6-4))
164 = 641 - 6*41 - 64*1 - (146+(6+1)*(4-1))
164 = 614 - 6*14 - 61*4 - (1+(16-(6-1))^(6-4))
164 = 1*64 + 16*4 + 6^(6-4*1)
164 = 4*61 - 46*1 - (14+(4-1))*(1*6-4)
164 = (1+64) + (16+4) + (61+6*(4-1))
164 = (4+61) + (46+1) + 4*(16-(4-1))
164 = (1+6+4)*((6-1)*(4-1)) - (6-4-1)
164 = (1*6+4)*16 + 16/4
164 = (1+6*4)*(16-(6+4)) + (6+1)*(6-4)
164 = (16-4)*(16-(4-1)) + (16/(6-4))
164 = (16+4)*((6-4)^(4-1)) + 16/4
164 = (1+64)*(6-(4-1)) - ((6-4)^(6-1)-1)

164 = 2*2*41 and 164*2241 = 367524 (digits 2-7 shown exactly once).

164^2+164 +/- 1 are twin primes.

164^4+1 is prime.

There is no prime between 1640 and 1649.

1*64 = 16*4
1*664 = 166*4
...

164^2+165^2 is prime.

164^4+164^3+164^2+164+1 is prime.

There are 164 ways to place 5 nonattacking queens on a 5 by 8 board.

164 squares on a scrabble board do not have any word or letter multiplier.

June 14th (165th Day of the Non-Leap Year)

Jun 14th, 6/14.

614 = 641 - (6-(4-1))^((6*1*4)/(14-6))
614 = 461 + 4*61 - 46*1 - (46-1)
614 = 416 + 41*6 - 4*16 +(6*1-4)^(16/4)
614 = 164 + 1*64 + 16*4 + 14*(16+(1+6))
614 = 146 + 1*46 + 14*6 + 2*(6+14/(6-4))^(6-1*4)
614 = 6*14 + 61*4 + (6+1+4)*(6*1*4+(6-1*4))
614 = 4*16 + 41*6 + 16*(14+(1+4))
614 = (6+14) + (61+4) + (4+16) + (41+6) + (6+1+4)*(6*(14/(6-4)))
614 = (6+1+4)*(61-6*1) + (14-(1+4))
614 = (6*1+4)*61 + 16/4
614 = (6+14)*(41-(6*1+4)) - (46-(6-1)*(14-6))
614 = (61+4)*(6-1+4) + (14+(6-1)*(4-1))
614 = (61-4)*(6+1+4) - (14-(6-1-4))

614^256+1 is prime.

165th Day of the Year.

165 = 156 + (15-6)
165 = 516 - 5*16 - 51*6 + (1+6)*5
165 = 561 - 5*61- 56*1 - (1+6)*5
165 = 651 - 6*51 - 65*1 - 5*(16+(1+6))
165 = 615 - 6*15 - 61*5 - 5*(16-5)
165 = 1*65 + 16*5 + (15+1*5)
165 = 5*61 - 56*1 - (16/(5-1))*(16+5)
165 = (1+65) + (16+5) + 6*(15-(6-5+1))
165 = (5+61) + (56+1) + (6-5+1)*(16+5)
165 = (1+6+5)*((6+1)*(6-5+1)) - 15/(1*5)
165 = (16-5)*15
165 = (1+6*5)*(6-1) - (1-6-5)
165 = (1+65)*(6/(6-5+1)) - (16-5)*(15/(1*5))
165 = (16+5)*(16/(6-5+1)) - 15/(1*5)

165 = 1 + (1+2) + (1+2+3) + ... + (1+2+3+4+5+6+7+8+9).

165 = 1^2 + 3^2 + 5^2 + 7^2 + 9^2.

165^4+165^3+165^2+165+1 is prime.

June 15th (166th Day of the Non-Leap Year)

Jun 15th, 6/15.

615 = 651 - 6*(5+1)
615 = 516 + 5*16 + (15+(5-1))
615 = 561 + 56*1 - (6-(5-1))
615 = 165 + 16*5 + 1*65 + 61*5
615 = 156 + 15*6 + 1*56 + 5*(65-1) - (56/16)*(6-(5-1))
615 = 6*15 + 61*5 + 5*(16-5)*(15-(6*1+5))
615 = 5*16 + 51*6 + (16-5)*(16+5) - (6-(5-1))
615 = (6+15) + (61+5) + (5+16) + (51+6) + (1*5*6)*15
615 = (6+1+5)*51 + 15/(1*5)
615 = (6*1+5)*56 - (6*1-5)
615 = (6+15)*(6*5-1) + (16-(6-1+5))
615 = (61-5)*(6*1+5) - (16-15)
615 = (61+5)*(15-6) + (6+15)

If 615 = n, 2n-1, 4n-1, 8n-1, and 16n-1 are all prime.

615^63 + 615^61 + 615^59 + ... + 615^3 + 615^1 + 1 is prime.

166th Day of the Year.

166 = 616 - 6*16 - 61*6 + (1*6+6)
166 = 661 - 6*61 - 66*1 - (1+6)*(16-(1+6))
166 = 1*66 + 1*6*6 + (1+6/6)^6
166 = 16*6 + (1+6)*(16-6)
166 = 6*61 - 66*1 - (1+6/6)*(1+66)
166 = (1+66) + (16+6) + (1+6)*(6+6-1)
166 = (6+61) + (66+1) + (1+6/6)^(6-1)
166 = (1+6+6)*(1+6+6) - (6/(1+6/6))
166 = (1*6+6)*(16-(1+6/6)) - (1+6/6)
166 = (1+6*6)*(66-61) - (16+(6/(1+6/6)))
166 = (16+6)*(1+6) + (1*(6+6))
166 = (16-6)*16 + 66/(6+6-1)

665/166 = 5 (cancel out 6's).

166 = 2*83 and 1+6+6 = 2+8+3.

