519

519 = 3 x 173.

519 is the sum of three consecutive primes: 167 + 173 + 179 = 519.

519 is the number of trees on 15 vertices with diameter 5.

519 is a number that cannot be written as a sum of three squares.

Telephone area code 519 is in Ontario, Canada.

Source: What's Special About This Number?

33

33 = 3 x 11.

33 is the smallest integer that cannot be expressed as a sum of different triangular numbers (1, 3, 6, 10, 15, 21, 28, . . . ).

The smallest run of three consecutive integers that are semi-primes (the product of two primes) begins with 33: 33 = 3 x 11, 34 = 2 x 17, 35 = 5 x 7.

33 is the smallest number with nine representations as a sum of three primes: 33 = 2 + 2 + 29 = 3 + 7 + 23 = 3 + 11 + 19 = 3 + 13 + 17 = 5 + 5 + 23 = 5 + 11 + 17 = 7 + 7 + 19 = 7 + 13 + 13 = 11 + 11 + 11.

A normal human spine has 33 vertebrae.

Source: 33 Mysteries

307

307 is a prime number.

307 is the smallest number that is the sum of any set of primes containing all digits: 2 + 5 + 41 + 67 + 83 + 109 = 307.

307² = 94249, which is a palindromic number.

307 is a prime of the form n² + n + 1, for n = 17.

307 is the telephone area code for the state of Wyoming.

Source: Number Gossip

86

86 = 2 x 43.

86 is conjectured to be the largest number n such that 2ⁿ (in decimal) doesn't contain a 0.

86 is 222 in base 6.

86 arises in the sequence generated by starting with 1, then adding 4 and reversing the digits to get the next term: 1, 5, 9, 13, 35, 57, . . . , 28, 86, 72, . . .

86 is the atomic number of radon.

In the TV series and movie Get Smart, the principal character Maxwell Smart was known as Agent 86.

Source: Number Gossip

122

122 = 2 x 61.

122 has a representation as a sum of two squares: 122 = 1² + 11².

The square of 122 minus each of 122's prime factors squared is a prime: 122² - 2² - 61² = 11159.

122 is the smallest sum of two non-consecutive factorials of distinct primes: 2! + 5! = 2 + 120 = 122.

122 is the number of integer partitions of 22 into distinct parts.

In the year 122, Roman Emperor Hadrian ordered the building of a 72-mile wall across northern Britain.

Source: Prime Curios!

18

18 = 2 x 3²

18 has a representation as a sum of two squares: 18 = 3² + 3².

18 = 9 + 9 and 81 = 9 x 9.

18 is the only number that is twice the sum of its digits: 18 = 2(1 + 8).

The cube together with the 4th power of 18 use all the digits 0 to 9 once each: 18³ = 5832 and 18⁴ = 104,976.

18 is the smallest number with two representations as a sum of three primes: 18 = 2 + 3 + 13 = 2 + 5 + 11.

18 is the sixth Lucas number.

18 is the number of integer partitions of 13 into distinct parts.

18 is 33 in base 5.

18 is the voting age in many countries.

Source: Number Gossip

1726

1726 = 2 x 863.

1726 is 23401 in base 5, with each digit from 0 to 4 represented once.

The 1726th prime is 14741, which is palindromic.

Six distinct permutations of the digits of 1726 give primes: 1627, 2617, 2671, 6217, 6271, and 7621.


Mathematician Nicolaus II Bernoulii, son of Johan and older brother of Daniel, died on July 31, 1726, in St. Petersburg, Russia.

Source: MacTutor History of Mathematics Archive