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 =  ((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]
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