20201003, 06:32  #45 
Romulan Interpreter
Jun 2011
Thailand
2499_{16} Posts 
Fact. However, P1 will duplicate the work every time (wasting resources, unless you have former saved files, and your software knows how to resume with extended B1, some time ago I posted a pari program who did that, the current P1 programs we use for Gimps do not know how to resume, you will still need a couple of multiplications and squarings, it is not just "continue from here"), while ECM will not waste (almost) any of the work, because each curve is randomized. Running two or more ECM curves with the same B1 will walk different paths and later curves may find factors missed by the first, while P1 walks the same path every time, so when you extend B1, you redo the former work to the former B1 from scratch.
Edit: sorry, I didn't see the other page. Most probably already replied, please ignore my post if so. Last fiddled with by LaurV on 20201003 at 06:35 
20201003, 06:43  #46  
Romulan Interpreter
Jun 2011
Thailand
3^{3}·347 Posts 
Quote:
Because in the first case, LCM(B1) was 2^4*3^2*5*7*11*13*17*19, while in the second case you have 2^5*3^3*5^2*7*11*13*17*19*23*29*31*37, and you have to compensate for all the missing primes. Last fiddled with by LaurV on 20201003 at 06:59 

20210203, 21:40  #47  
"Mihai Preda"
Apr 2015
3×11×41 Posts 
GpuOwl updated P1 calculator
Hi, recently I revisited the P1 calculator that's included with GpuOwl's source code https://github.com/preda/gpuowl/blob/master/pm1/pm1.cpp
The calculator is a small stanalone C++ program; to try it out check out gpuowl's source and invoke "make" in the pm1/ subfolder. In the calculator update, an error was fixed that was resulting in a bit of overoptimistic secondstage probabilities. In addition to that, a new simpler bounds cost model is implemented, and hopefully a more useful and informative output is generated. How to use it: invoke the executable "pm1" with an exponent and a "factoredto" bits, e.g.: ./pm1 105M 76 This will output a few B1/B2 choices, one per line  people should chose among them depending on how badly they desire to find P1 factors. The first line is the most efficient option, which should be chosen if one only cares about efficiency with little additional value assigned to a factor. Quote:
The bounds are by default computed based on the new "merged PRP+P1" first stage cost; but there is an option legacy which can be passed to estimate bounds for the classic P1: Quote:


20210204, 06:16  #48  
"Mihai Preda"
Apr 2015
10101001001_{2} Posts 
The program also allows to specify a fixed B1 or B2, and in that situation displays options for the other bound. Examples below with fixed B1=1M, or fixed B2=50M (note, the values below are good with the merged PRP+P1 first stage, unless legacy is used)
Quote:
Quote:
Some observations from my playing with these numbers are:  the bounds are remarkably resilient over a large range of values  i.e. they produce similar outcomes, with similar cost; there is not a huge difference between "the best" bounds and just some other bounds.  the rules of thumb for P1 at the wavefront might be: pick any B1 between 2M and 6M, pick any B2 between 10xB1 and 40xB1, and you should be fine. The effect of the new "merged first stage" is to increase the B1 by about a factor of 4, and to increase a tiny bit the B2. The probabilities of finding a factor in firststage or secondstage are roughly equal. A new way of seeing the bounds probability is to focus on B2 (instead of B1); basically P1 is run to B2, with some penalty applied from a low B1 in the form of some missed factors if they happen to have multiple subfactors in the [B1, B2] range. The percentage of such missed factors caused by the distance B1toB2 is now displayed. Last fiddled with by preda on 20210204 at 06:38 

20210206, 20:04  #49 
"Mihai Preda"
Apr 2015
3×11×41 Posts 
For what it's worth, on R7 I'm personally running with B1=9M, B2=180M for 102M103M exponents (factored to 76bits).

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