login
A125856
a(n) = least number k such that k^(2^n)+1, k^(2^n)+3, k^(2^n)+7 and k^(2^n)+9 are all prime.
0
4, 2, 83270, 5241160, 57171410, 359829200
OFFSET
0,1
COMMENTS
In 1958, Schinzel showed that for each n>0, there are infinitely many primes among the numbers k^(2^n)+{1,3,7, or 9}.
REFERENCES
Sierpinski, W. Elementary theory of numbers. Warszawa 1964 Monografie Matematyczne Vol. 42.
PROG
(PARI) a(n) = {k = 1; while(!isprime(k^(2^n)+1) || !isprime(k^(2^n)+3) || !isprime(k^(2^n)+7) || !isprime(k^(2^n)+9), k++); k; } \\ Michel Marcus, Nov 03 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 12 2006
EXTENSIONS
Edited by Don Reble, Dec 16 2006
One more term from Farideh Firoozbakht, Jan 01 2007
STATUS
approved