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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]