P-1 / P+1 / ECM strategy for PRP-CF

[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.

[ATH]

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.

[Prime95]

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.

[ATH]

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.

[Prime95]

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.

[masser]

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?

[masser]

Originally Posted by masser

Maybe something like this?

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).

[ATH]

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.

[Prime95]

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:

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.

[ATH]

Here are the P-1 data for exponents <1M:

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:

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.

[Prime95]

Originally Posted by ATH

Maybe goals like this for exponents with no known factors:

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