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
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