A247478 Primes p such that (p^4 + 5)/6 is prime.

7, 11, 17, 29, 53, 71, 101, 109, 127, 179, 227, 241, 281, 307, 349, 487, 587, 647, 683, 727, 829, 1009, 1061, 1109, 1289, 1487, 1511, 1523, 1567, 1621, 1627, 1709, 1847, 1987, 2017, 2027, 2087, 2099, 2297, 2311, 2393, 2437, 2447, 2521, 2531, 2617, 2729, 2887, 2909, 2969, 3167, 3221, 3301, 3319, 3329, 3347, 3413, 3527

Offset: 1

Author

Zak Seidov, Jan 19 2015

Keywords

• nonn

Comments

(p^4+5)/6 is an integer for all primes p>3, because then p == (1 or 5) (mod 6) as in A039704, therefore p^2 == 1 (mod 6) and finally p^4 == 1 (mod 6).

Examples

			(7^4+5)/6 = 401 prime, (11^4+5)/6 = 2441 prime.
		

Crossrefs

Cf. A118915.

Programs

Magma

[p: p in PrimesInInterval(3, 4000) | IsPrime((p^4+5) div 6)]; //  Vincenzo Librandi, Jan 21 2015

Mathematica

Select[Prime[Range[10^3]], PrimeQ[(#^4 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *)

PARI

lista(nn) = {forprime(p=4, nn, if (isprime((p^4 + 5)/6), print1(p, ", ")););} \\ Michel Marcus, Jan 20 2015