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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Subsequence of A269258.

Cf. A269257.

Sequence in context: A250842 A083389 A142909 * A269859 A049496 A049497

Adjacent sequences: A269256 A269257 A269258 * A269260 A269261 A269262

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Status

approved