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Old 2012-01-29, 22:15   #1
literka
 
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Mar 2010

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Default Fermat number F6=18446744073709551617 is a composite number. Proof.

Recently I did something similar for sixth Fermat number F6=18446744073709551617 as I did before for F5.
(see my thread "F5=4294967297 is a product of two integers."). Using elementary methods I proved that 274177 is a factor of F6.
Proof is on my www page http://www.literka.addr.com/mathcoun...mth/proof3.htm.
Proof of mentioned thread about F5 is on the web page http://www.literka.addr.com/mathcoun...mth/proof2.htm.
My web page http://www.literka.addr.com/mathcoun...mth/proof1.htm contains basic proof (not mine), which inspired me to do this job.
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