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Finding World Record Primes Since 1996


GIMPS newsletter #1, 24 February, 1996

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The Mersenne Newsletter, issue #1 February 24, 1996


Since launching the search in early January, many of the lower ranges
have been completed with no new Mersenne primes found.

We now have over 40 people and over 50 computers involved in the search.

In January, there were over 24,000 primes under 1,000,000 that needed
checking. Today there are now less than 21,000. Well done!

David Slowinski

As most of you know, David Slowinski has been searching for Mersenne primes
for 17 years using spare CPU cycles on his company's supercomputers.
Unfortunately, he has not shared any information on the primes he has already
tested. However, he did offer to verify the residues of a dozen primes to
make sure our Lucas-Lehmer test program is operating correctly.

He verified the residues for: 659077, 659101, 659173, 710207, 945151, 950617,
973289, 979691, 981023, 989477.

He had not tested: 719027, 732041

From this I concluded two things. One, there are indeed untested ranges
below 859433. Two, Mr. Slowinski has probably tested most of the primes
from 859,433 to 1,000,000 or more in an effort to find a new record.

As a result, I've opened up the ranges from 1000 to 1299 for searching.
If you want to find a new world record prime and have checked out a range
between 860 and 1000, I would suggest you pick a range above 1100. Just
mail me the results that you have already and the new range you'd like
to test. You'll also need to download the latest program and database to
test these new ranges.

What are the odds?

I'm often asked "What are my chances of finding a Mersenne prime?"
Should you be lucky enough to pick a range that David Slowinski has not
previously tested - the following table approximates your chances:

Prime Odds for one Lucas-Lehmer test Odds for an entire range
------ ------------------------------ ------------------------
400000 1 in 4000 about 1 in 130
600000 1 in 5900 about 1 in 200
800000 1 in 7550 about 1 in 250
1000000 1 in 9250 about 1 in 300
1200000 1 in 11000 about 1 in 370

The above odds are only for primes where the program did not find a factor.

Program News

The factoring part of the program was originally written for 386 computers.
Since 486 and Pentium machines have a floating point unit and a data cache,
there are new optimizations that can be made. So far, the factoring has
been improved by 30%.

Since the program can now factor faster it makes sense to check for more
factors before beginning a Lucas-Lehmer test. This will improve the
overall time spent testing a range by about 2%.

This new version of the program is now available on the Web.

By the way, if you're worried that your 486 cannot run Lucas-Lehmer tests
in a timely manner, you can now use your 486 for factoring only. See the
web pages for more details.

Happy hunting,
George Woltman