How to determine the P-1 boundaries?

[Boulder]

Is there a way to calculate the P-1 boundaries if I want to run P-1 for some exponents that have already been P-1'd earlier? Is there any use doing that or should I just let the program run the LL test; that is, are the boundaries already optimal when Prime95 runs the P-1?

[garo]

The boundaries are usually optimal when Prime95 runs the test EXCEPT when the computer does not have enough memory. In that case, often step 2 is not run.

Your best bet is to go to http://www.mersenne.org/status.htm and download the file pminus1.zip at the bottom of the page. Usually looking at the P-1 bounds of surrounding exponents will tell you if that exponent has had enough P-1 done.

In my experience, it is usually not efficient to run P-1. i.e. if any P-1 has been done before -- with reasonable limits -- do not run it again with higher limits.

[cheesehead]

Originally Posted by Boulder

are the boundaries already optimal when Prime95 runs the P-1?

Choosing "optimal" bounds depends on what goal one is optimizing in regard to.

When Prime95 chooses P-1 bounds, it is optimizing in regard to overall GIMPS throughput. It chooses bounds such that [time to run P-1 to chosen bounds]/[probability of finding a factor using chosen P-1 bounds] = [either 1.015 or 2.03]*[time to run L-L test]. If the P-1 run is being made before any L-L test, the multiplying factor is 2.03 because finding a factor then will save 2 L-L tests (original and doublecheck) and about 3% of L-L runs give erroneous results (usually because of hardware errors) which requires a third L-L run to determine the correct result. If the P-1 is being done after the first L-L, but before the doublecheck L-L, then the multiplying factor is halved.

When choosing P-1 bounds, Prime95 takes into account the amount of memory available. If that amount is insufficient for P-1 stage 2, then Prime95 chooses the optimal B1 bound for a stage-1-only run.

If you want to run P-1 to higher bounds than those chosen by Prime95 for the particular exponent, you're free to do so.

Originally Posted by garo

The boundaries are usually optimal when Prime95 runs the test EXCEPT when the computer does not have enough memory. In that case, often step 2 is not run.

Well, for a stage-1-only run Prime95 does choose a B1 bound that is optimal for that situation. The way I'd look at it is that if enough memory were available for stage 2, Prime95 would choose bounds which, being optimal for that different situation, give a higher probability of finding a factor than the stage-1-only B1 bound.

In my experience, it is usually not efficient to run P-1. i.e. if any P-1 has been done before -- with reasonable limits -- do not run it again with higher limits.

I agree with garo. Unless the already-done limits are very low (e.g., B1 and B2 less than 5000), ones ratio of [time] / [factors found] is better if one does P-1 on numbers which have had no prior P-1 work.

Caution: it appears that for exponents below 2 million, there has been considerable P-1 work done that has not been reported to GIMPS for inclusion in the pminus1.txt file. That is, folks who have done P-1 runs on exponents under 2 million for which no P-1 work has been recorded in pminus1.txt have found far fewer factors than would normally be expected for the bounds they used.