# 15

This number is a composite. If n is greater than 15, then there is at least one number between n and 2n which is the product of three different primes. [Sierpinski] The number of trees with 15 vertices is prime. 215 - 51 is prime. The smallest multi-digit integer I such that 4*I+1 and 4*I-1 are both primes. [Russo] There are exactly 15 palindromic primes of length three. [Patterson] 15 is the smallest number which is product of two distinct odd primes. [Capelle] !15 - 1 is prime. Note that !15 represents subfactorial 15. [Gupta] 15 is the only number m such that m = π(π(m)!2). [Firoozbakht] 15 is the smallest emirpime. [Post] 15 is the (1+5)th Lucky Number. [Post] (F015 + F115 + F215 + F315 + F415) and (F015 + F115 + F215 + F315 + F415 + 6) are sexy primes. Note that the first five Fermat numbers are all prime. [Wesolowski] 15!-14!+ ... +3!-2!+1! is prime. [Silva] The only known natural number n > 0 such that the sum of the five known Fermat primes raised to the power n is prime. Curiously, it is the product of the first two Fermat primes. [Capelle] π(15) = 1 + 5. [Kumar] The number of supersingular primes, i.e., primes that divide the order of the Monster group (an algebraic construction with 246 * 320 * 59 * 76 * 112 * 133 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 elements). [Capelle] 15π is closer to a prime than any multiple of π below it. [Honaker] The only known number n such that adding to it each of the first six powers 2^n, (where n = 1 to 6), the result is always a prime. [Loungrides]

(There are 10 curios for this number that have not yet been approved by an editor.)