## New big Fermat factor

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• Congratulations to Takahiro Nohara It is the big divider second after result Cosgrave for Fermat. Leonid Durman =============================== I found new
Message 1 of 1 , Aug 5, 2003
Congratulations to Takahiro Nohara
It is the big divider second after result Cosgrave for Fermat.

Leonid Durman

===============================
I found new divisor of Fermat number.
9*2^461081+1 divides F461076.

I show the log of Proth.exe

Mon Aug 04 09:24:01 2003 : Start: For n=461081 to 461081, For k=9 to 9 step
2, k*2^n+1.
Mon Aug 04 12:46:20 2003 : 9*2^461081 + 1 is prime! (a = 11) [138801 digits]
Mon Aug 04 16:05:53 2003 : 9*2^461081 + 1 is prime! (verification : a = 19)
[138801 digits]
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides F461076 !
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 3) !
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 6) !
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 12) !
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 doesn't divide any GF(5, m).
Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 doesn't divide any GF(10, m).
Tue Aug 05 16:10:28 2003 : 9*2^461081 - 1 factor : 7
Tue Aug 05 16:10:28 2003 : 9*2^461082 + 3 factor : 3
Tue Aug 05 16:10:28 2003 : 9*2^461082 + 1 factor : 73
Tue Aug 05 16:10:28 2003 : 9*2^461080 + 1 factor : 5
Tue Aug 05 16:10:28 2003 : Done.

I used NewPGen.exe and PRP.exe before Proth test.
I've searched prime with form 9*2^n+1. This prime number is 4th of I ever
found with same form.
And this is second divisor of Fermat number found on my PCs.
(My PCs are P3-600MHz*2.)

I send same message to Payam Samidoost.
Sorry, I can't send e-mail to Yahoo Group.