20180208, 19:09  #1 
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{3}·5·29 Posts 
Intermediate P1 results
Hey, everybody!
Since P1 is a huge part of GIMPS to find factors and there is now GCD powered by GMP, I was thinking about this: What would it be like to be able to do one or a few GCDs of intermediate results? Of course, this does not need to be a mandatory option. I'm not sure how the calculation of \[b^a  1 \text{ mod } n, \text{ where } a = \prod_{p \text{ prime},\ p < B_1} p^{e_p} \text{ with } e_x = \lfloor \log_x B_1 \rfloor\] is done internally in Prime95. Maybe one can find a factor when checking for the result of \(c_\text{max} > c \in \mathbb{N}\) \[\text{GCD}(b^{a_c}1,n), \text{ where } a_c = \prod_{p \text{ prime},\ p < \left\lceil \frac{B_1 \cdot c}{c_\text{max}} \right\rceil} p^{e_p} \text{ with } e_x = \lfloor \log_x B_1 \rfloor\] with some predifined \(c_\text{max}\). This is especially usefull when using huge bounds and the factor can be found early on. This could increase willingness to use higher bounds. Greetings, Oliver! Last fiddled with by Nick on 20180209 at 11:43 Reason: Amended at kruoli's request 
20180208, 19:18  #2 
Sep 2003
13·199 Posts 
I'm not sure how long P−1 will continue to play a huge part.
The larger exponents get, the easier it is to do TF to higher bit depths. On the other hand, the larger exponents get, the longer P−1 takes. At some point there will be diminishing returns to doing P−1 because most of the factors it might reasonably be expected to find will already have been found by TF. I was doing P−1 in the 85M range, and had a long dry spell. I started again recently, but wonder if it's still worth it. 
20180209, 06:33  #3 
"Jacob"
Sep 2006
Brussels, Belgium
2^{2}×3^{3}×17 Posts 
When I look at the success rate of the P1 my computers do (about 4 % on the current 85M range) and the time they spend on it compared to LL tests it is still worthwhile. The kind of factors are different : you will have to TF a long time to find a 80 or 90 bits factor in that range (85 bits average on my work in the 80M85M range.)
So, yes P1 is still useful. The whole project cannot be reduced to TF. Jacob 
20180209, 07:11  #4 
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{3}·5·29 Posts 
Can a moderator please change \(\frac{B_1 \cdot c_\text{max}}{c}\) to \(\frac{B_1 \cdot c}{c_\text{max}}\)? Otherwise it would be useless.

20180209, 07:41  #5 
"Oliver"
Sep 2017
Porta Westfalica, DE
10010001000_{2} Posts 
My experience with P1 is like Jacob's (S485122), in that there is a measurable use of it (and there is no decline to be expected, as far as I believe). Since TF requires double the work per bit level, I assume we can go a few levels higher in the next years, but definitely not something like 10 levels. Take a M85,000,000 exponent as example. PrimeNet wants factoring to \(2^{71}\), GPU72 to \(2^{75}\). Using Jacob's numbers, you would need to go up at least to \(2^{85}\) to find half of the factors that P1 should find. Doing that would require an estimated 92,185 GHzd in total. Going to larger exponent, e.g. M850,000,000, would only drop that cost by a factor of 10, but in that exponent range, \(2^{85}\) is already the bit level limit of GPU72, so would have to go even further.
I like the approach of finding an optimum between prefactoring and doing two LLtests. P1 is a big part of finding that approach! GP2; When I look at your P1 stat page, it seems like you use really high bounds (an average of 258,6 GHzd per assignment). Of course, that's nice for a higher probability of finding a factor, but that's nearly the cost of a LL in the 85M range. But a success rate of more than 20 % is really nice! So I do not get completely how your "dry spell"* happened. *= The german word for that, Durststrecke, is much more descriptive, it combines Durst (thirst) and Strecke (route), so it mentions the urge (thirst) to reach something and the way left behind not being successful. 
20180209, 16:49  #6  
Sep 2003
13·199 Posts 
Quote:
Right now I am only doing the automatically assigned P−1 exponents with automatically assigned B1 and B2 bounds, which are currently in the 85M range. 

20180624, 13:44  #7  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3·5·457 Posts 
Quote:


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