Total Project Time

paulunderwood · 2011-02-16, 23:14

Please may we have ballpark figures for the total amount of time it took to "bust" your five candidates, and how many GHz years to double check the 5 PRPs. If possible can we have a break down for each of the busted five.

philmoore · 2011-02-17, 00:09

It will take me awhile to get all the figures together, but I want to be sure I understand the question. By "total amount of time", do you mean calendar time? I started with two computers in the summer of 2007 testing eight sequences from the beginning, even though they had previously been tested by the people on Payam Samidoost's web-page (David Broadhurst, etc.) I had narrowed it down to five sequences and had tested all exponents up to 1.4 million at the time I started this project in October of 2008. So this project busted the remaining five sequences in 28 months, total time was more like 3.5 years if you include the time I was working alone.

Now GHz years, that is different. But I would guess that we have had something like 50 processors computing away most of the life of this project, so multiply 50 processors of typical speeds by 28 months, you have some kind of estimate. Maybe 350 GHz years or so.

By "double check the 5 PRPs", do you mean just the checking of the probable prime status once they were discovered, or do you mean double checking the entire sequence to be sure another prp was not missed? Only the first two sequences have been completely double checked, the other three would probably take about as much effort as the first time prp tests took. Of course, we would not do any more sieving or P-1 factoring.

If the time for a prp test is roughly proportional to the square of the exponent, the total time for a sequence would be proportional to the cube of the exponent of the prp, times the weight of the sequence. Of the orignal five sequences, the proportion of candidates in each sequence was as follows:

28433 - .128
2131 - .197
75353 - .219
40291 - .227
41693 - .229

So multiply these numbers by the cube of the prp found in the sequence, and you will have numbers roughly proportional to the total amount of effort devoted to each sequence. Of course, we sieved farther on 40291, and we also did P-1 factoring, so that would skew it a little bit, but this still should give you a pretty good idea. And it ignores the fact that we searched 75353 farther than we needed to...

So here is an estimate of the percentage of the total time spent on each sequence doing prp testing:

75353 - 0.3%
28433 - 0.7%
2131 - 8.5%
41693 - 14.0%
40291 - 76.5%

I hope this answers at least part of your question.

paulunderwood · 2011-02-17, 00:34

This does answer my question. Thankyou

2011-02-16, 23:14	#1
paulunderwood Sep 2002 Database er0rr 5·29·31 Posts	Total Project Time Please may we have ballpark figures for the total amount of time it took to "bust" your five candidates, and how many GHz years to double check the 5 PRPs. If possible can we have a break down for each of the busted five.

2011-02-17, 00:34	#3
paulunderwood Sep 2002 Database er0rr 5·29·31 Posts	This does answer my question. Thankyou Last fiddled with by paulunderwood on 2011-02-17 at 00:47

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2011-02-17, 00:09	#2
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2⁵×5×7 Posts	It will take me awhile to get all the figures together, but I want to be sure I understand the question. By "total amount of time", do you mean calendar time? I started with two computers in the summer of 2007 testing eight sequences from the beginning, even though they had previously been tested by the people on Payam Samidoost's web-page (David Broadhurst, etc.) I had narrowed it down to five sequences and had tested all exponents up to 1.4 million at the time I started this project in October of 2008. So this project busted the remaining five sequences in 28 months, total time was more like 3.5 years if you include the time I was working alone. Now GHz years, that is different. But I would guess that we have had something like 50 processors computing away most of the life of this project, so multiply 50 processors of typical speeds by 28 months, you have some kind of estimate. Maybe 350 GHz years or so. By "double check the 5 PRPs", do you mean just the checking of the probable prime status once they were discovered, or do you mean double checking the entire sequence to be sure another prp was not missed? Only the first two sequences have been completely double checked, the other three would probably take about as much effort as the first time prp tests took. Of course, we would not do any more sieving or P-1 factoring. If the time for a prp test is roughly proportional to the square of the exponent, the total time for a sequence would be proportional to the cube of the exponent of the prp, times the weight of the sequence. Of the orignal five sequences, the proportion of candidates in each sequence was as follows: 28433 - .128 2131 - .197 75353 - .219 40291 - .227 41693 - .229 So multiply these numbers by the cube of the prp found in the sequence, and you will have numbers roughly proportional to the total amount of effort devoted to each sequence. Of course, we sieved farther on 40291, and we also did P-1 factoring, so that would skew it a little bit, but this still should give you a pretty good idea. And it ignores the fact that we searched 75353 farther than we needed to... So here is an estimate of the percentage of the total time spent on each sequence doing prp testing: 75353 - 0.3% 28433 - 0.7% 2131 - 8.5% 41693 - 14.0% 40291 - 76.5% I hope this answers at least part of your question.