# Cousin prime

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 below 1000 are (also see

Sloane's

A023200 and

A046132):

- (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 441), (457, 461), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 891), (883, 887), (907, 911), (937, 941), (967, 971)

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}.