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

1,1

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Subsequence of A269259.

Cf. A269257, A269258.

Sequence in context: A083389 A142909 A269259 * A049496 A049497 A246842

Adjacent sequences: A269856 A269857 A269858 * A269860 A269861 A269862

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Status

approved