P-1 discussion

AntonVrba · 2007-03-25, 18:22

How does prime95 choose the B1 and B2 constants?
Can one read about how the todo file format is interpreted?

As an experiment I tried the P-1 factoring of Prime95
which I did not know it could do. With the data as given
Prime95 estimates a 5.6% chance of finding a factor
and takes about 205 seconds to complete -
so playing around with the to do file parameters and I
changed the the ...,33,1 to ...,23,2, Now Prime95 estimates
a 34% chance of finding a factor and after 1010 seconds
P-1 found a factor in stage #2, B1=40000, B2=700000.
1625879*2^1625879+1 has a factor: 500311388963
(this factor is not found with the ...,33,1 parameter)
but the next 5 exponents could not be factored.
end of experiment.

I have no idea what would be good B1 and B2 parameters,
Maybe somebody could advise, have i jumped the gun?
is P-1 testing done in progressive stages?

hhh · 2007-03-25, 21:20

P-1 is two-staged.
First stage:
If there is a factor $p$ , it will be found if $p-1$ has only factors below B1.
Second stage:
If there is a factor $p$ , it will be found if $p-1$ has only factors below B1, except one which can lie between B1 and B2.

How to choose B1/B2?
Prime95 calculates (in a very complicated formula) the best factor throughput by taking into account
-processor type (I guess),
-memory settings (stage 2 needs a lot of mem),
-factorworth (how many LLR tests are going to be saved by a factor, that is the final 1 in the Pfactor=... line),
-and up to where it has already been sieved (that's the 33: it has been sieved up to 2^33).
If you tell him that you sieved up to 2^50, it will tell you that P-1 isn't worth it and that you should directly LLR. If you lower the sieve value, it will raise the bounds. But that's not what one should do. Better it is to have faith in the wisdom of the MASTER, and feed the program the correct values. Tomorrow, the 33 would be a 35, for example, because we will have sieved more. But that dosn't change much.

Still questions?

Yours H.

PS. there is a way to chose the bounds manually, by a command i won't tell you, but which is far from secret. H.

Citrix · 2007-04-01, 18:46

Has anyone tried P+1 or ECM?

hhh · 2007-04-01, 18:54

Quote:

Originally Posted by Citrix

Has anyone tried P+1 or ECM?

Nope. ECM is slower than P-1, but why not, if it's still faster than LLR...
H.

ET_ · 2007-04-02, 18:53

Quote:

Originally Posted by hhh

Nope. ECM is slower than P-1, but why not, if it's still faster than LLR...
H.

Maybe after the end of trial-factoring to 30/35 bits ECM could be of some use, starting from the bigger exponents.

Luigi

geoff · 2007-04-04, 04:59

Is it worth using higher P-1 bounds than the Prime95 default, since unlike GIMPS, in this project finding a P-1 factor can also speed up the sieve a little bit?

The last field of the PFactor= line is the number of LL tests saved by finding a factor. I think this should be at least 2, maybe 3.

2007-03-25, 18:22	#1
AntonVrba Jun 2005 62₁₆ Posts	How does prime95 choose the B1 and B2 constants? Can one read about how the todo file format is interpreted? As an experiment I tried the P-1 factoring of Prime95 which I did not know it could do. With the data as given Prime95 estimates a 5.6% chance of finding a factor and takes about 205 seconds to complete - so playing around with the to do file parameters and I changed the the ...,33,1 to ...,23,2, Now Prime95 estimates a 34% chance of finding a factor and after 1010 seconds P-1 found a factor in stage #2, B1=40000, B2=700000. *16258792^1625879+1 has a factor: 500311388963** (this factor is not found with the ...,33,1 parameter) but the next 5 exponents could not be factored. end of experiment. I have no idea what would be good B1 and B2 parameters, Maybe somebody could advise, have i jumped the gun? is P-1 testing done in progressive stages? Last fiddled with by AntonVrba on 2007-03-25 at 18:27

2007-04-01, 18:46	#3
Citrix Jun 2003 1612₁₀ Posts	Has anyone tried P+1 or ECM? Last fiddled with by Citrix on 2007-04-01 at 18:46

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2007-03-25, 21:20	#2
hhh Jun 2005 101110101₂ Posts	P-1 is two-staged. First stage: If there is a factor $p$ , it will be found if $p-1$ has only factors below B1. Second stage: If there is a factor $p$ , it will be found if $p-1$ has only factors below B1, except one which can lie between B1 and B2. How to choose B1/B2? Prime95 calculates (in a very complicated formula) the best factor throughput by taking into account -processor type (I guess), -memory settings (stage 2 needs a lot of mem), -factorworth (how many LLR tests are going to be saved by a factor, that is the final 1 in the Pfactor=... line), -and up to where it has already been sieved (that's the 33: it has been sieved up to 2^33). If you tell him that you sieved up to 2^50, it will tell you that P-1 isn't worth it and that you should directly LLR. If you lower the sieve value, it will raise the bounds. But that's not what one should do. Better it is to have faith in the wisdom of the MASTER, and feed the program the correct values. Tomorrow, the 33 would be a 35, for example, because we will have sieved more. But that dosn't change much. Still questions? Yours H. PS. there is a way to chose the bounds manually, by a command i won't tell you, but which is far from secret. H.

2007-04-04, 04:59	#6
geoff Mar 2003 New Zealand 13·89 Posts	Is it worth using higher P-1 bounds than the Prime95 default, since unlike GIMPS, in this project finding a P-1 factor can also speed up the sieve a little bit? The last field of the PFactor= line is the number of LL tests saved by finding a factor. I think this should be at least 2, maybe 3.