Quote:
Originally Posted by R.D. Silverman
What you have posted is
(1) Not useful for QS
(2) Not really applicable to QS. All you have done is rediscover difference
of squares with exclusion moduli.

I suspect that most everyone who starts thinking about factorization algorithms other than trial division rediscovers this algorithm relatively early on. I certainly did, back when I was aged 14 or so.
I believe Fermat was the first person to systematize the idea and to use it to speed up his eponymous factoring algorithm. So the idea has been examined for at least 350 years.
Paul