A111981 -id:A111981 - cp's OEIS frontend

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

Gerard Schildberger, Jun 04 2004

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

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

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

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.

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

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

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

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

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

A088762 Numbers n such that (2n-1, 2n+3) is a cousin prime pair.

Original entry on oeis.org

2, 4, 7, 10, 19, 22, 34, 40, 49, 52, 55, 64, 82, 97, 112, 115, 139, 154, 157, 175, 190, 199, 220, 229, 232, 244, 250, 307, 322, 337, 370, 379, 385, 412, 427, 430, 439, 442, 454, 469, 484, 505, 544, 547, 607, 640, 649, 652, 712, 715, 724, 742, 745, 775, 784, 790

Offset: 1

Ray Chandler, Oct 26 2003

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..4200
Eric Weisstein's World of Mathematics, Cousin Primes

Essentially the same as A111981.

Cf. A087679, A088764, A088766, A088768, A088770.

[n: n in [1..1000] |IsPrime(2*n-1) and IsPrime(2*n+3)]; // Vincenzo Librandi, May 19 2017

Select[Range[2000],PrimeQ[2*#-1]&&PrimeQ[2*#+3]&] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

a(n) = (A087679(n)-1)/2 = (A023200(n)+1)/2 = (A046132(n)-3)/2.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions