# ECPP Version 6.4.5

## From 5.6.1 to 6.4.5

The code was modified as to match the material described in my
ANTS-III article
as well as some ongoing work on new class invariants, part of which was
described in my Durham
talk. As a result, there are now new data available, that make the program
faster.
Needless to say, a lot of bugs were corrected on the way. Special care was
given to the probable prime test used in the inner core of the algorithm, as
well as the problems mentionned in my
ISSAC92 paper.
## The Data part

For convenience (that is smaller files are easier to get than
larger ones), the data part has been divided into five parts.

*You need all of them!*
Here they are:

To give an example, on your machine `toto`, once you have ftp-ed the
file `ecppweber1.tar.gz`, you have to type:
toto% gzip -dc ecppweber1.tar.gz | tar xvf -

**Important remark:** the data part has been changed from 5.6.1. Though the
date of 5.6.1 can still be used, the new data lead to a more efficient program.
To understand these changes, see my article in
ANTS-III
and the slides of
Durham.
## The binaries part

Now, to get the binaries, select one of:

**Important remarks:** all the binaries are for Un*x-like operating
systems.

## Benchmarks

### 512-bit primes

The file `Bench/primes-b512x20` contains twenty 512 bit primes. We give
the average time for proving their primality below (with my personal version).
Pentium III (450MHz) 4.4 sec
Solaris 5.7 9.5 sec
Alpha EV56 (500MHz) 4 sec

### A larger number

This benchmark consists in proving the primality of the 222 decimal
digit cofactor of *2, 1958M = 2^979+2^490+1*.
66921125696\
3738586471992473357177695309368664238677386377989897942842973147723610\
2597067638539982680157521103531959968006552170889359188835475305453190\
56042889912017237320157749017499115968180112317315484537264218388048013

This number is taken from the tables of the Cunningham Project
("Factorizations of b**n+/-1 up to high
powers" by John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman
and S. S. Wagstaff, Jr., vol 22 of AMS Contemporary Mathematics
series), which are regularily updated by
Paul Leyland. It is the first non trivial number whose primality I proved
in 1987.
Proof Check
Pentium III (450MHz) 16 sec 3.1 sec
Solaris 5.7 38 sec 9.7 sec
Alpha EV56 (500MHz) 13 sec 1.9 sec

The benchmarks are given as is. In particular, they do not imply any
judgment of mine, or of my Laboratory.
## MANIFEST

This work uses the BigNum package developed jointly by INRIA and Digital PRL.
École polytechnique and CNRS make no representations, express or
implicit, with respect to the binaries given, including
without limitations, any implied warranties of merchandability or
fitness for a particular purpose, all of which are expressly
disclaimed. École polytechnique and CNRS shall in no event be liable
for any indirect, incidental or consequential damages.
The binaries can be used for research purposes as well as private use,
but not in any commercial product (including cryptographic
libraries -- of course -- actually, I have slowed down my program for
small numbers).
I do not give permission to use my program from a web page.
If you use my program to break records, I'd like to be informed
of that and I'd like to see my name as well as the version number of
the program associated to it.
Number of hits since 2001.04.02: