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.

4, 2, 83270, 5241160, 57171410, 359829200

Offset: 0

Author

Artur Jasinski, Dec 12 2006

Keywords

• nonn

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.

Crossrefs

Cf. A125855, A057015, A125779, A125780.

Programs

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

Extensions

Edited by Don Reble, Dec 16 2006

One more term from Farideh Firoozbakht, Jan 01 2007