mersenneforum.org Mersenne statistics on p-1 factoring
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 2010-11-13, 22:50 #1 diep     Sep 2006 The Netherlands 2C016 Posts Mersenne statistics on p-1 factoring hi, Rumours that reached me indicated that p-1 factoring gets used at highspeed for Mersenne. Is there statistics on how much p-1 factoring is removing after trial factoring has been applied to Mersenne? We're investigating that now for Wagstaff. That is, the statistics are most important to compare with alternatives i'll try, if those alternatives factor anything useful at all after deep trial factorisation. I do have a break even table on trial factorisation for mersenne, what break-even table is getting used for the p-1 factorisation? Thanks for sharing any info, Vincent
 2010-11-14, 12:51 #2 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts When you start a P-1, Prime95 tells you the expected chance of finding a factor. It depends on what B1 and B2 bounds were chosen, which depends on the memory you allowed it and the formula at The Math page, but I think it usually is around 5%. The current strategy is to do most of the TF, then P-1, then the last bit of TF. e.g. for a target TF depth of 70, you'd TF from 0 to 2^69, do P-1, then TF from 2^69 to 2^70. This was calculated to be marginally better than doing all TF, then the P-1.
2010-11-14, 12:58   #3
diep

Sep 2006
The Netherlands

70410 Posts

Quote:
 Originally Posted by Mini-Geek When you start a P-1, Prime95 tells you the expected chance of finding a factor. It depends on what B1 and B2 bounds were chosen, which depends on the memory you allowed it and the formula at The Math page, but I think it usually is around 5%. The current strategy is to do most of the TF, then P-1, then the last bit of TF. e.g. for a target TF depth of 70, you'd TF from 0 to 2^69, do P-1, then TF from 2^69 to 2^70. This was calculated to be marginally better than doing all TF, then the P-1.
Thanks!

Yes i also figured out that the last part of the TF is simply very expensive.

The odds you TF a number after having done nearly a 30 minutes of TF, it becomes real little after that to do another additional bit. Whereas the next bit takes 1+ hour.

Also the amount that gets TF'ed here with 1 additional bit of TF is a lot less than the VRB-Reix test takes; this of course because last few years cpu's have improved that much in floating point.

5% roughly is not bad for P-1 at Mersenne.

Is your roughly 5% indication, a percentage of the remainder or a percentage of the number of prime exponents?

Here TF removes roughly 60% of all prime exponents for wagstaff.

Regards,
Vincent

Last fiddled with by diep on 2010-11-14 at 12:59

2010-11-14, 15:40   #4
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by diep Is your roughly 5% indication, a percentage of the remainder or a percentage of the number of prime exponents?
For such a small number it's almost the same, but it's the chance that the P-1 will be successful, so it's not quite either. It's: 5% of P-1'd candidates are eliminated through a P-1 factor. e.g. if 100 exponents remained after TF to the P-1-appropriate level, 5 should be eliminated with 95 remaining.

2010-11-14, 18:15   #5
diep

Sep 2006
The Netherlands

10110000002 Posts

Quote:
 Originally Posted by Mini-Geek For such a small number it's almost the same,
not really.

5% from 100% = 5%
5% from 40% = 2%

Quote:
 but it's the chance that the P-1 will be successful, so it's not quite either. It's: 5% of P-1'd candidates are eliminated through a P-1 factor. e.g. if 100 exponents remained after TF to the P-1-appropriate level, 5 should be eliminated with 95 remaining.
Glad you explain it clearly. It is 2% that gets eliminated from the original candidates (that are prime themselves).

Means it improves the total factorisation rate to 62% roughly.

Vincent

 2010-11-14, 18:30 #6 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2×5×587 Posts Look at the top producers report for success rates. Here is some data I quickly gathered. I excluded ANONYMOUS because lots will not have had enough memory and Rob_Dee because it looks like he has done lots of low exponent p-1. These are the top 5 I thought were accurate expectations. Code: Attempts Successes %Success 3128 211 6.75 2070 167 8.07 3255 192 5.9 2974 196 6.59 1613 110 6.82 Last fiddled with by henryzz on 2010-11-14 at 18:32
2010-11-14, 18:41   #7
diep

Sep 2006
The Netherlands

26·11 Posts

Quote:
 Originally Posted by henryzz Look at the top producers report for success rates. Here is some data I quickly gathered. I excluded ANONYMOUS because lots will not have had enough memory and Rob_Dee because it looks like he has done lots of low exponent p-1. These are the top 5 I thought were accurate expectations. Code: Attempts Successes %Success 3128 211 6.75 2070 167 8.07 3255 192 5.9 2974 196 6.59 1613 110 6.82
Wow very useful, many thanks!

How much RAM are we speaking about?

My hardware here has lots of RAM...
...and yet very little if i calculate from the 90s using knuth's transistor doubling rate of factor 2 each 18 months.

2010-11-14, 19:09   #8
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

10110111011102 Posts

Quote:
 Originally Posted by diep Wow very useful, many thanks! How much RAM are we speaking about? My hardware here has lots of RAM... ...and yet very little if i calculate from the 90s using knuth's transistor doubling rate of factor 2 each 18 months.
I think the current recommendation is >= 500MB per core. The person with ~8% probably has more memory that the other people. As far as I know once you get to 1-1.5GB per core more memory doesn't help that much more.

2010-11-14, 19:13   #9
diep

Sep 2006
The Netherlands

26·11 Posts

Quote:
 Originally Posted by henryzz I think the current recommendation is >= 500MB per core. The person with ~8% probably has more memory that the other people. As far as I know once you get to 1-1.5GB per core more memory doesn't help that much more.
Oh really, do most people have so little RAM?

I thought most sold thing is a laptop and most laptops have at most 2 cores and 2GB ram default.

Am i wrong?

Vincent

2010-11-14, 19:22   #10
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

2·5·587 Posts

Quote:
 Originally Posted by diep Oh really, do most people have so little RAM? I thought most sold thing is a laptop and most laptops have at most 2 cores and 2GB ram default. Am i wrong? Vincent
Allocated to Prime95. :)
When my pc had 2GB of memory I would never have allocated more than 1GB because the pc would have become unusable. The operating system and other running programs need memory as well especially windows.

2010-11-14, 19:27   #11
diep

Sep 2006
The Netherlands

13008 Posts

Quote:
 Originally Posted by henryzz Allocated to Prime95. :) When my pc had 2GB of memory I would never have allocated more than 1GB because the pc would have become unusable. The operating system and other running programs need memory as well especially windows.
Ah yes i forgot, it's fulltime busy factorizing here at the machines, not there :)

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