A356079 Primes p such that p+6, p-6, 2*p+3 and 2*p-3 are prime.

13, 17, 53, 67, 157, 563, 613, 647, 1187, 1453, 1663, 4007, 4133, 5443, 5743, 6073, 6863, 7823, 8747, 11833, 12113, 12583, 12653, 15467, 21997, 23747, 25463, 25673, 26183, 41017, 42683, 59447, 60337, 65173, 67427, 68443, 75527, 80783, 89527, 94433, 95917, 100517, 101203, 104003, 110603, 111773

Offset: 1

Author

J. M. Bergot and Robert Israel, Jul 25 2022

Keywords

• nonn

Comments

p, q, 2*p+q, 2*p-q, p+2*q and p-2*q are all prime if and only if q = 3 and p is in this sequence.

Examples

			a(3) = 53 is a term because 53, 53+6 = 59, 53-6 = 47, 2*53 + 3 = 109 and 2*53 - 3 = 103 are all prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

filter:= proc(p) andmap(isprime,[p,p+6,p-6,2*p+3,2*p-3]) end proc:
select(filter, [seq(i,i=3..200000,2)]);

Mathematica

Select[Prime[Range[10^4]], AllTrue[{# - 6, # + 6, 2*# - 3, 2*# + 3}, PrimeQ] &] (* Amiram Eldar, Jul 25 2022 *)

Python

from sympy import isprime
def ok(p): return all(isprime(k) for k in [p, p+6, p-6, 2*p+3, 2*p-3])
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 25 2022