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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)