20210423, 21:30  #1 
P90 years forever!
Aug 2002
Yeehaw, FL
1110101010010_{2} Posts 
P1 / P+1 / ECM strategy for PRPCF
This thread has shown that we need a volunteer to organize a factoring for PRPCF project.
The volunteer would manage all exponents less than 15 or 20 million. It seems that exponents with known factors have had inadequate P1 done. Job #1 would be to decide what reasonable P1 and P+1 bounds should be. Job #2 would be to get all exponents adequately P1'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 doubleandtriple thread. Last fiddled with by Prime95 on 20210423 at 21:35 
20210424, 20:30  #2  
Einyen
Dec 2003
Denmark
5×17×37 Posts 
Quote:


20210425, 00:03  #3  
P90 years forever!
Aug 2002
Yeehaw, FL
2×3^{3}×139 Posts 
Quote:
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 P1 at least two levels higher (11M). Now you have to use some judgement  if P1 has already been run to B1=8M then don't bother. For P+1, I'd go to at least half the P1 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 P1 bounds for exponents below 1M and tell us what you think. 

20210425, 13:22  #4  
Einyen
Dec 2003
Denmark
6111_{8} Posts 
Quote:
Any exponent missing P1, we might as well do P+1 to the full P1 B1, since we get the P1 as well, since you recommended "at least half the P1" anyway. Exponents not missing P1 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. 

20210425, 16:08  #5  
P90 years forever!
Aug 2002
Yeehaw, FL
7506_{10} Posts 
Quote:
You could do three P+1 and find 87.5% of the P1 and 87.5% of the P+1 factors. But that makes little sense in that 1) P1 stage 1 is 50% faster, and 2) there are many more P1 factors to be found. 

20210425, 16:58  #6  
Jul 2003
wear a mask
5×7×47 Posts 
Quote:


20210425, 17:02  #7 
Jul 2003
wear a mask
66D_{16} Posts 
The geometric mean (the square root term) gets you a value intermediate to the ECM and P1 values for B1 and the other term might help with some degenerate cases where the P1 bounds might be less than the ECM bounds (or much too small relative to the ECM level).

20210425, 19:30  #8  
Einyen
Dec 2003
Denmark
5·17·37 Posts 
Quote:
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" P1 / P+1 levels for exponent ranges. 

20210426, 01:36  #9  
P90 years forever!
Aug 2002
Yeehaw, FL
2×3^{3}×139 Posts 
Quote:
Code:
exponent ECM goal P1 B1 P+1 B1 50K100K full B1=3M 30M 15M 100K250K half B1=3M 15M 8M 250K1M full B1=1M 10M 5M 1M4M half B1=1M 5M 3M There is no "right" answer here. Any coordinated effort will be better than what we have now. 

20210426, 23:53  #10 
Einyen
Dec 2003
Denmark
6111_{8} Posts 
Here are the P1 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 50K100K: 7 0 1 0 0 0 3770 87 100K200K: 6 0 0 0 0 0 6973 75 200K300K: 5249 759 214 35 31 12 187 31 300K400K: 5219 670 176 93 4 5 151 10 400K500K: 1846 283 3747 139 8 99 6 6 500K600K: 1609 314 3801 124 7 109 6 5 600K700K: 1796 3672 155 167 14 6 9 0 700K800K: 1660 3578 271 143 38 15 4 2 800K900K: 1216 4064 135 202 29 8 1 1 900K1000K: 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 50K100K: 1 1 0 0 0 0 402 191 100K200K: 0 2 0 0 0 0 1140 196 200K300K: 0 1 0 44 175 40 1146 89 300K400K: 0 0 0 0 0 0 1530 5 400K500K: 0 0 0 913 39 561 15 16 500K600K: 0 0 0 942 67 518 48 10 600K700K: 0 0 0 1427 99 53 20 27 700K800K: 1 0 0 1259 277 133 24 3 800K900K: 0 1 0 1440 183 15 25 3 900K1000K: 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 P1 B1 P+1 B1 50K250K 100M 50M 250K500K 30M 15M 500K1M 15M 8M 
20210427, 03:25  #11  
P90 years forever!
Aug 2002
Yeehaw, FL
1D52_{16} Posts 
Quote:
And for exponents with known factors, 5060% of those goals? Looks like the biggest need is P1 in the 200K to 1000K for exponents with known factors Last fiddled with by Prime95 on 20210427 at 03:25 

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