Sexy Primes

Sexy Primes
Basic Info
Discovered by
Number of
Description	p and p+6 are both primes.
First Few	(5, 11), (7, 13), (11, 17), (13, 19), (17, 23), (23, 29)

Sexy primes are numbers wherein two numbers have a gap of six. They are called that because sex is Latin for six.

In addition to sexy primes, if there is a prime number in between them (usually a twin prime or a cousin prime, where it is the lower prime), the sexy prime is part of the prime triplet.

Examples

5 and 11 are sexy primes.

23 and 29 are sexy primes.

41 and 47 are sexy primes.

251 and 257 are sexy primes.

Largest Known Sexy Primes

The largest known sexy prime pair was found by Serge Batalov in April 2022 with 51,934 digits and the primes are:
p = 11922002779 x (2¹⁷²⁴⁸⁶ - 2⁸⁶²⁴³) + 2⁸⁶²⁴⁵ - 5
p + 6 = 11922002779 x (2¹⁷²⁴⁸⁶ - 2⁸⁶²⁴³) + 2⁸⁶²⁴⁵ + 1

See Also

• Twin Primes, wherein the gap is two.
• Cousin Primes, wherein the gap is four.
• Prime Quadruplet, when the prime term is p, p+2, p+6, p+8