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 2021-04-23, 21:30 #1 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 52×311 Posts P-1 / P+1 / ECM strategy for PRP-CF This thread has shown that we need a volunteer to organize a factoring for PRP-CF project. The volunteer would manage all exponents less than 15 or 20 million. It seems that exponents with known factors have had inadequate P-1 done. Job #1 would be to decide what reasonable P-1 and P+1 bounds should be. Job #2 would be to get all exponents adequately P-1'ed. Job #3 would be to get all exponents to one decent P+1 run. Same 3 jobs for exponents with no known factors. We want to choose even more aggressive bounds for these exponents. I envision a thread similar to the strategic double-and-triple thread. Last fiddled with by Prime95 on 2021-04-23 at 21:35
2021-04-24, 20:30   #2
ATH
Einyen

Dec 2003
Denmark

3,257 Posts

Quote:
 Originally Posted by Prime95 This thread has shown that we need a volunteer to organize a factoring for PRP-CF project. The volunteer would manage all exponents less than 15 or 20 million. It seems that exponents with known factors have had inadequate P-1 done. Job #1 would be to decide what reasonable P-1 and P+1 bounds should be. Job #2 would be to get all exponents adequately P-1'ed. Job #3 would be to get all exponents to one decent P+1 run. Same 3 jobs for exponents with no known factors. We want to choose even more aggressive bounds for these exponents. I envision a thread similar to the strategic double-and-triple thread.
I do not know about organizing a thread, but if someone else decides "reasonable P-1 and P+1 bounds", I can search the database for inadequate P-1/P+1 and generate worktodo files.

2021-04-25, 00:03   #3
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

52×311 Posts

Quote:
 Originally Posted by ATH I do not know about organizing a thread, but if someone else decides "reasonable P-1 and P+1 bounds", I can search the database for inadequate P-1/P+1 and generate worktodo files.
Sweet!

I'll toss out an idea for a starting point. If ECM is currently being assigned at the B1=1M level, then we should choose a P-1 at least two levels higher (11M). Now you have to use some judgement - if P-1 has already been run to B1=8M then don't bother. For P+1, I'd go to at least half the P-1 recommendation. Say, B1=5.5M.

Now I say this without knowing how long each of these runs would take, nor how many exponents need work done, nor how many participants you'll get.

I can also see arguments for doubling or tripling this recommendation and taking longer to get these work done. You only get to do this once (without duplicating effort to go to a higher B1 bound).

Study the current P-1 bounds for exponents below 1M and tell us what you think.

2021-04-25, 13:22   #4
ATH
Einyen

Dec 2003
Denmark

3,257 Posts

Quote:
 Originally Posted by Prime95 I'll toss out an idea for a starting point. If ECM is currently being assigned at the B1=1M level, then we should choose a P-1 at least two levels higher (11M). Now you have to use some judgement - if P-1 has already been run to B1=8M then don't bother. For P+1, I'd go to at least half the P-1 recommendation. Say, B1=5.5M.
The new P+1 is also doing P-1, and the P-1 test works 100% of the time right? So any P+1 bounds I can count as P-1 as well, if they are higher than existing P-1?

Any exponent missing P-1, we might as well do P+1 to the full P-1 B1, since we get the P-1 as well, since you recommended "at least half the P-1" anyway.
Exponents not missing P-1 we might do a lower P+1 then at about half B1. Maybe we should ask the "<20M unfactored" group as well what they think.

2021-04-25, 16:08   #5
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

777510 Posts

Quote:
 Originally Posted by ATH The new P+1 is also doing P-1, and the P-1 test works 100% of the time right?
No, my understanding is that P+1 is really 50% P+1 and 50% P-1.

You could do three P+1 and find 87.5% of the P-1 and 87.5% of the P+1 factors. But that makes little sense in that 1) P-1 stage 1 is 50% faster, and 2) there are many more P-1 factors to be found.

2021-04-25, 16:58   #6
masser

Jul 2003
Behind BB

180810 Posts

Quote:
 Originally Posted by Prime95 I'll toss out an idea for a starting point. If ECM is currently being assigned at the B1=1M level, then we should choose a P-1 at least two levels higher (11M). Now you have to use some judgement - if P-1 has already been run to B1=8M then don't bother. For P+1, I'd go to at least half the P-1 recommendation. Say, B1=5.5M.
Maybe something like this?

$B_1^{P+1} = max\left(10B_1^{ECM},\sqrt{B_1^{ECM}B_1^{P-1}}\right)$

2021-04-25, 17:02   #7
masser

Jul 2003
Behind BB

180810 Posts

Quote:
 Originally Posted by masser Maybe something like this? $B_1^{P+1} = max\left(10B_1^{ECM},\sqrt{B_1^{ECM}B_1^{P-1}}\right)$
The geometric mean (the square root term) gets you a value intermediate to the ECM and P-1 values for B1 and the other term might help with some degenerate cases where the P-1 bounds might be less than the ECM bounds (or much too small relative to the ECM level).

