On Sat, 2012-04-21 at 19:21 -0400, Kermit Rose wrote:
> Hello friends.
> I've constructed a factoring algorithm that I call ProportionateFactor
> because, to factor positive integer z, it seeks to find four integers
> t0,t1,t2,t3 such that
> t0 + t1 + t2 + t3 = z
> t0 t3 = t1 t2.
> Then it checks to see if GCD(t0+t1,z) is strictly between 1 and z.
> It often happens that GCD(t0+t1,z) is exactly equal to z.
> In the following I have tested my new factoring algorithm against
> several other algorithms.
> The third number in the output vector is the number of cycles within
> algorithm that found the factors.
> ProportionateFactor appears to be in close competition with (p-1)
> factoring algorithm.
> I had had hopes that ProportionateFactor would be much faster, but I
> not anticipate that most of the time
> GCD(z,t0+t1) would be exactly equal to z.
Without any information on how you propose to find the t_i it's next to
impossible to give any meaningful analysis of your algorithm.