20030819, 14:16  #1 
May 2003
3·13 Posts 
How to determine the P1 boundaries?
Is there a way to calculate the P1 boundaries if I want to run P1 for some exponents that have already been P1'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 P1?

20030819, 21:36  #2 
Aug 2002
Termonfeckin, IE
2^{2}·691 Posts 
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 P1 bounds of surrounding exponents will tell you if that exponent has had enough P1 done. In my experience, it is usually not efficient to run P1. i.e. if any P1 has been done before  with reasonable limits  do not run it again with higher limits. 
20030820, 11:55  #3  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
When Prime95 chooses P1 bounds, it is optimizing in regard to overall GIMPS throughput. It chooses bounds such that [time to run P1 to chosen bounds]/[probability of finding a factor using chosen P1 bounds] = [either 1.015 or 2.03]*[time to run LL test]. If the P1 run is being made before any LL test, the multiplying factor is 2.03 because finding a factor then will save 2 LL tests (original and doublecheck) and about 3% of LL runs give erroneous results (usually because of hardware errors) which requires a third LL run to determine the correct result. If the P1 is being done after the first LL, but before the doublecheck LL, then the multiplying factor is halved. When choosing P1 bounds, Prime95 takes into account the amount of memory available. If that amount is insufficient for P1 stage 2, then Prime95 chooses the optimal B1 bound for a stage1only run. If you want to run P1 to higher bounds than those chosen by Prime95 for the particular exponent, you're free to do so. Quote:
Quote:
Caution: it appears that for exponents below 2 million, there has been considerable P1 work done that has not been reported to GIMPS for inclusion in the pminus1.txt file. That is, folks who have done P1 runs on exponents under 2 million for which no P1 work has been recorded in pminus1.txt have found far fewer factors than would normally be expected for the bounds they used. 

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