A375217 Primes p such that p^64 + 2^64 is prime.

37, 53, 181, 491, 547, 619, 661, 677, 911, 941, 1297, 1423, 1867, 2441, 2687, 3137, 3571, 5387, 5821, 5881, 6449, 6551, 6899, 8263, 8537, 8999, 9803, 9931, 10861, 11057, 11131, 11423, 12377, 12941, 13147, 14009, 14519, 14759, 14813, 15493, 16103, 16573, 19949

Offset

1,1

Comments

It is conjectured that solutions for p1^n + p2^n = p3 (where p1, p2, and p3 are all primes and n is a natural number) exist only when n is itself a power of two (when n is a number in A000079); and would have infinitely many solutions.

But it's proven that either p1 or p2 must be 2.

Links

Mykhailo Papenko, Table of n, a(n) for n = 1..8079

Mykhailo Papenko, Primes-Made-Up-of-Primes, GitHub.

Formula

p^64 + 2^64 in A000040.

Mathematica

Select[Prime[Range[2255]], PrimeQ[#^64+2^64]&] (* James C. McMahon, Nov 19 2024 *)

Prog

(Java) /* see link for code with instructions */

Crossrefs

6th row of A132260.

Sequence in context: A036540 A225214 A141166 * A242930 A139918 A289510

Adjacent sequences: A375214 A375215 A375216 * A375218 A375219 A375220

Keyword

nonn

Author

Mykhailo Papenko, Oct 17 2024

Status

approved