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GIMPS newsletter #12, 1 September, 1997

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The Mersenne Newsletter, issue #12 September 1, 1997

36th Known Mersenne Prime Discovered!!!

Congratulations to Gordon Spence. On August 24th he returned from
a short trip to find his computer beeping like crazy. He turned on
the monitor to find that his computer had proved 2^2976221 - 1 is prime!
This prime number is a whopping 895,932 digits long. The computation
took 15 days on his 100-MHz Pentium computer. David Slowinski confirmed
the find on August 29th.

Gordon was quite lucky. In the last "Top Producers" list, compiled
on August 6th, Gordon ranked 127th with only 61 exponents tested.

Congratulations and credit also go to every GIMPS searcher. It would
have taken Gordon nearly a millenium to find this prime if he had been
working alone.

If there are no Mersenne primes between M1398269 and M2976221, then the
gap between the 35th and 36th Mersenne primes will be the 4th largest
in percentage terms. However, there are 8,554 exponents left to test
below M2976221.

You can read the official press release at

IMPORTANT REMINDER: New Range Reservation Policy

Ranges will 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.

This policy will make it easier for me to detect people who have
dropped out of the search and will ensure that active testers will
always have the smallest possible ranges to choose from.

More Milestones!

GIMPS has finished testing all exponents below M1257787, confirming
that M1257787 is the 34th Mersenne Prime. GIMPS has now double-checked
all exponents below M756839 and M859433 - definitively proving
them to be the 32nd and 33rd Mersenne primes.

Status for exponents below 2,655,000

Since the last newsletter on May 26th, we've proved another
6,460 Mersenne numbers composite. There are now only 4,327 untested
exponents remaining below 2,655,000. The chance of finding
a new Mersenne prime in this range has fallen from 50% to 22%.

The time required to finish this range has dropped from
238 Pentium-90 CPU-years to 105.

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

Since May 26th, we've proved 9,363 Mersenne numbers composite.
There are now 65,186 exponents left to test. We've reduced the
work effort by 578 CPU years, leaving an estimated 5,655 P-90 CPU
years to complete.

Best wishes and good luck. Maybe you will be the one to find
the 37th Mersenne prime!

George Woltman