Test Progress

Ι am testing a number and i have done 18% of progress. I would like to ask you three questions:

1) What is «iterations»;
2) If the progress arrives to 99% (e.g.), then it means that the posibility to be Mersenne Prime is very high?
3) If it finds a factor in 25% of the process, it will immediately inform me or the results will appear when process arrives 100%;

Thank a lot for help.

[Uncwilly]

Check out this thread: when does prime seach stop?. I think that it has the answers that you seek.

Short answers:
1) To do the test involved, certain steps are performed and the results are then used as the input for the next step (which is the same calculation, just with different starting numbers). Each pass through this process is an iteration. Total number of required iterations is about equal to the exponent that you are testing.
2) No.
3) If you are doing Trial Factoring, yes. If you are doing L-L testing, no factors can be found, the test must run to the end.

[Christenson]

Originally Posted by Unregistered

Ι am testing a number and i have done 18% of progress. I would like to ask you three questions:

1) What is «iterations»;
2) If the progress arrives to 99% (e.g.), then it means that the posibility to be Mersenne Prime is very high?
3) If it finds a factor in 25% of the process, it will immediately inform me or the results will appear when process arrives 100%;

Thank a lot for help.

1) Iterations refers to iterations in the Lucas-Lehmer(or LL) test on the number you are testing. Basically, the LL test for primality, explained on the math page, takes a number, squares it, and subtracts 2, all modulo the number you are testing. The first iteration starts with 4, and, after as many iterations in the exponent of the number you are testing, then the number is prime if and only if the result is zero.

That is, if you are testing 2^43,112,609-1 for primality, 43,112,609 LL iterations are required to determine if the number is indeed prime.

2) Progress in percent is simply the fraction of those iterations you have completed. It will reach 100% in a few weeks, Prime95 will contact the server, and your userid will be credited with 25 to 100GHz-Days of credit, and, typically, GIMPS will have a half of evidence needed to be sure the number being tested is indeed not a prime number. Someone else duplicating that LL test, referred to as a double-check or LL-D, will be the other half of the evidence.

3) With a LL test, it is not known if the number is prime until the very end of the test.

Other kinds of testing are able to show, sometimes (maybe 10% of the time) that the mersenne number you are testing has a factor. However, these tests (TF -- Trial Factoring, and P-1) are significantly faster than LL tests. Some in this project run many of those tests to reduce the number of LL tests necessary to find the next Mersenne Prime.

The odds of testing on an actual unknown mersenne prime are, unfortunately, significantly worse than the odds on a lottery ticket.

Hope this helps... Happy testing. And do play around on www.mersenne.org -- read up a bit on "the math".

[Mini-Geek]

Originally Posted by Christenson

The first iteration starts with 4, and, after as many iterations in the exponent of the number you are testing, then the number is prime if and only if the result is zero.

That is, if you are testing 2^43,112,609-1 for primality, 43,112,609 LL iterations are required to determine if the number is indeed prime.

Well, technically, it's p-2 iterations, not p, so in your example, it'd be 43,112,607 LL iterations. It seems that Prime95 counts from 2 to p instead of from 0 to p-2, so that the final iteration is displayed as p, but the total number of iterations is still p-2.

Originally Posted by Christenson

The odds of testing on an actual unknown mersenne prime are, unfortunately, significantly worse than the odds on a lottery ticket.

In terms of "probability of success per run", Mersenne numbers are MUCH better than lottery tickets - 1/450,000 for a first-time Mersenne test vs 1/18,000,000 for an average state lottery ticket (or 1/13,000,000 for a Mersenne doublecheck or 1/120,000,000 for a multi-state lottery; probabilities for Mersennes found in Prime95 using new PrimeNet reservations). But in terms of return on investment (the prize money, either for a <100M digit or a >100M digit Mersenne prime) assuming you pay for electricity, the lottery is a better return on investment. This is, of course, because of the difference in cost and payout.

Originally Posted by Christenson

Hope this helps... Happy testing. And do play around on www.mersenne.org -- read up a bit on "the math".

Indeed! A very informative page.

[Mr. P-1]

Originally Posted by Unregistered

2) If the progress arrives to 99% (e.g.), then it means that the posibility to be Mersenne Prime is very high?

In case it isn't clear from the above replies, if the progress arrives to 99% all it means is that you've nearly finished the test.