166! - 1 is prime.

frac(e^166) > frac(e^x) for any x < 166.

166^4 + 167^4 is prime.

166^2+167^2+168^2+169^2+170^2+171^2 is prime.

166 = 246 in base 8 (Note the consecutive even numbers).

June 16th (167th Day of the Non-Leap Year)

Jun 16th, 6/16.

616 = 661 - (16-(1+6))*(6-1)
616 = 166 + 16*6 + 1*66 + (1+6/6)*(6+1*6)^(1+6/6)
616 = 6*16 + 61*6 + (6+6-1)*(16-(1+6/6))
616 = 66*1 + 6*61 + (16/(1+6/6))*(16+(1+6))
616 = (6-1)^(6-1-1^6) - (16-(1+6))
616 = (6+16) + (61+6) + (66+1) + (6*6-16)*(16+(1+6))
616 = (6+1+6)*(6*6+(6+6-1)) + (16-(6+6-1))
616 = (6*1+6)*(61-(6-1)*(1+6/6)) + (6-(1+6/6))
616 = (61+6)*(16-(1+6)) + (16-(6/(1+6/6)))
616 = (61-6)*(6+6-1) + (16-(6-1))
616 = (6+16)*(16+(6*1+6))

616^2 has all different digits (including a run of 3 consecutive increasing digits at the end).

616 is a palindrome and 616*(6+1+6) = 8008 is also a palindrome.

616^2 + 617^2 + 618^2 is prime.

The concatenation 616^4//616^3//616^2//616^1//616^0 is prime.

616 = (2!)^2 + (3!)^2 + (4!)^2.

616 in Roman numerals is DCXVI (all different letters).

616 is said to be the original number of the Beast; today it is usually known as 666.

167th Day of the Year.

167 = 176 - (16-7)
167 = 617 - 61*7 - 6*17 + (71+(7+1))
167 = 671 - 6*71 - 67*1 - (17-6)
167 = 716 - 7*16 - 71*6 - (17-6)
167 = 761 - 7*61 - 76*1 - (1+6)*(1*6+7)
167 = 1*67 + 16*7 - (7+6-1)
167 = 7*61 - 76*1 - (1+7)*(16+7)
167 = (1+67) + (16+7) + 76*1
167 = (7+61) + (76+1) + (7-6+1)*(17-6)
167 = (1+6+7)*(7+6-1) - 7/(6+1)
167 = (1*6+7)^(7-6+1) - (7-(6-1))
167 = (16+7)*(1+6) + (67-61)
167 = (16-7)*(6*(6/(7-(6-1)))) + (17-6*(7-6+1))
167 = (1+67)*(6/(7-(6-1))) - (7*(6-1)+(7-6+1))
167 = (1+6*7)*(67-(7*(16-7))) - (76-71)

167^4 begins with 4 7's then has decreasing digits afterwards (167^4 = 777796321).

167^2+167+1 is prime.

There is no prime between 1670 and 1679.

167^2+168^2 is prime.

167^16 + 168^16 is prime.

1 + 1/2 + 1/3 + ... + 1/167 has a prime on its numerator.

1/167 has a 166-digit pattern (the most possible).

167 = 2*3^4+5.

Indonesia has 167 volcanoes.

Bangkok has the longest place name on Earth. Its full Thai name is 167 letters.

191^181 == 179^173 mod 167 (Note all 5 numbers are consecutive primes).

June 17th (168th Day of the Non-Leap Year)

Jun 17th, 6/17.

617 = 671 - (61-7)

617 = 716 - (16-7)*(17-6)

617 = 761 - (6-(1-7))^(7-(6-1))

617 = 167 + 16*7 + (7-(6-1))*(6*1+7)^(7+1-6)

617 = 176 + 17*6 + (16-(6*1+7))*(167-(71-17))

617 = 6*17 + 61*7 + (7+1)*(17-6)

617 = (7+16) + (71+6) + (17-6)*(61-7*(7-(6-1)))

617 = 7*16 + 71*6 + (71+(7+1))

617 = (6+17) + (61+7) + (671 - (7-1+6)^(7-(6-1))-1)

617 = (6+1+7)*(6*1*7) + (16+(1*6+7))

617 = (6+1*7)*(71-6*(71-67)) + (67-61)

617 = (61+7)*(16-7) + (61-6*1)/(17-6)

617 = (61-7)*(17-6) + (6+17)

617 = (6+17)*(16+(17-6)) - (71-67)

617^2-617-1 is prime.

617 = (1!)^2 + (2!)^2 + (3!)^2 + (4!)^2.

617 + 6*1*7 is also prime.

617^47 + 617^45 + 617^43 + ... + 617^5 + 617^3 + 617^1 + 1 is prime.

617, 617^4-2, and (617^4-2)^4-2 are all primes (only 3-digit prime with this property).

617 = 222+333+55+7 (222333557 is prime).

617 = 22+33+555+7 (22335557 is prime).

168th Day of the Year.

168 = 186 - (1+8)*(8-6)

168 = 618 - 61*8 + (1*6*8-(16-1*6))

168 = 681 - 6*81 - (8-(6-1))^(18/6)

168 = 861 - 8*61 - (6-1)*(8*(6-1)+1)

168 = 816 - 81*6 - (16/8)*(8-(6-1))^(8/(8-6))

168 = 1*68 + 16*8 - (8-1)*(8/(8-6*1))

168 = 8*61 - 86*1 - 18*(8+(6-1))

168 = (1+68) + (16+8) + (8-(6-1))*(6-1)^(8-6)

168 = (8+61) + (86+1) + (18-6)

168 = (1+6+8)*(18-6) - (16-8/(8-6))

168 = (1*6+8)*(18-6)

168 = (1+6*8)*(8-(6-1)) + (8-1)*(8-(6-1))

168 = (16+8)*(8-1)

168 = (16-8)*(16+(6-1))

168 = (1+68)*(8-6*1) + 6*(6-1)

168 + (1*6*8)  is a cube (6^3).

