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Old 2013-11-15, 19:33   #20
literka
 
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Mar 2010

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Quote:
Originally Posted by Batalov View Post
literka,

Could you please present the number of operations needed to carry on all your calculation (1) - (5), etc, compared to a simple multiplication of two factors.

It appears that to assert these:
Code:
Several equalities will be needed:

(1)                          p=2086489992+1269455962 = 512 * q+1

(2)                          s = 208648999*52542249 + 126945596*31967597

(3)                          126945596*52542249 - 208648999*31967597 = 1

(4)                         309*q + r = 255

(5)                         r = (s div 512)+1
one will have to do much more than to simply assert
Code:
59649589127497217 *
5704689200685129054721
= 340282366920938463463374607431768211457 
= 2^128+1
And even less work in octal (with an octal multiplication table at your side)
Code:
2^128+1 = 4000000000000000000000000000000000000000001
(note: this equality you will have for free!) 
and then

3237257607274243001
*
1152401672664431414535001 
= 
4000000000000000000000000000000000000000001



Go to the page of Wikipedia, where the proof that 641 is a factor of F5. Compute the number of operations in this proof and number number of operations to multiply 641 by 6700417. Page of Wikipedia is not about F5 but about all Fermat numbers. Still, they thought that it is worthy to include proof about the number 641. So, if you have complains, write to Wikipedia first.
And yes, I have new ideas to find proofs corresponding to Fermat numbers with larger indexes.
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