20101113, 22:50  #1 
Sep 2006
The Netherlands
2C0_{16} Posts 
Mersenne statistics on p1 factoring
hi,
Rumours that reached me indicated that p1 factoring gets used at highspeed for Mersenne. Is there statistics on how much p1 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 breakeven table is getting used for the p1 factorisation? Thanks for sharing any info, Vincent 
20101114, 12:51  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
When you start a P1, 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 P1, then the last bit of TF. e.g. for a target TF depth of 70, you'd TF from 0 to 2^69, do P1, then TF from 2^69 to 2^70. This was calculated to be marginally better than doing all TF, then the P1.

20101114, 12:58  #3  
Sep 2006
The Netherlands
704_{10} Posts 
Quote:
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 VRBReix test takes; this of course because last few years cpu's have improved that much in floating point. 5% roughly is not bad for P1 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 20101114 at 12:59 

20101114, 15:40  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
For such a small number it's almost the same, but it's the chance that the P1 will be successful, so it's not quite either. It's: 5% of P1'd candidates are eliminated through a P1 factor. e.g. if 100 exponents remained after TF to the P1appropriate level, 5 should be eliminated with 95 remaining.

20101114, 18:15  #5  
Sep 2006
The Netherlands
1011000000_{2} Posts 
not really.
5% from 100% = 5% 5% from 40% = 2% Quote:
Means it improves the total factorisation rate to 62% roughly. Many thanks for the answer! Vincent 

20101114, 18:30  #6 
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 p1. 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 20101114 at 18:32 
20101114, 18:41  #7  
Sep 2006
The Netherlands
2^{6}·11 Posts 
Quote:
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. 

20101114, 19:09  #8 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
1011011101110_{2} Posts 
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 11.5GB per core more memory doesn't help that much more.

20101114, 19:13  #9  
Sep 2006
The Netherlands
2^{6}·11 Posts 
Quote:
I thought most sold thing is a laptop and most laptops have at most 2 cores and 2GB ram default. Am i wrong? Vincent 

20101114, 19:22  #10  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·5·587 Posts 
Quote:
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. 

20101114, 19:27  #11 
Sep 2006
The Netherlands
1300_{8} Posts 
Ah yes i forgot, it's fulltime busy factorizing here at the machines, not there :)

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