

A094343


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


10



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
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OFFSET

1,1


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


LINKS

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


FORMULA

a(2*n1)=A023200(n). a(2*n)=A046132(n).


EXAMPLE

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


MATHEMATICA

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


PROG

(PARI) isok(n) = (isprime(n) && isprime(n+4))  (isprime(n4) && isprime(n)); \\ Michel Marcus, Aug 26 2013


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.
Sequence in context: A010625 A011322 A140382 * A239126 A179873 A080457
Adjacent sequences: A094340 A094341 A094342 * A094344 A094345 A094346


KEYWORD

easy,nonn


AUTHOR

Gerard Schildberger, Jun 04 2004


EXTENSIONS

Description was corrupted up during editing; correct description restored Aug 21 2005.
a(3) = 7 added by Vincenzo Librandi, May 06 2016


STATUS

approved



