how fast can you factor

Feb 4, 2014  

For no other reason than because it’s there, here is the result of asking Mathematica to factor RSA 100.

In 1991,

… the factorization took a few days using the multiple-polynomial quadratic sieve algorithm on a MasPar parallel computer.

and now,

It takes four hours to repeat this factorization using the program Msieve on a 2200 MHz Athlon 64 processor.

In comparison, Mathematica took little more than an hour. Unfortunately, it was not able to parallelize it (for a real comparison, the Msieve code would have to be ported over).

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Update: This has been much better documented on this StackExchange thread, which also links to notes on internal implementation, in case you’re interested:

FactorInteger switches between trial division, Pollard , Pollard rho, elliptic curve, and quadratic sieve algorithms.

Finally, more on RSA Numbers, as well as a Mathematica Notebook, here