The Mersenne Newsletter, issue #9		January 15, 1997


M756839 is the 32nd Mersenne Prime
----------------------------------

Today, the last few Lucas-Lehmer results below 756839 trickled in.
Congratulations and thanks to all who contributed in "proving" this is
the 32nd Mersenne.

For those that are nit-pickers, you may be wondering what is the
chance that there was an error in our calculations and a Mersenne prime
escaped discovery.  There are roughly 1230 exponents that have
only been checked once, but not all of these have been sent to David
Slowinski for verification.  Assuming he will verify about half of 
these and assuming an error rate of 1%, then the chance of a missed
Mersenne prime is less than 1 in a 1000.


Happy Anniversary
-----------------

The Great Internet Mersenne Prime Search is now one year old.  The
first searcher, Reuven Singer, joined the first week in January.
Luke Welsh, who coined GIMPS, joined shortly thereafter.  On January 21,
we posted an invitation to sci.math.

I had hoped to gather 100 searchers to test all the exponents below
1,000,000 by 1999.  I sure did underestimate the response!  It has
been a pleasure working with all of you.  Thanks.


Welcome
-------

Since the last full newsletter 2 and a half months ago, the number of
searchers has swelled to 1150 - an increase of 430!  Welcome to all
the new searchers!


New Web Address
---------------

In case you haven't noticed, the web pages have moved to
http://www.mersenne.org/prime.htm.  This is much easier to
remember than the previous Compuserve address.  Many thanks to
Jeff Woods for hosting the web pages.


Program News
------------

Not much has happened since Version 13 was released in early November.
A few bugs have been fixed and there is now a version that can
run as a Windows NT service.

I've modified the error checking that is done every iteration.
The new test should catch more hardware errors and thus increase
the reliability of our results.  This new code is presently being tested
in the Linux version.

I am well aware that we are running out of ranges to test.  Who would
have imagined that?  I am working on code that will allow testing
exponents up to roughly 5,300,000.


Status
------

Since the beginning of November, we've proved 14,573 Mersenne
numbers composite (and one prime).  There are 31,927 exponents
remaining below 2,655,000.  The Pentium-90 CPU years estimate
dropped to 624 from 777.


PowerMac
--------

John Sweeney has continued to improve his C code.  If
you're not running version 1.4 please upgrade as soon as possible.


Miscellaneous
-------------

I now have a program to help me process results files.  Duplicate
results and results that are not in sorted order are no longer
a problem.

There is a small group working on automatically checking out ranges
and reporting results to a server on the Internet.  The present
manual system will still be available, but this new method will be
easier for me and for those of you managing multiple machines.
Email is not the most efficient way to manage a project of this size.
Hopefully, we'll have everything in place by summer.


Best wishes to all,
George Woltman
woltman@magicnet.net