168 - (1*6*8) is a factorial (5!).

There are 168 primes < 1000.

168^2+168+1 is prime.

168^3+168+1 is prime.

168^3-168-1 is prime.

168 is divisible by 1, 6, and 8.

168^19 + 168^17 + 168^15 + ... + 168^5 + 168^3 + 168^1 + 1 is prime.

168 = 6*28 (product of first 2 perfect numbers).

p^168 for all known primes p have every number 0 - 9 in their decimal representation.

There are 168 hours in a week (168 = 7*24).

June 18th (169th Day of the Non-Leap Year)

Jun 18th, 6/18.

618 = 681 - (8+1)*(6+1)

618 = 168 + 16*8 + (6*1+8)*(16+(1+6))

618 = 186 + 18*6 + 18^(16/8)

618 = 861 - 8*61 + (8*6+1)*(6-1)

618 = 816 - 81*6 + (8-6)*(18-6)^(16/8)

618 = 61*8 + 6*18 + (16+1*6)

618 = 8*16 + 81*6 + (16-(18-6))

618 = (6+18) + (61+8) + (16+(6-1))*(18+(8-1))

618 = (8+16) + (81+6) + (8-(6-1))*(8+6-1)^(16/8)

618 = (6+1+8)*(8*(6-1)+1) + (18/6)

618 = (6*1+8)*(61-16) - (18-6)

618 = (6+18)*(18+1*8) - (18/(8-(6-1)))

618 = (61+8)*(18/(8-6)) - (18/6)

618 = (61-8)*(18-6) - 6*(8-(6-1))

618 = (6*1*8)*(8+6-1) - (18/6)*(8-6)

618 = (0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 + (4!)^2.

The golden ratio (sqrt(5)-1)/2 = .618033989...

618^618 contains a 12-digit long palindrome in its decimal representation (smallest number with this property).

618^31 + 618^30 + 618^29 + ... + 618^3 + 618^2 + 618^1 + 1 is prime.

169th Day of the Year.

169 = 196 - (19+(9-1))

169 = (19-6)^(9-6-1)

169 = 691 - 69*1 - (9-6)*(196-9*(6-1))

169 = 619 - 6*19 - 16*(16+(6-1))

169 = 961 - 9*61 - (19-16)^(6-1)

169 = 916 - 91*6 - (9-6)*(61+6*1)

169 = 1*69 + 16*9 - (16+1*6)*(9-6-1)

169 = 9*61 - 96*1 - (9-(6-1))*(69+(16/(9-1)))

169 = (1+69) + (16+9) + (69+(96-91))

169 = (9+61) + (96+1) + (9-6-1)

169 = (1+6+9)*(19-1*9) + (16-(1+6))

169 = (1*6+9)*(19-(9-1)) + (9-(6-1))

169 = (1+6*9)*(9-6*1) + (19-(1*6+9))

169 = (1+69)*(9-6-1) + (19+(1+9))

169 = (16+9)*(16-9) - (16-(19-1*9))

169 = (16-9)*(6*(9-(6-1))) + (19-6*(9-6))

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

169^4-169-1 is prime.

In base 10, 11, 12, and 13, 169 is 169, 144, 121, and 100, respectively (all squares).

169 is prime when turned upside down (691).

169 is another square when flipped (196).

June 19th (170th Day of the Non-Leap Year)

Jun 19th, 6/19.

619 = 691 - (69+(9-6))

619 = 169 + 16*9 + (16+1)*(6*(9-6))

619 = 196 + 19*6 + (9-6)*(69-(9-6))

619 = 961 - 9*61 + (16+(1+6))*9

619 = 916 - 91*6 + (9-6)*(91-(9-1))

619 = 6*19 + 61*9 - (16+1*6)*(9-6-1)

619 = 9*16 + 91*6 - (91-(16+9))

619 = (6+19) + (61+9) + (9-(6-1))*(169-19*(9-6-1))

619 = (9+16) + (91+6) + (6+1)*(16+(9*6+1))

619 = (6+1+9)*(19*(9-6-1)) + (19-(9-1))

619 = (6*1+9)*(19+(16+1*6)) + (9-(6-1))

619 = (6+19)^(9-6-1) - (16-(1+9))

619 = (61+9)*9 - (16-(6-1))

619 = (61-9)*(6*(9-6-1)) - (19-(6+1)*(9-6-1))

1/619 repeats after the 618th decimal digit (longest possible).

619^10 + 619^9 + 619^8 + ... + 619^3 + 619^2 + 619^1 + 1 is prime.

619^2-619-1 is prime.

619 = 6! - 5! + 4! - 3! + 2! - 1!

619 + 6*1*9 is prime.

170th Day of the Year.

170 = 107 + 7*(10-7^0)

170 = 71*(10-7) - (17+(17+10-1))

170 = 701 - 70*1 - (107+(7-1)*(70-(10+1)))

170 = 710 - 7*10 - (17+(7-1)*(10/(1+7^0)))*10

170 = 1*70 + 10^(10-7-1)

170 = (1+70) + (17+0) + (1+(10-1)^(1+7^0))

170 = (1+7+0)*(17+(10-7)) + (17-1*7)

170 = 17*(17-1*7)

170 = 17*71 - 710 - (10-7)*(107+(10/(1+7^0)))

170 = 17*(1+7) + (70/(1+7^0)-1)

170 is of the form n^2+1 (n = 13, a prime) and 170^2+1 is prime.

170^4+170+1 is prime.

171^11 - 170^11 is prime.

There are 170 4-digit twin prime pairs.

170! is the largest factorial that can be stored in double-precision floating point format.

(Google's built-in calculator can only calculate factorials up to and including 170!)

June 20th (171st Day of the Non-Leap Year)

Jun 20th, 6/20.

