About Fermat’s Integer Factoring algorithm

An implementation of Fermat’s algorithm that is a slight improvement on code in this book is here.

FermatFactor[n_?OddQ]:=Module[{s=Floor@Sqrt[n+0``1],r,u,v=1},   If[s^2==n,Return@{s,s}];   {r,u}={(s+1)^2-n,2*s+3};   While[r!=0,     While[r>0,       r-=v;v+=2     ];     If[r<0,r+=u;u+=2]   ];   (u+{-v,v-2})/2 ] 

The main improvement above is the fast implementation of Floor[Sqrt[n]] from MichaelE2. The above implementation will factor the following in less than 0.1 seconds!

SeedRandom[100]; p=10^50; n=NextPrime@RandomInteger[{p-80000,p-60000}]*NextPrime@RandomInteger[{p+80000,p+60000}]; FermatFactor[n] (*{99999999999999999999999999999999999999999999920467,100000000000000000000000000000000000000000000075667}*) 

I have Mathematica Version 12.0.0 and FactorInteger[n] takes a very long time on that example. Can FactorInteger in Mathematica 12.2 do it in a reasonable amount of time?

The post About Fermat’s Integer Factoring algorithm appeared first on 100% Private Proxies - Fast, Anonymous, Quality, Unlimited USA Private Proxy!.