A167771 Twice-isolated primes: primes p such that neither p+-2 nor p+-4 is prime.

2, 53, 89, 157, 173, 211, 251, 257, 263, 293, 331, 337, 359, 367, 373, 389, 409, 449, 479, 509, 541, 547, 557, 563, 577, 587, 593, 607, 631, 653, 683, 691, 701, 709, 719, 727, 733, 751, 787, 797, 839, 919, 929, 947, 953, 977, 983, 991, 997, 1039, 1069, 1103

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 11 2009

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007510, A137869.

Programs

Mathematica

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

Extensions

Comment from Charles R Greathouse IV, Nov 12 2009