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.
n# notation
As used in this article, n# stands for the product 2 · 3 · 5 · 7 · … of all the primes ≤ n.
Types of groupings
Sexy prime pairs
The sexy primes (sequences
A023201 and
A046117 in OEIS) below 500 are:
As of May 2009 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 prime triplets
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 (
A046118,
A046119,
A046120):
As of 2013 the largest known sexy prime triplet, found by Ken Davis had 5132 digits: