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Primes p such that p + 6^k is also prime at least for k = 1, 2, 3 and 4.
1

%I #11 Oct 07 2014 13:01:47

%S 7,11,23,131,157,193,227,271,331,571,947,977,1013,1087,1283,1453,1657,

%T 1871,2341,2671,2693,3607,3637,3691,4013,4951,5407,5653,6211,6353,

%U 6653,6827,6977,6991,7541,7717,8053,8081,8537,9203,9613,9643,10853,11113,11251,11933

%N Primes p such that p + 6^k is also prime at least for k = 1, 2, 3 and 4.

%H K. D. Bajpai, <a href="/A247590/b247590.txt">Table of n, a(n) for n = 1..12638</a>

%e a(1) = 7 is prime. 7 + 6^1 = 13, 7 + 6^2 = 43, 7 + 6^3 = 223 and 7 + 6^4 = 1303 are also prime. It is the smallest such set of 5 primes; (Quintet).

%t Select[k = {1, 2, 3, 4}; Prime[Range[500]], And @@ PrimeQ[# + 6^k] &]

%o (PARI)

%o forprime(p=1,10^4,c=1;for(k=1,4,if(!isprime(p+6^k),c--;break));if(c,print1(p,", "))) \\ _Derek Orr_, Sep 20 2014

%Y Cf. A000040, A049494, A049495.

%K nonn,easy

%O 1,1

%A _K. D. Bajpai_, Sep 20 2014