A167771 - OEIS

%I #7 Sep 21 2016 16:40:20

%S 2,53,89,157,173,211,251,257,263,293,331,337,359,367,373,389,409,449,

%T 479,509,541,547,557,563,577,587,593,607,631,653,683,691,701,709,719,

%U 727,733,751,787,797,839,919,929,947,953,977,983,991,997,1039,1069,1103

%N Twice-isolated primes: primes p such that neither p+-2 nor p+-4 is prime.

%C 2 together with primes p with property that (p-previous prime)>=6 and (next prime-p)>=6.

%C By the finitude of the generalized Brun constants, this sequence includes almost all primes.

%H Harvey P. Dale, <a href="/A167771/b167771.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1)=2 (-2,0,4,6 are nonprimes); a(2)=53 (49,51,55,57 are nonprimes).

%t Join[{2},Select[Prime[Range[200]],NoneTrue[#+{4,2,-2,-4},PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 21 2016 *)

%Y Cf. A007510, A137869.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 11 2009

%E Comment from _Charles R Greathouse IV_, Nov 12 2009