In mathematics, a cousin prime is a pair of prime numbers that differ by four; compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences A023200 (http://www.research.att.com/projects/OEIS?Anum=A023200) and A046132 (http://www.research.att.com/projects/OEIS?Anum=A046132) in OEIS) below 1000 are:

It follows from the first Hardy-Littlewood conjecture that cousin primes have the same asymptotic density as twin primes. An analogy of Brun's constant for twin primes can be defined for cousin primes, with the initial term (3, 7) omitted:

Using cousin primes up to 2^{42}, the value of B_{4} was estimated by Marek Wolf in 1996 as

B_{4} ≈ 1.1970449

This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted B_{4}.

In mathematics, a sexy prime is a pair of prime numbers that differ by six; compare this with twin primes, pairs of prime numbers that differ by two, and cousinprimes, pairs of prime numbers that differ by four.

Like twin primes, sexy primes can be extended to larger constellations.

Sexy prime quadruplets can only begin with primes ending in a 1 in their decimal representation (apart from 5); the sexy prime quadruplets (sequences A046121, A046122, A046123 and A046124 in OEIS) below 1000 are:

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