A093179 - OEIS (original) (raw)

A093179

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

14

3, 5, 17, 257, 65537, 641, 274177, 59649589127497217, 1238926361552897, 2424833, 45592577, 319489, 114689, 2710954639361, 116928085873074369829035993834596371340386703423373313, 1214251009, 825753601, 31065037602817, 13631489, 70525124609

COMMENTS

a(14) might need to be corrected if F(14) turns out to have a smaller factor than 116928085873074369829035993834596371340386703423373313. F(20) is composite, but no explicit factor is known. - Jeppe Stig Nielsen, Feb 11 2010

REFERENCES

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 73.

EXAMPLE

F(0) = 2^(2^0) + 1 = 3, prime.

F(5) = 2^(2^5) + 1 = 4294967297 = 641*6700417.

So 3 as the 0th entry and 641 is the 5th term.

MATHEMATICA

Table[With[{k = 2^n}, FactorInteger[2^k + 1]][[1, 1]], {n, 0, 15, 1}] (* Vincenzo Librandi, Jul 23 2013 *)

PROG

(PARI) g(n)=for(x=9, n, y=Vec(ifactor(2^(2^x)+1)); print1(y[1]", ")) \\ Cino Hilliard, Jul 04 2007

CROSSREFS

Leading entries in triangle A050922.