A094343 List of pairs of primes (p, q) with q - p = 4.

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

Offset: 1

Author

Gerard Schildberger, Jun 04 2004

Keywords

• easy
• nonn

Comments

The two primes p and p+4 are not necessarily consecutive primes (for that, see A111980).

The pairs are listed in order, sorted by their smallest member. - N. J. A. Sloane, Dec 27 2019

Examples

			The pairs are (3,7), (7,11), (13,17), etc.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Cousin Primes

Crossrefs

Almost identical to A111980.

Union of A023200 and A046132.

Cf. twin primes (A001097).

See also A000040, A111981, A001097.

For a gap of 6 (which initially is very common) see A140546.

Programs

Mathematica

Flatten[{#,#+4}&/@Select[Prime[Range[200]],PrimeQ[#+4]&]] (* Harvey P. Dale, Apr 13 2011 *)

PARI

isok(n) = (isprime(n) && isprime(n+4)) || (isprime(n-4) && isprime(n)); \\ Michel Marcus, Aug 26 2013

Formula

a(2*n-1)=A023200(n). a(2*n)=A046132(n).

Extensions

Description was corrupted up during editing; correct description restored Aug 21 2005.

a(3) = 7 added by Vincenzo Librandi, May 06 2016