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Old 2005-03-08, 14:55   #1
HuzursuZ
 

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Default Testing exponents smaller than latest prime?

Hi there... I congratulate everyone for last victory... great job...

Now here is my question is thet could mersenne prime.net server sends new works lower then lasted known prime ? To see this I backuped my old work (24175741) and try to get a new one and I got (25136317) isn't that lower then current known prime ? will my computer run for nothing ?
 
Old 2005-03-08, 17:23   #2
Peter Nelson
 
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Quote:
Originally Posted by HuzursuZ
Now here is my question is thet could mersenne prime.net server sends new works lower then lasted known prime ? To see this I backuped my old work (24175741) and try to get a new one and I got (25136317) isn't that lower then current known prime ? will my computer run for nothing ?
Right now, (2^25964951)-1 is the largest known prime.

If you test 25136317 it cannot ever be the largest known prime, but it may still be prime, and would qualify you for a small cash prize via GIMPS (assuming we subsequently find a >10m digit one) and some fame.

Numbers in this range will not be over 10 million digits long but are faster to test.

You will not be wasting your time at all in terms of the project.

The reason is that we need to fill in the gaps. There are many numbers which have not been LL tested yet, and some of these MIGHT be prime. It is for this reason that 25964951 is the 42nd KNOWN mersenne prime, but we cannot say definitively that it is the 42nd mersenne prime until we confirm there are no lower undiscovered ones.

Everything up to the 38th mersenne prime has been tested which confirms it as M6972593. For higher mersenne primes (39th through 42nd known), we won't know that they are the 39th and 42nd until more testing is done.

The project is moving towards proving M13466917 as the 39th at the moment.
The combined test (with double checking) is up to 9889900, while first time tests are up to 15130000 (ie have exceeded it making it probably M39).

This exhaustively checks all exponents in the range, whereas higher exponents are not known sequentially because of time of assignment, speed of machines, machines giving up etc.

From status.htm page on www.mersenne.org:

All exponents below 9,889,900 have been tested and double-checked.
All exponents below 15,130,000 have been tested at least once.
Countdown to testing all exponents below M(20996011) once: 2,164
Countdown to testing all exponents below M(24036583) once: 10,938
Countdown to testing all exponents below M(25964951) once: 25,476
Countdown to proving M(13466917) is the 39th Mersenne Prime: 5,656
Countdown to proving M(20996011) is the 40th Mersenne Prime: 165,286
Countdown to proving M(24036583) is the 41st Mersenne Prime: 231,057
Countdown to proving M(25964951) is the 42nd Mersenne Prime: 273,161

In short, any exponent you are assigned between circa 15million and 33million could make you a discoverer of a new prime if it turns out to be one. We won't know that until the test is done by someone, and that someone could be you. The current M42 might then get numbered M43 for instance. The smaller the exponent the quicker to test so you may benefit from doing tests on these [relatively] small numbers. Testing > about 34 million takes longer but might gain the big prize.

So, any exponent you are assigned is worth doing. If you really want a chance at breaking a world record you will need an exponent bigger than 25964951.

If you get given an assignment you don't want then please use the Manual Unreserve Exponent facility to give it back to the primenet server rather than just backup or delete the files containing it. This will allow someone else to begin working on it without a long timeout delay.
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Old 2005-03-08, 19:24   #3
Uncwilly
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Quote:
Originally Posted by HuzursuZ
will my computer run for nothing ?
In addition to Peter's excelent answer; I wish to add the following:

You may want to select only 10M digit numbers to test. This way you know that if you find a prime, it will be the largest, however it may take a month or more to complete a number. If you decide to do that, please let the number that you are working on complete, so that the effort that you have put into it is not wasted.
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Old 2005-03-09, 06:16   #4
cheesehead
 
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Quote:
Originally Posted by HuzursuZ
Now here is my question is thet could mersenne prime.net server sends new works lower then lasted known prime ? To see this I backuped my old work (24175741) and try to get a new one and I got (25136317) isn't that lower then current known prime ? will my computer run for nothing ?
Let me expand upon a phrase in Peter Nelson's reply: "not known sequentially because of time of assignment, speed of machines, machines giving up etc."

Although an overall goal of GIMPS is to test all possible exponents from the smallest on up, there are several reasons why PrimeNet does not actually assign numbers to test in a strictly sequential way.

One reason is that some people quit an assignment before completion, so that someone else has to start over later on that exponent even though higher exponents may have already been tested.

Another reason is that most exponents are first assigned for trial factoring (TF), then assigned for L-L testing only after the TF assignment is completed. If one exponent is TFed on a 600 MHz computer while the next higher exponent is TFed on a 3.4 GHz computer, the higher exponent will become available for L-L testing before the lower exponent can be assigned for L-L testing.

Add in the possibility that the lower exponent's first TF assignee may quit before finishing, so that that exponent has to be re-assigned for TF before it even gets to L-L, plus the possibilities for abandonment and reassignment in the L-L queue, and you can see why it's easy for some high exponents to have L-L completed before some lower exponents are even assigned for L-L to you.
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