The Mersenne Newsletter, issue #5		July 31, 1996


Welcome
-------

Since the last newsletter 50 days ago, we've more than doubled our ranks!
There are now more than 280 people involved in the search.  Welcome to all
the new searchers!

Status
------

The last 50 days has also seen great progress in our search.  We've proven
a whopping 4,796 Mersenne numbers composite!  This leaves us with only
17,603 untested Mersenne numbers with exponents below 1,300,000 and 
57,424 below 2,630,000.  If you use a 90 MHz Pentium as a standard, all of
these numbers can be tested in 1,146 CPU years.

For those that would like a breakdown, here are the number of exponents
that need testing in each 100,000 range as compared to 50 days ago.

300000-400000	18	vs.	49
400000-500000	229	vs.	357
500000-600000	1067	vs.	2084
600000-700000	1243	vs.	2625
700000-800000	2663	vs.	3030
800000-900000	2670	vs.	2891
900000-1000000	2677	vs.	2760
1000000-1100000	2889	vs.	3040
1100000-1200000	2427	vs.	2819
1200000-1300000	1720	vs.	2210

Factoring
---------

Brian Beuning and Torbjorn Granlund used 100 SPARC machines over 6 months
to factor Mersenne numbers.  Their work gave us over 2000 previously
unknown factors.  Thanks!

I'd also like to thank Conrad Walter Curry and Will Edgington.  Each has
dozens of computers working at finding even more new factors.

Double-checking
---------------

Thanks to the "Amdahl 6" and David Slowinski for supplying residues to
aid in the double-checking process.  This is extremely important to be
absolutely sure that a Mersenne prime hasn't gone unnoticed due to an
errant Lucas-Lehmer test.  Errors during Lucas-Lehmer tests are not
that uncommon.  Over 100 have been found already.

I'm sure everyone is curious about the famous Slowinski gaps.  Over 200
of the residues sent to Slowinski for verification had never been tested
before.

Interim Goals
-------------

I have two realistic goals for the next 6 months.  1) Show that M756839
is the 32nd (or 33rd!) Mersenne prime.  2) Double-check every exponent
below 400,000.

All the ranges below M756839 are currently being tested.  Some are being
tested by 486s so they may take a while to complete.

To complete the second goal, we'll need 486 owners and UNIX owners
that are running Crandall's lucas.c to test less than 2,000 exponents.
Pentium owners should continue testing large exponents so that 486 users
have useful work to do -- it just takes too long for a 486 to test a
large exponent.

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

The program has been ported for use on 486 and Pentium Linux systems.
There are also Windows screen saver versions available (only recommended
for Windows 3.1 and for some reason only works on half the machines that
have tried it).

Jason Kline has improved Crandall's lucas.c.  This version can be
up to twice as fast as lucas.c.  You can download this version from
http://www.scruznet.com/~luke/freeware.htm.  Others are working on
even faster versions!

As always, comments and suggestions for future program enhancements
are welcome.


Happy hunting,
George Woltman
74473.2626@compuserve.com