### GIMPS newsletter #1, 24 February, 1996

Back to list of newslettersThe Mersenne Newsletter, issue #1 February 24, 1996

Status

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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

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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?

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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

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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

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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