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Old 2013-11-15, 19:09   #17
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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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=208648999^2+126945596^2 = 512 * q+1

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

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

(4)                         309*q + r = 2^55

(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

Last fiddled with by Batalov on 2013-11-16 at 02:49 Reason: 309*q + r = 2^55. Very important and extremely easy to verify! ;-)
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