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 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]
(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 only 15 invertible primes that consist of
distinct digits. [Gupta]
Gauss, at age 15, began to study the distribution of prime numbers
by counting them in ranges, such as consecutive thousands.