41. The precision of the factorization is maximized using a Newton-type iteration. 42. More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization . 43. This asymmetry is analogous to the one between integer factorization and integer multiplication. 44. All these algorithms use the algorithms for factorization of polynomials over finite fields. 45. The number field sieve is the fastest general-purpose factorization algorithm known. 46. Squarity testing can be used as alternative way in factorization of large numbers. 47. Cooley Tukey algorithm corresponds closely to a recursive factorization . 48. The factoring challenge was intended to track the cutting edge in integer factorization . 49. Cash prizes of varying size were offered for factorization of some of them. 50. The factor base for this factorization contained 524339 primes.
