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Quadratic residues given by a certain polynomial and divisible by a particular prime are regularly spaced. (Don't ask why unless answerer is Math Whiz).
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In sieving you add the log of the prime every such regular distance through initially zeroed memory, for each prime in the factor base.
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When done, we pick out places where the accumulation exceeds a threshold; that's where you find quadratic residues divisible by lots of small primes.
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These residues are therefore more likely to be double-partial, partial, or full relations!
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