mersenneforum.org HOW MANY CALCULATIONS AT ONCE??
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 2003-06-19, 17:43 #1 alienz   Jun 2003 3×7 Posts HOW MANY CALCULATIONS AT ONCE?? To complete a result takes poss 4 weeks +-, How many seperate or different prime numbers are tested in this period? It must be more than 1 number?? 1) The counter would continually reset after finding the number was not prime and then go on to the next one, only with prime numbers taking the full time to work out. 2) A computer must be able to calculate several numbers in a month. ???
2003-06-19, 17:52   #2

"Richard B. Woods"
Aug 2002
Wisconsin USA

11110000011002 Posts
Re: HOW MANY CALCULATIONS AT ONCE??

Quote:
 Originally Posted by alienz To complete a result takes poss 4 weeks +-, How many seperate or different prime numbers are tested in this period?
Only one Mersenne number is tested at a time.

Quote:
 It must be more than 1 number??
We're working with very large numbers now. :)

Quote:
 2) A computer must be able to calculate several numbers in a month.
Sure, if the numbers are small enough.

But GIMPS has already tested all the smaller numbers, and the very large ones it's testing now take a long time to test.

Which number are you testing? What type and speed is your computer?

2003-06-19, 18:11   #3
eepiccolo

Dec 2002
Frederick County, MD

2·5·37 Posts
Re: HOW MANY CALCULATIONS AT ONCE??

Quote:
 Originally Posted by alienz 1) The counter would continually reset after finding the number was not prime and then go on to the next one, only with prime numbers taking the full time to work out.
No, for the Lucas-Lehmer test, which is what we use for Mersenne numbers, it needs to be completed entirely for all numbers, prime or not. These numbers have millions of digits, which is why it takes weeks to test just one number.

 2003-06-19, 22:10 #4 alienz   Jun 2003 3×7 Posts I have a 3.06 P IV with 2gb Ram and a fast graphics card. 49.61% through a number in approx 2 weeks. Does this mean that for instance if the number is "test/3" it completes and moves onto the next?? If it is still running weeks later it is possibly closer to a prime??? These prime number tests really show how unadvanced single computers really are. In ten years time when we have faster machines, the prime numbers will be exponentially larger I guess.
 2003-06-19, 22:13 #5 alienz   Jun 2003 3·7 Posts how do you know what number you are testing??? 19463897 is obviously the start, is there any more info on the number I am testing??
 2003-06-19, 23:17 #6 xtreme2k     Aug 2002 17410 Posts The number you are testing is 2^19463897-1 which is a faily large number.
 2003-06-19, 23:26 #7 Kevin     Aug 2002 Ann Arbor, MI 433 Posts some of this stuff should go into an FAQ somewhere...... The number you are testing is actually 2^19463897 -1. (edit: go to http://www.mersenne.org/prime5.txt to see what 2^13466917 -1 looks like. ) To prove it's prime, you have to do recursive series. If, in this case, the 19463897th term is 0, than 2^19463897 -1 is prime. But you have to complete the whole test to figure out whether or not it ends in 0.
2003-06-19, 23:38   #8
trif

Aug 2002

CA16 Posts

Quote:
 Originally Posted by alienz I have a 3.06 P IV with 2gb Ram and a fast graphics card. 49.61% through a number in approx 2 weeks. Does this mean that for instance if the number is "test/3" it completes and moves onto the next?? If it is still running weeks later it is possibly closer to a prime??? These prime number tests really show how unadvanced single computers really are. In ten years time when we have faster machines, the prime numbers will be exponentially larger I guess.
Exponents are trial factored for small factors (small being relative since current LL tests being handed out will have no factors less than 66 bits) before going to LL testing. If you look at the Primenet reports availble on the web site, you will see that there are three kinds of assignments, the LL testing, trial factoring, and double checking of the original LL test. Trial factoring does end immediately if a factor is found (and the exponent won't be LL tested), but for most exponents in Primenet a factor won't be found, so the trial factoring test will go all the way to the end and then the exponent will slated for LL testing.

It takes so long because we are testing numbers that are huge. Back when double checks were still doing 4.5 million range exponents, they took about a week on my 466 Celeron.

2003-06-20, 03:21   #9

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 Originally Posted by alienz Does this mean that for instance if the number is "test/3" it completes and moves onto the next??
Can you tell us in more detail what you mean by "if the number is 'test/3'"?

Quote:
 These prime number tests really show how unadvanced single computers really are.
On the contrary: Several years ago, the only computers capable of testing such large numbers were supercomputers costing millions of dollars. It is a sign of the personal computers' great progress in performance per price that a thousand-dollar PC can handle these computations now.

Quote:
 how do you know what number you are testing??? 19463897 is obviously the start, is there any more info on the number I am testing??
Note, as others pointed out earlier, that 19463897 is not itself the number being tested, but merely the exponent of the Mersenne number 2^19463897-1, which is the actual number your computer is testing.

19463897 has only 8 digits. 2^19463897-1, if written out in decimal form, has 5,859,217 digits.

The numbers we're working on are so big that in GIMPS discussions we commonly refer to them by just the exponent. So when you see folks write that they're working on "12345679", they really mean they're working on 2^12345679-1. To avoid confusion, it is customary to write "M" just before the exponent, like "M12345679", to denote that the number under discussion is the Mersenne number 2^12345679-1, but some folks don't bother with that in forum postings.

 2003-06-20, 12:25 #10 epatka   Jun 2003 1000002 Posts I had a silly idea but I deleted it :)
 2003-06-21, 08:40 #11 alienz   Jun 2003 3·7 Posts I understand a little better now, thanks. It is a very big number. "HUGE" If I am working on M19463987, and each of us are working on single exponents of a 5.5 million digit number, how can any individual be responsible for finding a prime, I am sure the ansswer is obvious but I am just missing somthing I guess

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