A023271 Primes p such that p, p+6, p+12, p+18 are all primes.

5, 11, 41, 61, 251, 601, 641, 1091, 1481, 1601, 1741, 1861, 2371, 2671, 3301, 3911, 4001, 5101, 5381, 5431, 5641, 6311, 6361, 9461, 11821, 12101, 12641, 13451, 14621, 14741, 15791, 15901, 17471, 18211, 19471, 20341, 21481, 23321, 24091, 26171, 26681

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Smallest member of a "sexy" prime quadruple.

For n > 1, a(n) ends in 1. - Robert Israel, Jul 16 2015

The only sexy prime quintuple corresponding to (p, p+6, p+12, p+18, p+24) starts with a(1) = 5, so this quintuple is (5, 11, 17, 23, 29) (see Wikipedia link and A206039). - Bernard Schott, Mar 10 2023

Links

• Matt C. Anderson and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..100 from Matt C. Anderson)
• Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes. - _N. J. A. Sloane_, Mar 07 2021]
• Wikipedia, Sexy prime.

Crossrefs

Cf. A023201, A046117, A046122, A046123, A046124, A206039.

Programs

Magma

[p: p in PrimesInInterval(2, 1000000) | forall{i: i in [ 6, 12, 18] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 15 2015

Maple

for a to 2*10^5 do
if `and`(isprime(a), isprime(a+6), isprime(a+12), isprime(a+18))
then print(a);
end if;
end do;
# code produces 109 primes
# Matt C. Anderson, Jul 15 2015

Mathematica

Select[Prime[Range[1000]], PrimeQ[# + 6] && PrimeQ[# + 12] && PrimeQ[# + 18] &] (* Vincenzo Librandi, Jul 15 2015 *)
(* The following program uses the AllTrue function from Mathematica version 10 *) Select[Prime[Range[3000]], AllTrue[# + {6, 12, 18}, PrimeQ] &] (* Harvey P. Dale, Jun 06 2017 *)

PARI

main(size)=my(v=vector(size),i,r=1,p);for(i=1,size,while(1,p=prime(r);if(isprime(p+6)&&isprime(p+12)&&isprime(p+18),v[i]=p;r++;break,r++))); v \\ Anders Hellström, Jul 16 2015

Extensions

Edited by N. J. A. Sloane, Aug 04 2009 following a suggestion from Daniel Forgues