What happens to unsuccessful P-1 trials?

[Silbe]

A P-1 factoring trial was performed on a certain Mersenne number with B1 and B2, and no factor was found.
1. Can the calculation be repeated with another pair B3,B4 where B3>B2?
2. Will it be worth to repeat the calculation on a machine with more memory (e.g. in 5 years when average user has more memory)?

[chalsall]

Originally Posted by Silbe

A P-1 factoring trial was performed on a certain Mersenne number with B1 and B2, and no factor was found.

The young can be so interesting to observe... Do you remember being that ignorant? Beautiful innocence.

P.S. Very importantly, ignorant != stupid.

P.P.S. Ignorant simply means you don't understand something fully. Stupid is what I am quite regularly.

[mathwiz]

Originally Posted by chalsall

The young can be so interesting to observe... Do you remember being that ignorant? Beautiful innocence.

P.S. Very importantly, ignorant != stupid.

P.P.S. Ignorant simply means you don't understand something fully. Stupid is what I am quite regularly.

What exactly was the point of this post?

As you might say, "this is a serious question".

[axn]

Originally Posted by Silbe

1. Can the calculation be repeated with another pair B3,B4 where B3>B2?

Can? Yes. Although ... B3>B2 is a bit ambitious. More realistic would be B1<B3<B2<B4.

Originally Posted by Silbe

2. Will it be worth to repeat the calculation on a machine with more memory (e.g. in 5 years when average user has more memory)?

Depends. If the goal is to find a factor and save PRP/LL test, it would be too late. If the goal is to find a factor, period, then it might be worth it. There would be other competing options like ECM, P+1, additional TF, but typically P-1 would still offer better bang for buck (as long as it it not "too close" to previous P-1 bounds, nor "crazy high" bounds with diminishing returns).

[chalsall]

Originally Posted by mathwiz

What exactly was the point of this post?

To make an observation. On the meaning of Life, the Universe, and Everything. And that Children can be taught.

Originally Posted by mathwiz

As you might say, "this is a serious question".

Fair. Serious (real-time) answer. I hope this satisfies your requirements.

Any further questions?

Seriously.

[kriesel]

Originally Posted by Silbe

A P-1 factoring trial was performed on a certain Mersenne number with B1 and B2, and no factor was found.
1. Can the calculation be repeated with another pair B3,B4 where B3>B2?
2. Will it be worth to repeat the calculation on a machine with more memory (e.g. in 5 years when average user has more memory)?

Yes, this is all too common, when B2=B1. There's an active subproject to redo thousands of such cases, between the DC wavefront and first-test wavefront, with prime95 v30.8 and adequate ram and substantial bounds.

It's preferable (more efficient) to use optimal bounds on adequate memory the first time.
Some users don't know to adjust the initial conservative low allowed stage 2 ram setting upward, or just can't allocate enough ram. If lacking ram, they should probably leave P-1 to those who have enough ram.

[chalsall]

Originally Posted by kriesel

Yes, this is all too common, when B2=B1.

Yes. Many have thought deeply about this kind of thing.

The resolution of the problem space seems to be a bit of a personal thing... I don't fully understand why... 9^)

[S485122]

Originally Posted by kriesel

...
It's preferable (more efficient) to use optimal bounds on adequate memory the first time.
Some users don't know to adjust the initial conservative low allowed stage 2 ram setting upward, or just can't allocate enough ram. If lacking ram, they should probably leave P-1 to those who have enough ram.

I think your explanation of the the mprime/Prime95 PRP entries in the worktodo file is not correct :

PRP (and PRP DC for manual assignments, or most versions)
PRP=[<AID>,|N/A,|<nul>]<k>,<b>,<n>,<c>[,<how_far_factored>,<tests_saved>[,<prp_base>,<residue_type>[,"comma-separated-list-of-known-factors"]]]
PRP=N/A,1,2,82589933,-1 (mersenne prime record)
PRP=N/A,1,2,268435459,1,80,0,3,5,"3" (Wagstaff number)
PRP=1,2,82589933,-1,82,0 (to have PrimeNet issue an AID for it at the next checkin)
NOTE: as of v30.x, it's recommended to include <how_far_factored,<tests_saved>, to prevent repeating unnecessary TF from 0 bits, and prevent repeating unnecessary P-1 factoring

