A269259 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10 and p+2^12 are all primes.

37, 163, 15667, 22093, 40177, 47287, 53593, 114577, 120607, 142543, 234067, 242377, 255907, 263047, 263803, 305407, 388117, 444607, 460387, 503287, 527143, 607093, 671353, 784897, 904663, 938947, 1063903, 1086493, 1172803, 1216807, 1233523, 1288543

Offset: 1

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

• nonn

Examples

			The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061 and 37 + 4096 = 4133 are all primes.
The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187 and 163 + 4096 = 4259 are all primes.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10476

Crossrefs

Subsequence of A269258.

Cf. A269257.

Programs

Magma

[p: p in PrimesInInterval(2,1600000) | forall{i: i in [16,64,256,1024,4096] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

Mathematica

m = {2^4, 2^6, 2^8, 2^10, 2^12}; Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)

PARI

is(n) = for(k=2, 6, if(!ispseudoprime(2^(2*k)+n), return(0))); return(1)
forprime(p=1, 16e5, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Jul 12 2016

Perl

use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096); # Dana Jacobsen, Jul 13 2016