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
B4 was estimated by Marek Wolf in
1996 as
- B4 ≈ 1.1970449
This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted
B4.
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