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A064539
Numbers n such that 2^n + n^2 is prime.
6
1, 3, 9, 15, 21, 33, 2007, 2127, 3759, 29355, 34653, 57285, 99069, 1933695
OFFSET
1,2
COMMENTS
Values 2^2007+2007^2, 2^2127+2127^2, 2^3759+3759^2 were proved prime with Primo.
n is always an odd multiple of 3 (except for the first term), i.e., a(n) is a subsequence of A016945. - Lekraj Beedassy, Jan 01 2007
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019
REFERENCES
J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 165 pp. 30, 160, Ellipses Paris 2004.
LINKS
Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n+n^2.
PROG
(PARI) for(n=1, 5000, if(isprime(2^n+n^2), print(n)))
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Jason Earls, Oct 16 2001
EXTENSIONS
a(10)-a(13) from Hugo Pfoertner, Jun 26 2004
a(14) from Ryan Propper, May 11 2023. n=1933695 corresponds to a probable prime with 582101 digits, and was PRP tested with PFGW.
STATUS
approved