A269258 Primes p such that p+2^4, p+2^6, p+2^8 and p+2^10 are all primes.

7, 37, 163, 337, 2647, 5023, 9157, 9277, 15667, 22093, 24907, 40177, 43597, 47287, 53593, 56893, 59077, 59497, 66553, 78877, 83407, 84793, 92737, 93307, 102043, 111577, 114577, 116953, 120607, 135193, 137383, 141397, 142543, 150067, 165463, 173713, 180007, 181903, 183943

Offset: 1

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

• nonn

Examples

			The prime 7 is in the sequence because 7+16 = 23, 7+64 = 71, 7+256 = 263 and 7+1024 = 1031 are all primes.
The prime 37 is in the sequence because 37+16 = 53, 37+64 = 101, 37+256 = 293 and 37+1024 = 1061 are all primes.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10727
• Debapriyay Mukhopadhyay, C program to generate the terms of the sequences A269257, A269258, A269259, A269859 and A270203 up to 10^8

Crossrefs

Subsequence of A269257.

Programs

Magma

[p: p in PrimesInInterval(2,200000) | forall{i: i in [16,64,256,1024] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

Mathematica

Select[Prime@ Range[10^5], Times @@ Boole@ PrimeQ[# + 2^{4, 6, 8, 10}] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)

Perl

use ntheory ":all"; say for sieve_prime_cluster(2,1e5, 16,64,256,1024); # Dana Jacobsen, Jul 13 2016

Formula

A269257 INTERSECT A361485. - R. J. Mathar, Mar 26 2024