620 = 602 + 6*(6/(2-0))

620 = 206 + 20*6 + 6*(6+2^0)^(6/2-2^0)

620 = 260 + 2*60 + (20+(6-2))*(6-6^0)*2

620 = 6*20 + 62*(6-2) + 6*(6+2^0)

620 = 26*(2+6) + 2*206

620 = (6+20) + (62+0) + (20-6)*(20+6*(6/2))

620 = (6+2+0)*(62+(20-6)) + (20-6)

620 = (6+20)*(26-6/2) + (20+(6/2-2^0))

620 = (6*2+0)*(26*2) - (6-2-0)

620 of the first 1000 primes do not contain a 9.

620 = 0! - 1! + 2! - 3! + 4! - 5! + 6!

620^9 + 620^7 + 620^5 + 620^3 + 620^1 + 1 is prime.

620^59 + 620^57 + 620^55 + 620^53 + ... + 620^5 + 620^3 + 620^1 + 1 is prime.

171st Day of the Year.

171 = 117 + (1+1+7)*(7-1)

171 = 711 - 71*1 - 7*(71-(11-7))

171 = 711 - 7*11 - 117 - 171 - (17+1)*(11+1+7)

171 = 1*71 + 17*1 + ((11-(7+1))^(11-7)+1)

171 = 11*7 + (1+1)*(71-(11-7)*(7-1))

171 = (1+71) + (17+1) + (71+(17-1*7))

171 = (1+7+1)*(17+(1+1))

171 = (17+1)*(1+7+1) + (11-(1+1))

171 = (17-1)*11 - (7-1-1)

171 = (1+71)*(1+1) + (1+7+1)*(11-(7+1))

171^7 is the next power of 171 > 1 that contains a 7.

171 = 1+2+3+4+...+18.

There are 171 distinct values of 2^2^2^2^2^2^2^2^2^2 (depending on the parentheses).

171^16 + 172^16 is prime.

171^4+171+1 is prime.

10^171 - 171 is prime (only 2 numbers higher that also work).

If 171 = n, 2n3n5n7n11n13 is prime (Meaning, 21713171517171711117113 is prime).

France scored a record 171 goals at the 1998 World Cup.

1234567890123456... (171 digits) is prime (smallest run of digits that makes a prime).

June 21st (172nd Day of the Non-Leap Year)

Jun 21st, 6/21.

621 = 612 + (6+1+2)

621 = 162 + 1*62 + 16*2 + (6-1)*(61+12)

621 = 126 + 12*6 + (6+2+1)*(62-(21-6))

621 = 216 + 2*16 + 21*6 + (21-2*1)*(12+(2-1))

621 = 261 + 2*61 + 26*1 + (16-(6-1))*(61-(12+6))

621 = 6*21 + 62*1 + (2*216+1)

621 = 1*26 + 12*6 + ((21+2*1)^2-6)

621 = (6+21) + (62+1) + (6+2+1)*(61-2)

621 = (1+26) + (12+6) + (21+(2+1))^(6/(2+1))

621 = (6+2+1)*(62+(6+1))

621 = (6+2*1)*(61+16) + (21-6)/(2+1)

621 = (6*2+1)*(62-(21-6)) + 2*(6-1)

621 = (6+21)*(21+2*1)

621 = (62+1)*(6+2+1) + (61-(6+1))

621 = (62-1)*(2*(6-1)) + (16-(6-1))

621^19 + 621^17 + 621^15 + ... + 621^5 + 621^3 + 621^1 + 1 is prime.

621^23 + 621^21 + 621^19 + ... + 621^5 + 621^3 + 621^1 + 1 is prime.

If 621 = n, 2n3n5n7n11n13 is prime (Meaning, 26213621562176211162113 is prime).

172nd Day of the Year.

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

172 = 217 - 17*2 - (17-(7-1))

172 = 271 - 27*1 - 1*72

172 = 721 - 7*21 - (7-1)*(72-(7-2))

172 = 712 - 7*12 - (17+2)*(17+1*7)

172 = (1+72) + (17+2) + (1+7)*(1+7+2)

172 = (2+71) + (27+1) + (72-1)

172 = (1+7+2)*17 + (12-(1+7+2))

172 = (1*7+2)*(17+2) + (17-2*(1+7))

172 = (1+7*2)*(17-(7-1)) + (12-(7-2))

172 = (1+72)*(21-(17+2)) + (27-1)

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

172^3 does not contain a 1, 7, or 2.

There are 172 primes < 2^10.

172^2 + 173^2 is prime.

172^4 + 173^4 is prime.

172^4 + 172^3 + 172^2 + 172^1 + 1 is prime.

172^10 + 172^9 + 172^8 + ... + 172^3 + 172^2 + 172^1 + 1 is prime.

172^4 - 172 - 1 is prime.

7^172 is the smallest power of 7 to contain 5 consecutive identical digits.

If 172 = n, the n0123456789 is prime (Meaning, 1720123456789 is prime).

17 2's followed by 2 17's is prime.

June 22nd (173rd Day of the Non-Leap Year)

Jun 22nd, 6/22.

622 = 262 + 2*62 + (6-2)*(62-6/2)

622 = 226 + 2*26 + (6+2)*(62-(22-6/2))

622 = 22^(6-2-2) + 6*(22+2/2)

622 = (22+6)^(6-2-2) - 2*(6/2)^(2+2)

622 = 6*22 + 62*2 + 6*(62-2/2)

622 = 2*26 + 22*6 + (62+22/2)*6

622 = (6+22) + (62+2) + (6+2+2)*(26*2+2/2)

622 = (6+2+2)*62 + (6-2-2)

622 = (6*2+2)*(22*2) + 6*(2/2)

622 = (62+2)*(6+2+2) - (22-(2+2))

622 = (62-2)*(6+2+2) + (6*2+(6+2+2))

622 = (6+22)*22 + (22+2)/(6-2)

622^6 does not contain a 6 or a 2.

There are 622 primes < 10^70 of the form x^16+1.

The standard diameter of a bicycle wheel is 622 mm.

173rd Day of the Year.

