A070592 Largest prime factor of the n-th Fermat number F(n) = 2^(2^n) + 1.

3, 5, 17, 257, 65537, 6700417, 67280421310721, 5704689200685129054721, 93461639715357977769163558199606896584051237541638188580280321

Offset: 0

Author

Benoit Cloitre, May 12 2002

Keywords

• nonn
• hard

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 72.

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..11
• C. L. Stewart, On Divisors of Fermat, Fibonacci, Lucas, and Lehmer Numbers, Proceedings of the London Mathematical Society, Vol. s3-35, No. 3 (1977), pp. 425-447. See p. 430.
• Eric Weisstein's World of Mathematics, Fermat Number.

Crossrefs

Cf. A000215, A006530, A050922, A093179.

Programs

PARI

a(n) = vecmax(factor(2^(2^n) + 1)[,1]); \\ Michel Marcus, Jul 05 2017

Formula

From Amiram Eldar, Oct 25 2024: (Start)

a(n) = A006530(A000215(n)).

a(n) > c * n * 2^n for n >= 1, where c is a positive absolute constant (Stewart, 1977). (End)

Extensions

Offset changed by Arkadiusz Wesolowski, Jul 09 2011