A269859 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12 and p+2^14 are all primes.

37, 163, 15667, 47287, 120607, 142543, 234067, 263047, 263803, 444607, 607093, 671353, 1447153, 1457857, 1562983, 2162323, 2694157, 2841337, 2979043, 3362143, 3567337, 4890307, 5037433, 5353987, 5772097, 6404773, 6776023, 7717873, 9139453, 9549373, 10550467

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, 37 + 4096 = 4133 and 37 + 16384 = 16421 are all primes.
The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259 and 163 + 16384 = 16547 are all primes.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10801

Crossrefs

Subsequence of A269259.

Cf. A269257, A269258.

Programs

Magma

[p: p in PrimesInInterval(2,12000000) | forall{i: i in [16,64,256,1024,4096,16384] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

Mathematica

m = Map[2^# &, 2 Range[2, 7]]; Select[Prime@ Range[10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)

Perl

use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096,16384); # Dana Jacobsen, Jul 13 2016