173 = 137 - (1-37)

173 = 317 - 3*17 - (73+(17+3))

173 = 371 - 37*1 - 7*(17+(7-1))

173 = 731 - 7*31 - (1+7+3)*31

173 = 713 - 71*3 - (7-3-1)*(137-(1+3)*7)

173 = 1*73 + 17*3 + 7^(3-1)

173 = 3*71 - 37*1 - (7-3-1)

173 = (1+73) + (17+3) + (71+(7+1))

173 = (3+71) + (37+1) + (71-(7+3))

173 = (1+7+3)*(17-3) + (13+3!)

173 = (1*7+3)*17 + (7-3-1)

173 = (1+7*3)*(1+7) - (7-3-1)

173 = (17+3)*(13-(7-(3-1))) + (7-(3-1))

173 = (17-3)*((7-1)*(3-1)) + (17-(3-1))/3

173^2 does not contain a 1, 7, or 3.

173^3 contains 3 7's.

173*173 doesn't contain a 1, 7, or 3.

173173*173 doesn't contain a 1, 7, or 3.

173173173*173 doesn't contain a 1, 7, or 3.

...

Concatenating 173 and 1*7*3 gives the decimal digits of sqrt(3) = 1.7321... (173//21).

173^2+173+1 is prime.

173, 17, 13, and 73 are all prime.

173^2 contains exactly two different digits.

173 = 1 + 2^2 + 2^3 + 2^5 + 2^7 (prime exponents).

From the movie The Sandlot, the Beast (a ferocious dog) is said to have eaten 173 people.

173^2 and 173^3 consist of different digits (largest prime with this property).

1^3 + 7^3 + 3^3 = 371 (reverse of 173).

June 23rd (174th Day of the Non-Leap Year)

Jun 23rd, 6/23.

623 = 632 - (6*2-3)

623 = 362 + 36*2 + (23-6)*(36-(23+6))

623 = 326 + 3*26 + (62+(6+2+3))

623 = 236 + 23*6 + 3*(62+26-(2+3))

623 = 263 + 2*63 + (23-(2+3))*(6*2+(3-2))

623 = 6*23 + 62*3 + 23*(26/(2^3-6))

623 = 3*26 + 32*6 + (236+3*(36+(6-3)))

623 = (6+23) + (62+3) + 23^(6/3)

623 = (3+26) + (32+6) + (6-2)*(23*6+6/(3*2))

623 = (6+2+3)*(6*3^2) + (6+23)

623 = (6*2+3)*(23+6*3) + (26-6*3)

623 = (6+2*3)*(26*(6/3)) - (6-2-3)

623 = (6+23)*(26-3) - 2*(26-(6-2))

623 = (62+3)*(6*2-3) + (32+6)

623 = (62-3)*(6+2+3) - (23+6/2)

623 = 7*89 (all different digits, consecutive on the right hand side).

2^623 - 623^2 is prime.

With 623 people, there's a 50% chance that 7 people share a birthday.

If 623 = n, then 987654321n is prime (Meaning, 987654321623 is prime).

If 623 = n, then 123456789n is prime (Meaning, 123456789623 is prime).

623+624+625+626+627 (5 numbers ) = 3125 = 5^5 (a 5th power).

100...0900...001 (623 digits) is prime (largest known number with this property).

101^623 - 100 is prime.

174th Day of the Year.

174 = 147 + (41-14)

174 = 417 - 4*17 - 7*(4+1)^(7-4-1)

174 = 471 - 47*1 - (17+(1+7))*(14-1*4)

174 = 741 - 7*41 - (1*7*4)*(7+4-1)

174 = 714 - 71*4 - (7-4-1)^(14-(7-1))

174 = 1*74 + 17*4 + (7-4-1)^(4+1)

174 = 4*71 - 47*1 - (14-7)*(17-(1+7))

174 = (1+74) + (17+4) + (17-4)*(7-1)

174 = (4+71) + (47+1) + 17*(7-4*1)

174 = (1+7+4)*14 + (14/7+4)

174 = (1*7+4)*(17-1) - (7-4-1)

174 = (1+7*4)*(14/7+4)

174 = (17+4)*(14-(7-1)) + (14-7-1)

174 = (17-4)^(7-4-1) + (14/7+(7-4*1))

174 = (1+74)*(7-4-1) + (17+1*7)

174^4+1 is prime.

174^2+175^2 is prime.

174^3-174-1 is prime.

174^4-174-1 is prime.

The sum of the first 174 primes divides the product of the first 174 primes.

The concatenation of the first 174 primes is prime.

There are more primes in [174,174*2] than [174^2,175^2].

There are 174 twin prime pairs among the first 1000 primes.

June 24th (175th Day of the Non-Leap Year)

Jun 24th, 6/24.

624 = 642 - (24-6)

624 = 246 + 24*6 + (24-6)*(26/(4-2))

624 = 264 + 26*4 + 2^(6*2-4)

624 = 462 + 46*2 + (6+4)*(6/2+4)

624 = 426 + 42*6 - (24+6/2)*(4-2)

624 = 6*24 + 62*4 + (6*2-4)*(26+6/2)

624 = 4*26 + 42*6 + 4*(64+6/2)

624 = (6+24) + (62+4) + (6+2)*(62+4)

624 = (4+26) + (42+6) + 42*(26/(6-4))

624 = (6+2+4)*(26*(4-2))

624 = (6*2+4)*(6*2+24+6/2)

624 = (6+2*4)*(46-2) + (6*2-4)

624 = (6+24)*(26-4) - 6^(4-2)

624 = (62+4)*(6*2-4) + 24*(6-2)

624 = (62-4)*(6*2-6/(4+2)) - (6+2*4)

624^3, 624^5, 624^7, ... all end in 624.

624 is divisible by 6, 2, 4, 6*2*4, and 6+2+4.

624 = 2*2*2*2*3*13 and 2+2+2+2+3+13 = 24, a divisor of 624.

