A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r = ⌊sqrt(n)⌋ + k, where k = 1, 2, ... and ⌊x⌋ is the floor function. We are then looking for factors p such that n congruent r^2 (mod p), which means that only numbers with Legendre symbol (n/p) = 1 (less than N = π(d) for trial divisor d, where π(d) is the prime counting function) need be considered. The set of primes for which this is true is known as the factor base.
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