2021-04-25, 19:30   #8
ATH
Einyen

Dec 2003
Denmark

3,257 Posts

Quote:
 Originally Posted by Prime95 No, my understanding is that P+1 is really 50% P+1 and 50% P-1. You could do three P+1 and find 87.5% of the P-1 and 87.5% of the P+1 factors. But that makes little sense in that 1) P-1 stage 1 is 50% faster, and 2) there are many more P-1 factors to be found.
Should I use individual ECM level for each exponents or the "general" ECM level in the range, for example the ranges 50461-177763 and 250037-251257 are generally at B1=3M ECM for those with no known factor, but there are individual exponents in the range with more ECM and exponents with known factors have less ECM.

I can use individual ECM for each exponent, I got the full list from the ECM Progress page, but I'm just not sure if it would be better with "general" P-1 / P+1 levels for exponent ranges.

2021-04-26, 01:36   #9
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

52·311 Posts

Quote:
 Originally Posted by ATH Should I use individual ECM level for each exponents or the "general" ECM level in the range, for example the ranges 50461-177763 and 250037-251257 are generally at B1=3M ECM for those with no known factor, but there are individual exponents in the range with more ECM and exponents with known factors have less ECM.
I think it should be "general" ECM level. We are picking long-term ECM goals and P-1/P+1 bounds that are compatible with those goals. One might propose that for Mersenne's with known factors:

Code:
exponent     ECM goal    P-1 B1    P+1 B1
50K-100K    full B1=3M    30M         15M
100K-250K  half B1=3M   15M          8M
250K-1M     full B1=1M     10M         5M
1M-4M        half B1=1M     5M          3M
or some such. Mersenne's without known factors might have different long-term goals.

There is no "right" answer here. Any coordinated effort will be better than what we have now.

 2021-04-26, 23:53 #10 ATH Einyen     Dec 2003 Denmark 3,257 Posts Here are the P-1 data for exponents <1M: Code: With known factors: B1>1M B1>5M B1>10M B1>15M B1>30M Exponents B1=0 B1<=1M B1<=5M B1<=10M B1<=15M B1<=30M B1<=100M B1>100M 50K-100K: 7 0 1 0 0 0 3770 87 100K-200K: 6 0 0 0 0 0 6973 75 200K-300K: 5249 759 214 35 31 12 187 31 300K-400K: 5219 670 176 93 4 5 151 10 400K-500K: 1846 283 3747 139 8 99 6 6 500K-600K: 1609 314 3801 124 7 109 6 5 600K-700K: 1796 3672 155 167 14 6 9 0 700K-800K: 1660 3578 271 143 38 15 4 2 800K-900K: 1216 4064 135 202 29 8 1 1 900K-1000K: 217 4620 439 225 0 5 51 0 ------------------------------------------------------------------------------- Total: 18825 17960 8939 1128 131 259 11158 217 No known factors: B1>1M B1>5M B1>10M B1>15M B1>30M Exponents B1=0 B1<=1M B1<=5M B1<=10M B1<=15M B1<=30M B1<=100M B1>100M 50K-100K: 1 1 0 0 0 0 402 191 100K-200K: 0 2 0 0 0 0 1140 196 200K-300K: 0 1 0 44 175 40 1146 89 300K-400K: 0 0 0 0 0 0 1530 5 400K-500K: 0 0 0 913 39 561 15 16 500K-600K: 0 0 0 942 67 518 48 10 600K-700K: 0 0 0 1427 99 53 20 27 700K-800K: 1 0 0 1259 277 133 24 3 800K-900K: 0 1 0 1440 183 15 25 3 900K-1000K: 0 0 0 1628 3 4 16 16 -------------------------------------------------------------------------------- Total: 2 5 0 7653 843 1324 4366 556 Maybe goals like this for exponents with no known factors: Code: Exponent P-1 B1 P+1 B1 50K-250K 100M 50M 250K-500K 30M 15M 500K-1M 15M 8M I will have to check stats for exponents >1M, maybe tomorrow, but I can generate worktodo files, but no point in creating them too far in advance, since new factors are found all the time.
2021-04-27, 03:25   #11
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

52·311 Posts

Quote:
 Originally Posted by ATH Maybe goals like this for exponents with no known factors: Code: Exponent P-1 B1 P+1 B1 50K-250K 100M 50M 250K-500K 30M 15M 500K-1M 15M 8M I will have to check stats for exponents >1M, maybe tomorrow, but I can generate worktodo files, but no point in creating them too far in advance, since new factors are found all the time.
Looks reasonable to me. Best of all 0-400K is already P-1 done.

And for exponents with known factors, 50-60% of those goals? Looks like the biggest need is P-1 in the 200K to 1000K for exponents with known factors

Last fiddled with by Prime95 on 2021-04-27 at 03:25

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