624^19 + 624^17 + 624^15 + ... + 624^5 + 624^3 + 624^1 + 1 is prime.

If 624 = n, n^2+5 and 5^n-2 are both prime.

There are 624 ways to get a 4-of-a-kind in poker.

175th Day of the Year.

175 = 157 + (7-1)*(7-(5-1))

175 = 517 - 5*17 - (157+(15-1*5)^(7-5))

175 = 571 - 57*1 - (7-(5-1))*(157-(5-1)*(7+5-1))

175 = 751 - 7*51 - (7-5)*(157+(1+7)*5)

175 = 715 - 71*5 - (5*7+(7-5))*5

175 = 1*75 + 17*5 + 5*(7-(5-1))

175 = 5*71 - 57*1 - (7-(5-1))*(57-(7-5)^(5-1))

175 = (1+75) + (17+5) + 7*(7+5-1)

175 = (5+71) + (57+1) + (5*7+(5+1))

175 = (1+7+5)^(1*7-5) + (57-51)

175 = (1*7+5)*15 - (15/(7-(5-1)))

175 = (1+7*5)*5 - (17-(1*7+5))

175 = (1+75)*(7-5*1) + (17+(7-1))

175 = (17+5)*(15-7) - (7-5-1)

175^5 is the next power of 175 > 1 that contains a 1.

175^4+175^3+175^2+175^1+1 is prime.

7^175 is the smallest power of 7 that contains 6 consecutive identical digits.

1^1 + 7^2 + 5^3 = 175.

175^5 - 174^5 is prime.

175^6 +/- 6 are consecutive primes (smallest number with this property).

175^3 has only odd digits.

June 25th (176th Day of the Non-Leap Year)

Jun 25th, 6/25.

625 = 25^(6/(5-2))

625 = 652 - (6/2)^(5-2)

625 = 256 + 25*6 + (5-2)*(56+(6*2+5))

625 = 265 + 2*65 + (26-6/2)*(2*5)

625 = 526 + 5*26 - (6+25)

625 = 562 + 56*2 - (6*2-5)^2

625 = 6*25 + 62*5 + (6*5/2)*(6*2-(6-5))

625 = 5*26 + 52*6 +(6/2)*(65-(6-2))

625 = (6+25) + (62+5) + (6+25)*(6*2+5)

625 = (5+26) + (52+6) + (6/2+5)*(62+5)

625 = (6+2+5)*(52-(6-2)) - (6-2-5)

625 = (6+2*5)*(52-(6+2+5)) - (6-2-5)

625 = (6*2+5)*(6^2) + (6+2+5)

625 = (6+25)*(26-5) - (6+2+5)*2

625 = (62+5)*(6+5-2) + (26-(6-2))

625 = (62-5)*(6+5) - 2*(6-5)

625^n always ends in '0625' for all n > 0.

625^11 + 625^9 + 625^7 + 625^5 + 625^3 + 625^1 + 1 is prime.

625 is a Friedman number since 625 = 5^(6-2).

176th Day of the Year.

176 = 167 + (16-7)

176 = 617 - 6*17 - (17-7*(7-(6-1)))*(167-6*(16-7))

176 = 671 - 67*1 - (17-(1*7+6))*(167-6*(17-1*7))

176 = 761 - 7*61 - (167-(16-7))

176 = 716 - 71*6 - (17+(7-(6-1)))*6

176 = 1*76 + 17*6 - (7-(6-1))

176 = 6*71 - 67*1 - (16-(1*7+6))*61

176 = (1+76) + (17+6) + 1*76

176 = (6+71) + (67+1) + (1*7*6-(17-6))

176 = (1+7+6)*(1*7+6) - (67-61)

176 = (1*7+6)^(7-(6-1)) + 7*(17-16)

176 = (1+7*6)*(17-(1*7+6)) + (16-(7-(6-1)))

176 = (17+6)*7 + (17-(7-(6-1)))

176 = (17-6)*16

176^n ends in 76 for all n > 0.

176^2 + 1 is prime.

176^16 + 1 is prime.

176^2 + 176 +/- 1 are twin primes.

176^3 - 176 - 1 is prime.

176^16 + 177^16 is prime.

The 176th and 177th prime are twin primes.

1 + 1/3 + 1/5 + 1/7 has 176 on the numerator.

176^7 - 175^7 is prime.

(1+7+6) can be partitioned in 176 ways.

A cake can be cut into 176 pieces with just 10 cuts.

June 26th (177th Day of the Non-Leap Year)

Jun 26th, 6/26.

626 = 662 - 6^2

626 = 266 + 2*66 + (6+6)*(26-(6+6/6))

626 = 266 + 26*6 + (6*2)*(6*2+(6-6/6))

626 = 6*26 + 62*6 + 2*(6+6/6)^2

626 = 66*2 + 6*6*2 + 266 + 6*26

626 = (6+26) + (62+6) + (26-6/2)^2 - (6-6/2)

626 = (26-6/6)^2 - (6/6)

626 = 26^2 - 2*(26-6/6)

626 = (66+2) + (6+2+6) + (6+26)*(6+2+6+6/2)

626 = (6+2+6)*((6+6/2)*(6-6/6)) - 6*6/(6+6/2)

626 = (6*2+6)*(6+26) + (26-6/6)*2

626 = (6+26)*(26-6) - (6+2+6)

626^10 + 626^9 + 626^8 + 626^7 + 626^6 + 626^5 + 626^4 + 626^3 + 626^2 + 626^1 + 1 is prime.

1062601 is a prime (Note 626 is also a palindrome).

177th Day of the Year.

