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 2013-11-15, 19:09 #17 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×29×113 Posts 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! ;-)