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Old 2010-02-11, 11:32   #2
R.D. Silverman
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"Bob Silverman"
Nov 2003
North of Boston

22·5·373 Posts

Originally Posted by Random Poster View Post
As most readers probably know, the quadratic sieve factors a number n by finding values of x such that P(x) = x^2 - n is a product of small factors.
May I suggest that you read about the algorithm? Your description
described the algorithm as it was implemented in 1982 by J. Gervers.
It has not been implemented this way since 1984.

This could be also done with multiples of n; more precisely, let m range from 1 to M and sieve for P(x) = x^2 - mn with x near sqrt(mn). Any thoughts?
You are 25 years too late with your suggestion. Read my 1987 paper:

The Multiple Polynomial Quadratic Sieve
Math. Comp. 1987
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