177 = 771 - 7*71 - (17+(17-7/7)*(7-1-7/7))

177 = 717 - 7*17 - 1*7*7 - (7+7-7/7-1)*(17+1*7+7)

177 = 1*77 + 17*7 - (17+7/7+1)

177 = 7*71 - 77*1 - (17-(1*7+7))^(7-(1+7/7))

177 = (1+77) + (17+7) + (77-(1+7/7))

177 = (7+71) + (77+1) + 7*(17-(1*7+7))

177 = (1+7+7)*(17-(7-1)) + (17-(7-7/7-1))

177 = (1*7+7)*(7+7-1) - (7-(1+7/7))

177 = (1+7*7)*(17-(1*7+7)) + (17+(17-1*7))

177 = (17+7)*7 + (17-(1+7))

177 = (17-7)*17 + 7*(7/7*1)

177^5 is the next power of 177 > 1 to have a 7.

177^3+177+1 is prime.

177^4+177^3+177^2+177^1+1 is prime.

177 becomes a palindrome through the 'Reverse-And-Add' process after 15 iterations (the smallest number to have exactly 15 iterations).

177^4 - 177 - 1 is prime.

177^5 - 177 - 1 is prime.

At the 177th decimal digit of pi, three 5's appear.

There are more primes between [177, 2*177] than between [177^2, 178^2].

If 177 = n, then 2n3n5n7n11 is prime (Meaning, 217731775177717711 is prime).

(1!)^2 + (2!)^2 + (3!)^2 + ... + (177!)^2 is prime.

177 = 7^2 + 2^7.

June 27th (178th Day of the Non-Leap Year)

Jun 27th, 6/27.

627 = 267 + 26*7 + 178 (178th Day of the Year)
627 = 267 + (76+(7+6)) + 26*7
627 = 276 + 27*6 + (7+2)*(27-6)
627 = 672 - (7-2)*(7+2)
627 = 726 - 7*26 + (62+7*6/2)
627 = 762 - 76*2 + (7*2+6/2)
627 = 6*27 + 62*7 + (6*(7-2)+(2-(7-6)))
627 = 7*26 + 72*6 + (27-2*7)
627 = (6+27) + (62+7) + (27-6)*(7-2)^2
627 = (7+26) + (72+6) + (6*2)*(27+2^(6-2))
627 = (6+2+7)*(6*7) - (7-(6-2))
627 = (6*2+7)*(6+27)
627 = (6+2*7)*(6*(7-2)) + (6/2)^(2+7-6)
627 = (62+7)*(2+7) + (27-(7*6/2))
627 = (62-7)*(6-2+7) + (27-(7-2))

627^5 is the next power of 627 that contains a 7.

627 = 3*11*19 and 6+27 = 3+11+19.

20 can be partitioned in 627 different ways.

178th Day of the Year.

178 = 187-(17-8)
178 = 718 - 71*8 + 7*(8^(1/((17-8)-(7-1))))
178 = 781 - 7*81 - (7-1)^(8-(7-1))
178 = 817 - 81*7 - 8*(17-8)
178 = 871 - 8*71 - (17-(7-1)*(8-(7-1)))^(17-(7*(8-(7-1))))
178 = 1*78 + 17*8 - 18*(8-(7-1))
178 = 8*71 - 87*1 - (871-8*71)
178 = (1+78) + (17+8) + (18+1*7*8)
178 = (8+71) + (87+1) + (18-7)
178 = (1+7+8)*(18-7) + (8-(7-1))
178 = (1*7+8)*(18-(7-1)) - (8-(7-1))
178 = (1+7*8)*(18/(7-1)) + (18-1*8)
178 = (17-8)*(18+(8-(7-1))) - (8-(7-1))
178 = (1+78)*(8-(7-1)) + ((17-8)+(18-7))

178^5 begins with 178.

178 = 2*89 (289-178 = 111 -- repeating digit)

June 28th (179th Day of the Non-Leap Year)

Jun 28th, 6/28.

628 = 682 - 2*(6/2)^((8-2)/(8-6))
628 = 862 - 8*62 + (286-8*6/2)
628 = 826 - 8*26 + (8*2-6)
628 = 286 + 28*6 + 6*(26+6/2)
628 = 268 + 26*8 + 2*(82-6)
628 = 6*28 + 62*8 - (8-2)^(8-6)
628 = 8*26 + 82*6 - (82-(8+2))
628 = (6+28) + (62+8) + 682 - 2*(82-6/2)
628 = (8+26) + (82+6) + (28-6)*(26-6/2)
628 = (6+2+8)*(28+(8+6/2)) + (6*2-8)
628 = (6+28)*(26-(2+6)) + 2^(8/2)
628 = (62+8)*(6*2-6/2) - (6-8/2)
628 = (62-8)*(8*2-8/2) - (6*8-28)
628 = (6*2+8)*(28+6/2) + (6*2-8/2)
628 = (6+2*8)*(26+6/2) - (8*2-6)

June 28th is my birthday :)

628 = 157*2*2 and 628*15722 contains all different digits (7 total).

628 is the concatenation of the first two perfect numbers 6 and 28. So, 6/28 is mathematically a "perfect" day.

6 and 28 are the first two perfect numbers. The third is 62*8 = 496.

628^8 + 629^8 is prime.
628^32 + 629^32 is prime.

628^43 + 628^41 + 628^39 + ... + 628^3 + 628^1 + 1 is prime.

628 is the highest known even number that is not the sum of two non-Ramanujan primes.

628^7 + 628^5 + 628^3 + 628^1 + 1 is prime.

The smallest prime > 2^628 is a twin prime (628 is the second largest known exponent with this property).

Happy Tau Day! (Tau = 2*pi = 6.2831853...)

179th Day of the Year.

