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GIMPS newsletter #7, 1 November, 1996

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The Mersenne Newsletter, issue #7 November 1, 1996


Since the last full newsletter 3 months ago, the number of searchers
has skyrocketed! There are now 720 people involved compared to 280
three months ago. Welcome to all the new searchers!

Big Program News

Version 13 of the Pentium Lucas-Lehmer test program is now available.
It is a *lot* faster on exponents above 675,000.

The Lucas-Lehmer assembly code was almost completely rewritten
to increase modularity and readability. This also reduced L2 cache
activity which can speed up the Lucas-Lehmer test by up to 10%.
I also added a little bit of PFA (Prime Factor Algorithm FFT).
Where the old code supported FFT sizes of 64K and 128K, the new code
supports 64K, 80K, 96K, 112K, and 128K. Here are the iteration
timings I get with the old and new version.

Exponent CPU old code new code savings
675,000-1,330,000 Pro200 0.072 0.072 0%
1,330,000-1,675,000 Pro200 0.159 0.096 40%
1,675,000-2,000,000 Pro200 0.159 0.117 27%
2,000,000-2,330,000 Pro200 0.159 0.142 11%
2,330,000-2,630,000 Pro200 0.159 0.159 0%
675,000-1,330,000 P90 0.177 0.165 7%
1,330,000-1,675,000 P90 0.426 0.227 47%
1,675,000-2,000,000 P90 0.426 0.272 36%
2,000,000-2,330,000 P90 0.426 0.332 22%
2,330,000-2,630,000 P90 0.426 0.371 13%

The new program is SLOWER on exponents below 675,000. I strongly
encourage all users testing exponents above 675,000 to download the
new program. Follow the easy steps below.

1) Go to
Download either,, or mprime.tgz.
2) Unzip the new version on top of the old version.
3) Run the new program and choose Range / Continue.
4) You will be required to run a new one-hour self-test. This will
happen automatically. You do not need to run the 5 hour self-test
from the Options / Self-test choice.
5) You do not need to download a new database. You can install the
new version even if you're in the middle of testing an exponent.

A side note - when the new program continues a Lucas-Lehmer test
started by the previous version, it will not use the smaller length
FFT. When the new version starts the next exponent in your range
you'll get the full benefit of the smaller FFT run length.

Status and New Goals

The last three months has seen great progress in our search. We've
proven over 11,000 Mersenne numbers composite! There are no untested
exponents below 559,000 and only a few hundred exponents left to test
below 756,839.

This progress cut our Pentium-90 estimate to 1020 CPU years. The
new program reduces this estimate to 777 CPU-years to test all 46,501
remaining exponents below 2,655,000.

I've also adjusted our goals slightly. I now hope to test all exponents
below 1,345,000 by the end of 1997 and all exponents below 2,655,000 by
the year 2000. This minor change is related to the new program's ability
to test more exponents in a given FFT run length.

Source code

Source code is now available on the net! Download
from my "Source code!" page.


John Sweeney has taken many of my FFT tricks and put them in
a C program that runs on PowerMac PCs. His program has excellent
performance. You can download his program from my "Free Software!"
web page. This was a tremendous undertaking by John. Thanks!


If you've sent any results to me, then your name should appear
on my "Credits" web page. If I have forgotten, misspelled, or
misalphabetized your name, then please let me know. By the way,
I now know how to add accents and umlauts so check that too.

The web site now has a spiffier status page (thanks Luke) and
a top fifty producers page.

I sent 6,000 residues to David Slowinski for verification.
Of the 5,000 he was able to verify, there were fewer than 50
mismatches. This amount to a COMBINED error rate of less than 1%!
This is excellent!

I'm swamped! I'm not complaining. Managing 700+ testers takes a
fair amount of time. Until I can write a few programs to automate
my work, here's a couple little things you can do to lighten my load.
Only send results once a month or when your range ends. Daily or
weekly email adds to my overhead. After sending results place a
"marker" in the results file indicating results after this point
are new results. I know this may not be feasible for those of
you running the program on several machines - that's OK. Of course,
if you find a new Mersenne prime, send that right away :-)

Best wishes to all,
George Woltman