A046117 Primes p such that p-6 is also prime. (Upper of a pair of sexy primes.)

11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• 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, A098428, A087695.

Programs

Magma

[p:p in PrimesInInterval(7,650)| IsPrime(p-6)]; // Marius A. Burtea, Jan 03 2020

Mathematica

q=6; a={}; Do[p1=Prime[n]; p2=p1+q; If[PrimeQ[p2], AppendTo[a, p2]], {n, 7^2}]; a "and/or" Select[Prime[Range[3, 7^2]], PrimeQ[ # ]&&PrimeQ[ #-6]&] (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Prime[Range[4,200]],PrimeQ[#-6]&] (* Harvey P. Dale, Mar 31 2018 *)

PARI

forprime(p=2,1e4,if(isprime(p-6),print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A087695(n) + 3.

a(n) = A023201(n) + 6. - M. F. Hasler, Jan 02 2020

Extensions

Name edited by M. F. Hasler, Jan 02 2020