rec.puzzles Archive

What is the largest number factored by a general purpose algorithm, and how was it done?

arithmetic/factoring.record New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What is the largest number factored by a general purpose algorithm,
and how was it done?

[ Editor: problem statement reconstructed from the postings (Robert
Silverman's announcement of a factoring record, with a follow-up
question). ]
Show solution
I have just established two new factoring records.  I just finished
factoring the following 88 digit number:

   94
 10  + 1
---------
101.45121

It was factored by a parallel version of the Multiple Polynomial
Quadratic Sieve (MPQS) and is the largest number ever factored by a
general purpose algorithm.  It also represents the first time a 40
digit penultimate factor of a number has been found.  The factorization
is:

2144906157509411684424913774078958939881

times

1023037643093214557651333120422980213172396059301

-- Bob Silverman <bs@linus.UUCP>

In article <7876@mimsy.UUCP>, lls@mimsy.UUCP (Lauren L. Smith) writes:

> Impressive.  I'm interested in parallel algorithms and am wondering
> about a couple of things - How long did the factoring take?  What
> parallel machine did you run?  Did the algorithm exploit fine-grained
> parallelism or large-grained or both?  Do you have any idea of the
> speedup?

The algorithm was implemented on a network of 24 SUN-3 microcomputers.
The algorithm was designed and written in such a way that N machines
do, in practice and in theory yield an N-fold speedup.  The total
number of CPU hours, summed over all 24 machines was 11,400 hours or
about 475 hours/machine.

I have a paper, to appear in Volume I, #3 of the Journal of
Supercomputing, describing the algorithm and its implementation.

-- Bob Silverman <bs@linus.UUCP>

[ Editor: the announcement mentions two records but describes only
one. ]