Recently I have written a page

http://www.literka.addr.com/mathcoun...mth/proof4.htm with a proof that59649589127497217 is a factor of Fermat number F7. It is something similar to my previous work about F5 and F6 (see my posts in this section "Factoring" or visit my description page

http://www.literka.addr.com/mathcountry.

Unfortunately factors of F7 are large numbers, hence some computation had to be with numbers of same size. Still these numbers are incomparably smaller than F7.