# 15

This number is a composite.

If *n* is greater than 15, then there is at least one number between *n* and 2*n* which is the product of three different primes. [Sierpinski]

The number of trees with 15 vertices is prime.

The Fascinating World of Prime Numbers: 15 Fun and Amazing Insights. [Prongo]

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]

(F_{0}^{15} + F_{1}^{15} +
F_{2}^{15} + F_{3}^{15} +
F_{4}^{15}) and (F_{0}^{15}
+ F_{1}^{15} + F_{2}^{15} +
F_{3}^{15} + F_{4}^{15} +
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 2^{46} *
3^{20} *
5^{9} *
7^{6} *
11^{2} *
13^{3} * 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 only 15 invertible primes that consist of distinct digits. [Gupta]