179 = 197 - 9*(9-7*1)
179 = 719 - 71*9 + (91+(9-1))
179 = 791 - 7*91 + (19-7*(9-7))^(9-7*1)
179 = 971 - 9*71 - (9-(7-1))*(17*(9/(9-(7-1))))
179 = 917 - 91*7 - (91+(9+1))
179 = 1*79 + 17*9 - (79-(17+9))
179 = 9*71 - 97*1 - 3*(19-(9-1))^(9-7)
179 = (1+79) + (17+9) + (97-(19-7)*(1*9-7))
179 = (9+71) + (97+1) + (9-(7+1))
179 = (1+7+9)*(19-(9-1)) - (9-7)^(9-(7-1))
179 = (17+9)*(19-(9-7)*(7-1)) - (9-(7-1))
179 = (17-9)*(19+(9-(7-1))) + (17-7*(9-7))
179 = (1+79)*(9-7^1) + (17+(9-7*1))
179 = (1*7+9)*(19-(9-1)) + (9-(7-1))
179 = (1+7*9)*(9-(7-1)) - (19-(7-1))

179^2 uses 0,1,2,3,4 only once.

179^3 = 5735339 (Note: no even numbers).

179, 17, 19, and 79 are all prime.

179 is the 41st prime. (41 is my favorite number (for other reasons)...this is a neat coincidence that my birthday is on the 41st prime day of the year!)

1/179 repeats after 178 decimal digits (the longest run possible).

There are 179 days of the year that are even.

9//10//11//12//13//... (for 179 consecutive numbers) is prime.

The maximum number of games a Major League Baseball team could play is 179.

179 = (17*9) + (17+9).

Between the 3 in 3.14159... And the 179th digit of pi, the numbers 0, 3, 4, 5, and 9 all appear the same number of times (18 times each).

June 29th (180th Day of the Non-Leap Year)

Jun 29th, 6/29.

629 = 692 - (62+(9-(6+2)))
629 = 269 + 26*9 + (9-2)*(9*2)
629 = 296 + (6^2+(9-(6+2)))*9
629 = 962 - 9*62 + (9+6)^2
629 = 926 - 92*6 + (9+6)*(6+2+9)
629 = 6*29 + 62*9 + (92+(9+2))
629 = 9*26 + 92*6 + (69+(6+2)*(2+9))
629 = (6+29) + (62+9) + (9+26) + (92+6) + (9*2-(6+2))*(62-(29-6))
629 = (6+2+9)*(26+(9+2))
629 = (6+2*9)*26 + (6*2-(9-2))
629 = (6*2+9)*29 + (6-2)*(9-(6-2))
629 = (6+29)*(2*9) - (9-(6+2))
629 = (62+9)*9 + (6/2+(9-2))
629 = (62-9)*(9+6/2) - (9*2-(9+2))

629^27 + 629^25 + 629^23 + ... + 629^5 + 629^3 + 629^1 + 1 is prime.

180th Day of the Year.

180 = 108 + 8*(10-1^0)
180 = 18*10
180 = 81*(10-8) + 18
180 = 81*8 - 810 - (8+(18-(8-1)*(1+8^0)))*(18+(10-8+1)*(8-1))
180 = 81*8 - 8*18 - 18^(10-8)
180 = (1+80) + (18+0) + 81
180 = (1+8+0)*(18+(10-8))

180^1+1 is prime.
180^2+1 is prime.
180^4+1 is prime.

180^3+180+1 is prime.

180^6+180^5+180^4+180^3+180^2+180+1 is prime.

The 5th derivative of x^(x^x) at x = 1 is 180.

180 has more divisors than any number below it.

180 = 19+23+29+31+37+41 (6 cons primes).
180 = 11+13+17+19+23+29+31+37 (8 cons primes).

180° is halfway around a circle.

180 is the maximum possible score you can get at darts with one dart.

June 30th (181st Day of the Non-Leap Year)

Jun 30th, 6/30.

630 = 603 + 3^(6-3)

630 = 306 + 30*6 + (6*(3-3^0))^(6/3)

630 = 360 + 3*60 + (6+3)*((6/3)*30/6)

630 = 6*30 + 3*60 + 30*(6+3)

630 = 63*(6+3) + (6+3)*(6+3^0)

630 = 36*(3*6) - (30-6*(6/3))

630 = 63*(6*3) - 603 + (6+3)*(6+30/6)

630 = 63*(6-3) + (30-(6+3))^(6/3)

630 = (6+3+0)*(60+(6+3+63^0))

630 = (6+30)*(6*3) - (36/(6/3))

630 = 63*((6/2)*(30/6))

630 = 1+2+3+4+...+35.

181st Day of the Year.

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

181 = 811 - 8*11 - 118 - 8*(18+(8-1)*(11-(8-1-1))

181 = 811 - 81*1 - (8+1)*(81-(18+1+1))

181 = 1*81 + 18*1 + (1+81)

181 = 11*8 + (11-8)*(18+(11+(1+1)))

181 = (1+81) + (18+1) + (81-1)

181 = (11+8) + 11*8 + (1+1)*(18+(18+1))

181 = (1+8+1)*18 + ((11-8)-(1+1))

181 = (1*8+1)*(18+1) + (1+8+1)

181 = (18-1)*(1+8+1) + (18-(8-1))

181 is a palindromic prime.

181-(1+8+1) = 171 is a palindrome.

181+(1+8+1) = 191 is prime.

181 is a Natural Lucky number.

{Start with 1, 2, 3, 4, 5, 6, ... and delete every 2nd term}

{Now have 1, 3, 5, 7, 9, 11, 13, 15, 17, ... and delete every 3rd term}

{Now have 1, 3, 7, 9, 13, 15, 19, 21, 25, 27, ... and delete every 4th term}

{Now have 1, 3, 7, 13, 15, 19, 25, 27, ... delete every 5th term}

{and so on... 181 remains in the sequence.}

1/181 has 180 digits before it repeats (most it can have).

181 = 14^2 - 14 - 1. And 181^2 - 181 - 1 is prime.

181 is found in 6666 sequences in the OEIS (as of July 21, 2014).

There are 181 digits in 111!

The sum of the first 181 primes - 181 is prime.

777...777181777...777 (181 total digits) is prime.

181 pennies weigh within one penny of a pound.

The year Al Gore won the Nobel Peace Prize, 181 candidates were nominated.

Every number > 181 can be expressed as 8*x + 27*y for some nonnegative x and y.

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