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Re: Integer factorization in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg39486] Re: Integer factorization in Mathematica
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 19 Feb 2003 04:42:00 -0500 (EST)
• References: <200302172317.SAA14738@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Check the on-line documentation of Mathematica version 4.2, located at

The Mathematica Book > Mathematica Reference > Some Notes on
Implementation > Numerical and Related Functions

Under subheading Number-theoretical functions we find

"\[FilledSmallCircle] FactorInteger switches between removing small
primes by trial division and using the Pollard p-1, Pollard rho and
quadratic sieve algorithm."

Specifically, MPQS is used.

I should note that "fastest" is quite dependent on the sizes of factors
as well as the size of the number itself.


Daniel Lichtblau
Wolfram Research

• References:
  • Integer factorization in Mathematica
    • From: "Jes Hansen" <eq0y4q5qvpbfvv8tyylmwxj02@sneakemail.com>