mersenne.ca

[James Heinrich]

Originally Posted by harlee

On the Exponents that were poorly P-1 factored page, what do you think about adding an option to find and display exponents with one or more known factors AND has P-1 results (exclude no P-1 work)?

I think I found a way to make it work. Please test it for me.

[harlee]

Originally Posted by James Heinrich

I think I found a way to make it work. Please test it for me.

The basics work. Did a quick search leaving everything as defaults except the following:

Exponent range 2000000 3000000
Factored: known factors

Issue I see is the TF depths doesn't match. The left hand side says TF is 67, Pfactor says 64, Pminus1 says 67. Do a search with the above so see what I mean.

Did another search with Exponent range 4000000 5000000. Same issue with the reported TF depths.

Don't know how you handle conflicting P-1 bounds. Noticed the search results shows P-11 bounds of B1=2048, B2=204800. If you look at M2951891
, the bounds is what was returned on 2003-12-13. However, on 2003-12-23, another P-1 result was returned with B1=10000, B2=10000 -- Larger B1 but smaller B2. This is another issue that probably doesn't really matter.

Another issue that has started to bother me is for some reason must of the exponents between 550K through 4.99M has 67 as the TF depth. M2951891 shows a TF result of up to 2^60 but 67 keeps being used. Is this some kind of default for lower exponents?

[James Heinrich]

Originally Posted by harlee

The left hand side says TF is 67, Pfactor says 64, Pminus1 says 67

This is on purpose. The Pfactor lines use Primenet-CPU-TF limit rather than actual or GPU72 TF limit, in addition to a very large number of tests-saved (generally 10 in your example range) to encourage Prime95 to pick larger bounds.

Originally Posted by harlee

Don't know how you handle conflicting P-1 bounds. Noticed the search results shows P-11 bounds of B1=2048, B2=204800. If you look at M2951891
, the bounds is what was returned on 2003-12-13. However, on 2003-12-23, another P-1 result was returned with B1=10000, B2=10000 -- Larger B1 but smaller B2.

The highest-probability P-1 is the one whose bounds are considered, doesn't matter whether it was run earlier/later, nor whether the B1 is bigger/smaller.

Originally Posted by harlee

exponents between 550K through 4.99M has 67 as the TF depth. M2951891 shows a TF result of up to 2^60 but 67 keeps being used. Is this some kind of default for lower exponents?

All Primenet-range exponents have been systematically TF'd (although not in the traditional sense) by the efforts of TJAOI. As of right now, there shouldn't be any undiscovered factored for any exponent smaller than 67.66 bits. Since mersenne.org and mersenne.ca operate on bitlevels rather than k values this is rounded down to 67 for now. In 6-9 months or so they'll pass 68 bits equivalence so all exponents will get their TF level bumped.

[harlee]

Thanks for the explanation. Just looks weird. Wonder how many others will mention the same thing about the bounds not matching - even between what "Factoring Beyond First Factor" and "Exponents that were poorly P-1 factored" returns for the same exponent. Thank you for your hard work. Hopefully, other will put this to good use.

[alpertron]

In the page https://www.mersenne.ca/pm1_worst.php , I would like that when I input 0.0 for the box immediately right of the text "Probability range", the output should include the exponents for which no P-1 was done because these should be the first to attempt factorization.

[Andrew Usher]

This seems to be related to what I and one other user have stated in the next thread below: https://www.mersenneforum.org/showthread.php?t=28403 .

I think it's intentional that 0 gives any amount of P-1, not none (making it unnecessary to specify a lower limit in the intended use). In most ranges the number of factored exponents with no P-1 is too large for this tool to be useful, and 'Factoring Beyond First Factor' already gives a 'no P-1' option if that is what's desired.

[alpertron]

The title of that page is Exponents that were poorly P-1 factored.

It is clear that if the Mersenne number has no P-1 done, it is "poorly P-1 factored".

If I want to use this tool to find Mersenne numbers to factor using P-1, it should show first the exponents where no P-1 was executed on them.

Another option is to add a checkbox that says "Include Mersenne numbers with no P-1 done".

[Rubiksmath]

This works pretty decently for lower exponents with known factors. The main discrepancy is between the percentage probability reported by this page and the actual probability with actual TF as reported on the exponent page itself for lower exponents.

When the TF level is "unknown" as reported by the exponent page they both match up perfectly. When they don't line up you get the search yielding exponents with a stated probability of 10% but with an 'actual' probability of 0.2% (the actual probability will be lower again due to ECM).

I believe this is due to probabilities with this tool being calculated as if TF was done to default (<2^50 for lower exponents), when they have been TF to at least 67 by TJAOI. Again it's only an issue for low exponents where the default TF is significantly below TJAOI limit. I personally would like to be able to use this tool to search by the "actual" probabilities as reported on the exponent pages even if I know they are wrong due to ECM. Maybe an option to change between calculating probability by default TF and actual TF? if it's too hard don't bother it isn't a big deal, more of a nice to have imo.

[Uncwilly]

Originally Posted by alpertron

It is clear that if the Mersenne number has no P-1 done, it is "poorly P-1 factored".
....
Another option is to add a checkbox that says "Include Mersenne numbers with no P-1 done".

I would say that none being done is not the same as poorly. Poorly means some was done, but that it does not meet expected levels.

Adding the "with no P-1 done" is a valid option though.

[Andrew Usher]

Yes, that is it. I would not think 'poorly' to include 'not at all', but the checkbox would be an acceptable compromise.

For unfactored exponents it does make a difference as the server will assign primality tests on exponents with poor P-1 but not with none; this was probably dates to when most users didn't have the memory to run stage 2 at all. The tool may be used to find those exponents and re-do P-1 before a first test or DC.

I just saw someone turn in a 100Mdigit LL assignment where the exponent had B1=B2=100K !

Rubiksmath:
Using actual TF was probably rejected because that can change, while the optimal TF doesn't. But the default 2^40 for exponents < 1M is just not really sensible, and forcing the minimum to the TJAOI level would be a reasonable answer, as is done on the exponent pages - can you point out one that says 'unknown' and doesn't do this?

[Rubiksmath]

Originally Posted by Andrew Usher

can you point out one that says 'unknown' and doesn't do this?

Okay here is one https://www.mersenne.ca/exponent/13877
It only says "unknown" for already factored exponents, and only some of the time.