A124582 Primes p such that q-p >= 6, where q is the next prime after p.

23, 31, 47, 53, 61, 73, 83, 89, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 359, 367, 373, 383, 389, 401, 409, 421, 433, 443, 449, 467, 479, 491, 503, 509, 523, 541, 547, 557, 563, 571, 577

Offset: 1

Author

N. J. A. Sloane, Dec 19 2006

Keywords

• nonn

Links

• R. Zumkeller, Table of n, a(n) for n = 1..1000
• K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18.
• Index entries for primes, gaps between

Crossrefs

Complement of A124589.

Cf. A134099, A134100, A134101.

Programs

Maple

d:=6; M:=1000; t0:=[]; for n from 1 to M do p:=ithprime(n); if nextprime(p) - p >= d then t0:=[op(t0),p]; fi; od: t0;

Mathematica

t={};q=6;Do[If[Prime[n+6]-Prime[n+5]>=q,AppendTo[t,Prime[n+5]]],{n,1,200}];t (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
Transpose[Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]] >= 6&]] [[1]] (* Harvey P. Dale, May 15 2013 *)

PARI

is(n)=!isprime(n+2) && !isprime(n+4) && n>2 && isprime(n) \\ Charles R Greathouse IV, Jun 04 2015

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jun 04 2015