A160026 Primes p such that p^4 + 17^4 + 3^4 is prime.

13, 29, 37, 59, 89, 101, 107, 241, 263, 293, 373, 409, 569, 683, 821, 971, 1033, 1187, 1229, 1277, 1289, 1423, 1511, 1627, 1759, 1823, 1901, 1907, 1973, 2011, 2069, 2083, 2099, 2207, 2311, 2473, 2593, 2633, 2707, 2719, 2753, 2819, 3023, 3137, 3209, 3221

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 = 17, r = 3.

It is conjectured that the sequence is infinite.

There are consecutive primes (1901, 1907) in the sequence.

Links

Table of n, a(n) for n=1..46.

Example

p = 3: 3^4 + 17^4 + 3^4 = 83683 = 67*1249, so 3 is not in the sequence.
p = 1901: 1901^4 + 17^4 + 3^4 = 13059557751203 is prime, so 1901 is in the sequence.
p = 1907: 1907^4 + 17^4 + 3^4 = 13225216032803 is prime, so 1907 is in the sequence.

Prog

(Magma) [ p: p in PrimesUpTo(3250) | IsPrime(p^4+83602) ]; // Klaus Brockhaus, May 03 2009

Crossrefs

Cf. A158979, A159829, A160022.

Sequence in context: A322388 A096451 A090690 * A141555 A036974 A045472

Adjacent sequences: A160023 A160024 A160025 * A160027 A160028 A160029

Keyword

easy,nonn

Author

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

Extensions

Edited, 409 inserted and extended beyond 2069 by Klaus Brockhaus, May 03 2009

Status

approved