A158361 Primes p with property that Q=p^4+2^4 is prime.

3, 5, 7, 11, 17, 19, 23, 37, 41, 59, 61, 71, 79, 97, 131, 139, 179, 223, 227, 229, 241, 283, 313, 317, 359, 367, 379, 383, 389, 439, 449, 461, 487, 503, 521, 569, 593, 617, 619, 631, 661, 683, 709, 733, 811, 821, 853, 911, 977, 1049, 1061, 1063, 1069, 1091, 1093, 1117

Offset

1,1

Comments

Q is always congruent to 1 (mod 4).

Q is divisible by 17 if p is congruent to 1, 4, 13, or 16 (mod 17).

It is conjectured that sequence a(n) is infinite.

Q is in A094479. - Zak Seidov, Jul 08 2020

References

Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005

Richard Guy, "Unsolved Problems in Number Theory"

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

3 is in the sequence since for p=3: p^4+2^4 = 3^4+16 = 97 is prime.
29 is not in the sequence since 29^4+2^4 = 707297 = 73 x 9689 is not prime.

Mathematica

Select[Range[10^3], PrimeQ[#] && PrimeQ[#^4 + 16] &] (* Vincenzo Librandi, Jun 18 2014 *)
Select[Prime[Range[200]], PrimeQ[#^4+16]&] (* Harvey P. Dale, Jun 23 2014 *)

Prog

(PARI) isA158361(n) = isprime(n) && isprime(n^4+16)
(Magma) [p: p in PrimesUpTo(2000) | IsPrime(p^4+16)]; // Vincenzo Librandi, Jun 18 2014

Crossrefs

Cf. A062324, A094479, A157950, A157764.

Sequence in context: A226653 A128926 A139559 * A342692 A048184 A290283

Adjacent sequences: A158358 A158359 A158360 * A158362 A158363 A158364

Keyword

nonn,easy

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 17 2009

Extensions

Corrected and edited by Michael B. Porter, Dec 17 2009

Status

approved