New Factor of F11 (?)
 

I wrote a quick and dirty program to find factors of Fermat numbers. Not that there are programs out for this, but I wanted my own :smile: . I ran it overnight and was completely astonished to find a factor of F11 which was not listed in Wilfrid Keller's table ([URL="http://www.prothsearch.net/fermat.html"]http://www.prothsearch.net/fermat.html[/URL]). According to this table, the factorization of F11 is complete and has 5 factors, but the one I found is not among these. I tried several methods to verify this factor, and all agreed that it is indeed a factor of F11.

The factor I found is: 19009615*2^14 + 1.

The question I have: who made a mistake?

Your number is composite:

19009615*2^14 + 1 = 311453532161 = 319489 x 974849.

[QUOTE=ChriS]The factor I found is: 19009615*2^14 + 1.

The question I have: who made a mistake?[/QUOTE]

Keller's table lists only PRIME factors of Fermat numbers. Your factor is the product (39*2^13 + 1) * (119*2^13 + 1) of the two smallest prime factors.

Don't feel bad! Several of us have run ECM with Prime95 without downloading the lowm.txt or lowp.txt files first and have gotten excited about thinking that we have discovered new factors.

You're right.

Oh dear.....:no: