A352170 Primes p such that p+4, 3*p+4 and 3*p+8 are also prime.

3, 13, 103, 223, 823, 2953, 7873, 11113, 11863, 13033, 13963, 16063, 22153, 23743, 24763, 27733, 30133, 31513, 34213, 35593, 39883, 41893, 43063, 50383, 51043, 54493, 62983, 65323, 66343, 68473, 71593, 72643, 87793, 88423, 98893, 101203, 106363, 110563, 127873, 134593, 136603, 158563, 164623, 165703

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 07 2022

Keywords

• nonn

Comments

Members p of A023200 such that 3*p+4 is also in A023200.

Except for 3, all terms == 13 (mod 30).

Examples

			a(4) = 223 is a term because 223, 223+4 = 227, 3*223+4 = 673 and 3*223+8 = 677 are all prime.
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A023200, A023209 and A023210.

Programs

Maple

select(p -> isprime(p) and isprime(p+4) and isprime(3*p+4) and isprime(3*p+8), [3,seq(i,i=13..10^6,30)]);

Mathematica

Select[Range[200000], AllTrue[{#, # + 4, 3*# + 4, 3*# + 8}, PrimeQ] &] (* Amiram Eldar, Mar 07 2022 *)

Python

from sympy import sieve, isprime
for p in sieve.primerange(0, 10**6):
    if(all(isprime(q) for q in [p+4, 3*p+4, 3*p+8])):
        print (p, end=", ") # Martin Ehrenstein, Mar 09 2022