A160023 Primes p such that p^4 + 7^4 + 3^4 is prime.

11, 37, 71, 101, 149, 163, 191, 271, 293, 379, 409, 419, 647, 661, 709, 1153, 1193, 1231, 1277, 1523, 1583, 1619, 1667, 1693, 1753, 1777, 1787, 1913, 2089, 2099, 2161, 2213, 2441, 2473, 2531, 2551, 2609, 2711, 2749, 2909, 2953, 2999, 3221, 3257, 3469

Offset

1,1

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 7, r = 3.

It is conjectured that the sequence is infinite.

There are prime twins (6197, 6199) and other consecutive primes (409, 419; 2089, 2099) in the sequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

p = 7: 7^4 + 7^4 + 3^4 = 4883 = 19*257, so 7 is not in the sequence.
p = 11: 11^4 + 7^4 + 3^4 = 17123 is prime, so 11 is in the sequence.
p = 101: 101^4 + 7^4 + 3^4 = 104062883 is prime, so 101 is in the sequence.

Mathematica

Select[Prime[Range[500]], PrimeQ[#^4+2482]&] (* Harvey P. Dale, Jan 31 2017 *)

Prog

(Magma) [ p: p in PrimesUpTo(3500) | IsPrime(p^4+2482) ]; // Klaus Brockhaus, May 03 2009

Crossrefs

Cf. A158979, A159829, A160022.

Sequence in context: A265767 A031381 A358079 * A263201 A337832 A188135

Adjacent sequences: A160020 A160021 A160022 * A160024 A160025 A160026

Keyword

easy,nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Extensions

Edited and extended beyond 2441 by Klaus Brockhaus, May 03 2009

Status

approved