A270203 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12, p+2^14 and p + 2^16 are all primes.

163, 15667, 234067, 607093, 671353, 1447153, 1457857, 2162323, 5772097, 7717873, 9139453, 9549373, 11170933, 12039883, 13243063, 16442407, 16836163, 17784253, 18116473, 19433863, 21960577, 28209703, 29175283, 32380177, 33890803, 34613287, 34682113

Offset: 1

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

• nonn

Examples

			The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259, 163 + 16384 = 16547 and 163 + 65536 = 65699 are all primes.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10957

Crossrefs

Subsequence of A269859.

Cf. A269257, A269258, A269259.

Programs

Magma

[p: p in PrimesInInterval(2,40000000) | forall{i: i in [16,64,256,1024,4096,16384,65536] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

Mathematica

m = {2^4, 2^6, 2^8, 2^10, 2^12, 2^14, 2^16}; Select[Prime@ Range[3*10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)
Select[Prime[Range[22*10^5]],AllTrue[#+2^Range[4,16,2],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 12 2018 *)

Perl

use ntheory ":all"; say for sieve_prime_cluster(2,1e8, 16,64,256,1024,4096,16384,65536); # Dana Jacobsen, Jul 13 2016