"tests_saved" ? by doing a test ? Isn't it "p-1_done" ?
not signing to save space

[LaurV]

"Tests saved" used to refer to PRP/LL tests that would be "saved" if a factor is found. PRP/LL tests take a while to do. If P-1 founds a factor, there is no need to run the costly PRP/LL tests. Before, when we were doing LL, each factor you found saved between 0 and about 2.5 LL tests, depending when the factor was found (before any LL, after the LL, but before DC, or after DC, as people still like to find record factors and they were trying to factor even after DC - the fraction part comes from errors, re-doing tests, triple checks, whatever). Since we do PRP+Cert, each factor you find saves between 0 and ~1.3 PRP tests, more or less. So, if a PRP test takes a week to run on your hardware, and a P-1 test with 5% chance to find a factor takes 7 hours, then you better do P-1, this way you will run ~24 tests in 7 days, having a much better chance to clear one exponent (by finding a factor in average for every 20 tests you run) in the same time (plus, chance to find a record factor, but on the other hand, no chance to find a prime).

In the past, this "tests saved" was used by P95 to establish the B1/B2 limits according with your hardware. You could artificially increase it (edit the file by hand) to force P95 to do more P-1 (we did this, it was a common practice). Since new versions of P95 have other habits in doing stage 2, with a much larger B2, we don't know how the things are done currently, and how the parameter is still used.

[kriesel]

A better place for https://mersenneforum.org/showpost.p...58&postcount=8 would have been the reference info discussion thread.

Test (first LL) and DoubleCheck (LLDC) use a field P-1_done (boolean, true=1, false=0). (Server-issued example for P-1 already done: DoubleCheck=(aid),74213963,75,1)
(LL and DoubleCheck worktodo formats were mostly set before P-1 factoring was added to prime95.)

PRP uses a field tests_saved (~number of primality tests expected saved by finding a factor, and prime95 and the server support limited precision reals, such as 1.3 which the server currently emits, or 0. Server-manual-issued example: PRP=<aid>,1,2,74214079,-1,75,0). There was a discussion re Mlucas only supporting for PRP, 0, 1, or 2 in that field a while back, and before that a discussion for gpuowl implementation.
Similarly to PRP, Pfactor issues with number_of_tests_saved_by_finding_a_factor.
Work assignments for P-1 retry, on exponents that only got a stage 1 P-1 and have been LL or PRP tested once but need a DC, are all being issued P-1 with tests_saved=1 also: https://mersenneforum.org/showthread.php?t=28038

"Tests_saved" is in units of primality tests performed on the same hardware. LL and PRP are in math terms, about the same effort required, for the same efficiency of code.

Generally, for the worktodo formats, anything I post there is verified by multiple in-the-wild examples and/or the result of also consulting the program authors, PrimeNet API, or application source code. Note, the posted API is not current, but see its 5.3.5.1.2 for parameters p1 and saved. They're quite different. Section 7.2 shows use of p1 for LL or LLDC. There's a bit of supplementary information provided in a reference post.
See also the assignment examples explanations in https://www.mersenneforum.org/mayer/README.html toward its end.

Originally Posted by LaurV

In the past, this "tests saved" was used by P95 to establish the B1/B2 limits according with your hardware. You could artificially increase it (edit the file by hand) to force P95 to do more P-1 (we did this, it was a common practice). Since new versions of P95 have other habits in doing stage 2, with a much larger B2, we don't know how the things are done currently, and how the parameter is still used.

And CUDAPm1 mimicked traditional prime95's P-1 provisions, using the same worktodo entry formats for P-1, and accepting tests_saved values up to 9 IIRC. Inflated values were helpful in pushing bounds up to desired values on low-ram GPUs.

[lycorn]

Originally Posted by chalsall

P.P.S. Stupid is what I am quite regularly.

True. Yet another time. You never learn, do you?