Answer to Question #90680 in Combinatorics | Number Theory for Vasiliy

Question

What are sexy prime numbers?

Answer 1

Sexy primes are pairs of prime numbers of the form (p, p+6). They are called ’sexy primes’ since ‘sex’ is the Latin word for six. The first few sexy prime pairs are: (5,11), (7,13), (11,17), (13,19), (17, 23).

There are also exist sexy triplets, quadruplets and a single sexy quintuplet.

The first few sexy triplets (numbers of the form (p, p+6, p+12) and each of them is prime but p+18 is not prime) are (7, 13, 19), (17, 23, 29), (31, 37, 43), …

The first few sexy quadruplets are (11, 17, 23, 29), (41, 47, 53, 59), (61, 67, 73, 79), …

There is only a single sexy quintuplet (5, 11, 17, 23, 29).

References:

1. Weisstein, Eric W. "Sexy Primes." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SexyPrimes.html