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

> and

> 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

> the

> 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

> did

> 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.

Paul