The Mersenne Newsletter, issue #13 February 2, 1998

37th Known Mersenne Prime Discovered!!!
---------------------------------------

Congratulations to Roland Clarkson. On January 27th he discovered
that 2^3021377 - 1 is prime! This prime number is 909,526 digits long.
The computation took 46 days part-time on his 200-MHz Pentium computer.
David Slowinski confirmed the find on January 31st.

Roland is a 19 year-old sophmore at California State University
Dominguez Hills. He is the third youngest Mersenne prime discoverer -
behind Noll and Nickel. Incredibly, this was only the 8th exponent
he has tested!

Unlike the previous GIMPS finds, Roland let the PrimeNet server
(see Program News below) choose the lucky exponent. At first,
he did not want to test the exponent. Roland said, "I never would
have imagined two Mersenne primes would be so close together!".
In fact, in percentage terms, the gap between the 36th and 37th Mersenne
primes is the smallest ever.

To acknowledge Scott Kurowski's work on the PrimeNet server and
every GIMPS participants diligent work, official credit for this
prime will go to "Clarkson, Woltman, Kurowski, et.al.".

You can read the official press release at
http://www.mersenne.org/3021377.htm and be sure to check out
Chris Caldwell's web pages starting at
http://www.utm.edu/research/primes/notes/3021377/


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

Version 15 of prime95 is now available. This version contacts a central
server on the Internet to get exponents to test and report past results.
We call this PrimeNet. Many thanks to Scott Kurowski who wrote all the
server and client-side networking code. He also keeps the server
running smoothly. PrimeNet should greatly reduce my work load so that
I can write new code to let us test even larger exponents!

Version 15 is only available for Windows 95 and Windows NT, but the other
ports should be available in the coming weeks.

The best time to upgrade is when you are within a month of finishing
your current range. Just download and unzip the new prime95.exe on top
of the old prime95.exe. Read the readme and whatsnew files.
Run the program, answer the questions, and you're done. The new version
should finish off your old range, then report results and get new exponents
from the PrimeNet server! No more email!!

Need another reason to upgrade? Scott is offering a cash prize if
you find the 38th Mersenne Prime using PrimeNet.


More Milestones!
----------------

GIMPS has finished testing all exponents below 1,800,000, confirming
that M1398269 is the 35th Mersenne Prime.


Status for exponents below 2,655,000
------------------------------------

Since the last newsletter on September 1st (I apologize for the long gap
between newsletters), we've proved another 3,670 Mersenne numbers composite.
There are now only 657 untested exponents remaining below 2,655,000. The
chance of finding a new Mersenne prime in this range has fallen
from 22% to 3%. The time required to finish this range has dropped
from 105 Pentium-90 CPU-years to 18.


Status for exponents from 2,655,000 to 5,260,000
------------------------------------------------

Since September 1st, we've proved 20,128 Mersenne numbers composite.
There are now 45,058 exponents left to test. We've reduced the
work effort by 1,348 CPU years, leaving an estimated 4,307 P-90 CPU
years to complete.


IMPORTANT REMINDER: Range Reservation Policy
--------------------------------------------

Ranges may be returned to the available pool if no results
are reported during a 4 month period.

Hopefully, this will not be a burden to anyone - especially since I
encourage you to send in results once every month or two. As always,
I can make exceptions if you let me know ahead of time.



Best wishes and good luck. Maybe you will be the one to find
the 38th Mersenne prime! It could be over a million digits long.

George Woltman
woltman@magicnet.net