Inclusion–exclusion principle

In mathematics, cousin primes are 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 Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland. and Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland. in OEIS) below 1000 are:

(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, 443), (457, 461), (463,467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971)

Properties

The only prime belonging to two pairs of cousin primes is 7. One of the numbers n, n+4, n+8 will always be divisible by 3, so n = 3 is the only case where all three are primes.

Template:As of the largest known cousin prime was (p, p + 4) for

p = (311778476 · 587502 · 9001# · (587502 · 9001# + 1) + 210)·(587502 · 9001# − 1)/35 + 1

where 9001# is a primorial. It was found by Ken Davis and has 11594 digits.

The largest known cousin probable prime is

474435381 · 2⁹⁸³⁹⁴ − 1

474435381 · 2⁹⁸³⁹⁴ − 5.

It has 29629 digits and was found by Angel, Jobling and Augustin. While the first of these numbers has been proven prime, there is no known primality test to easily determine whether the second number is prime.

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, called Brun's constant for cousin primes, with the initial term (3, 7) omitted:

$B_4=(\frac{1}{7}+\frac{1}{11})+(\frac{1}{13}+\frac{1}{17})+(\frac{1}{19}+\frac{1}{23})+\cdots .$

Using cousin primes up to 2⁴², 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.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.