This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 NumberTheory`FactorIntegerECM` This package implements Lenstra's Elliptic Curve method of factorization. The package is designed to find prime factors of up to about 18 digits in reasonable time (up to three hours on a workstation). This extends Mathematica's integer factoring to all numbers of 40 digits or less. The program in the package is a fairly direct implementation of the algorithm described in P. L. Montgomery's, "Speeding up the Pollard and Elliptic Curve Methods of Factorization," Mathematics of Computation 48 (1987), pages 243-264. Using FactorIntegerECM. The algorithm returns a single factor (not necessarily a prime). To obtain a complete factorization, you should use FactorIntegerECM or the built-in FactorInteger on the factor and cofactor. The algorithm is probabilistic, so there could be a large variance in running times, even for similar inputs. SeedRandom[101] is used to generate pseudorandom numbers for the algorithm, so the program will always run exactly the same on the same input. FactorIntegerECM should be used as an enhancement to the built-in functions PrimeQ and FactorInteger. The algorithm will always fail if the input is a prime. A prime number should never be given as input to FactorIntegerECM. Before using FactorIntegerECM, you should always use PrimeQ to make sure that your number is not prime. The algorithm is designed with the assumption that the number given was not factored by FactorInteger, and so its smallest prime factor is at least . The algorithm is optimized to find factors of digits or less, so it should factor most numbers of digits or less (and such numbers will probably only have two prime factors if they are hard to factor). This loads the package. In[1]:= <