Sexy prime

In mathematics, sexy primes are prime numbers that differ from each other by six. For example, the numbers 5 and 11 are both sexy primes, because they differ by 6. If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime triplet.

The term "sexy prime" stems from the Latin word for six: sex.

As used in this article, n# stands for the product 2 · 3 · 5 · 7 · … of all the primes ≤ n.

The sexy primes (sequences   and   in OEIS) below 500 are:

As of May 2009^[update] the largest known sexy prime was found by Ken Davis and has 11,593 digits. The primes are (p, p+6) for

9001# = 2×3×5×...×9001 is a primorial, i.e., the product of primes ≤ 9001.

Sexy primes can be extended to larger constellations. Triplets of primes (p, p + 6, p + 12) such that p + 18 is composite are called sexy prime triplets. Those below 1000 are ( ,  ,  ):

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