mersenne.ca

[James Heinrich]

Originally Posted by 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".

Not quite, actually. "Poorly P-1 factored" means that P-1 was done, but badly. This is different from "Not P-1 factored".

The purpose of the "poorly P-1 factored" page (and George's DC thread) is to find exponents were P-1 was done badly and get it re-done better, because PrimeNet won't hand out P-1 assignments if any P-1 work was done, even if it's near-useless.

Semantics aside, there's the practical issue of differentiating exponents with no P-1 where it maybe should've been done but wasn't, vs hasn't been done because nobody got around to it yet. The vast majority of exponents above ~130M or so have no P-1, but that's normal and expected, and when the wavefront moves there PrimeNet will assign those exponents out for P-1 factoring.

If you're looking for exponents that haven't had any P-1 work done, presumably you're not looking for exponents in the 130M-999M range that haven't been tested because nobody got there yet. Which only leaves the exponents that PrimeNet skipped over assigning for P-1 factoring because they're proven-composite, either by LL+DC, PRP+DC, PRP+proof, or factored. For factored exponents, you can/should use Factoring Beyond First Factor with the "No P-1" filter set.

I will consider how to possibly incorporate no-PM1-proven-composite exponents into this tool.

[alpertron]

Most Mersenne numbers already factored in the M17.1 range have no P-1 done.

Since that page now includes numbers that have at a least one prime factor, it would be very useful to show what numbers have no P-1 done in order to know what numbers have to be processed first.

[James Heinrich]

Originally Posted by alpertron

Most Mersenne numbers already factored in the M17.1 range have no P-1 done.
Since that page now includes numbers that have at a least one prime factor, it would be very useful to show what numbers have no P-1 done in order to know what numbers have to be processed first.

That's easily accomplished on the Factoring Beyond First Factor page. Just enter your exponent range and select No P-1 under "Filter by P-1 status".

[James Heinrich]

I've been poking around in the database looking for exponents that are:
* not prime
* not PRP
* have no factors
* have no P-1 effort

I haven't found anything under 100M. Perhaps I'm overlooking something, and would appreciate any counter-examples anyone wants to provide.

The smallest example I found in my data is 104818627 but that's also weird -- there is no logged P-1 effort, but PrimeNet does indicate that P-1 has been done (B1=763k,B2=~23M) but with no record of who/when. There seem to be quite a few like that in the 104M-107M range, only above 108M do I start finding exponents where PrimeNet really doesn't think any P-1 has been done.

[Rubiksmath]

I found the same - nothing under 100M fit those criteria it seems.

[alpertron]

Originally Posted by James Heinrich

That's easily accomplished on the Factoring Beyond First Factor page. Just enter your exponent range and select No P-1 under "Filter by P-1 status".

Thanks. I will use that.

[Andrew Usher]

Rubiksmath: Thanks for the example. I imagine exponents like 13877 are actually calculated using 2^40, and despite the 10% stated probability that's about the worst P-1 you'll see.

[masser]

Originally Posted by James Heinrich

The smallest example I found in my data is 104818627 but that's also weird -- there is no logged P-1 effort, but PrimeNet does indicate that P-1 has been done (B1=763k,B2=~23M) but with no record of who/when. There seem to be quite a few like that in the 104M-107M range, only above 108M do I start finding exponents where PrimeNet really doesn't think any P-1 has been done.

Can you see the program used to run these weird cases? Could this be the server not properly recognizing the P-1 aspect of GPUowl's PRP-1 calculations?

[kriesel]

Originally Posted by masser

Could this be the server not properly recognizing the P-1 aspect of GPUowl's PRP-1 calculations?

Not likely in the case of https://www.mersenne.org/report_expo...=1&swversion=1 which shows mprime 30.3b6 as the PRP software used.
Also, gpuowl v7.x generates separate PM1 and PRP result lines, as for 75164563 and those were properly recognized and stored.
Note time skew between lines is tens of hours.

{"status":"NF", "exponent":"75164563", "worktype":"PM1", "B1":"1000000", "B2":"30000000", "fft-length":"4194304", "program":{"name":"gpuowl", "version":"v7.2-53-ge27846f"}, "user":"kriesel", "computer":"asr2/radeonvii4", "aid":"redacted", "timestamp":"2022-09-16 00:55:44 UTC"}
{"status":"C", "exponent":"75164563", "worktype":"PRP-3", "res64":"cebed481e49f5d58", "residue-type":"1", "errors":{"gerbicz":"0"}, "fft-length":"4194304", "proof":{"version":"1", "power":"10", "hashsize":"64", "md5":"redacted"}, "program":{"name":"gpuowl", "version":"v7.2-53-ge27846f"}, "user":"kriesel", "computer":"asr2/radeonvii4", "aid":"redacted", "timestamp":"2022-09-16 21:58:06 UTC"}

https://www.mersenne.org/report_expo...=1&swversion=1

[Andrew Usher]

Well, I have just run into Rubiksmath's original problem, which is more evident with factored exponents included: the tool is useless below 1M due to a combination of the unrealistic 2^40 assumed TF and the 20% maximum probability. The Factoring Limits on mersenne.org does not do factored exponents, leaving no automated way to find such. Some can be found by using the stage-1-only option of "Factoring Beyond First Factor", but the actual limit would still need to be checked on individual exponent pages.

[LordJulius]

Something for the tail-end of your too long to-do list:
On https://www.mersenne.ca/pm1_worst.php, when the 'known factors' or 'either' box checked, the results TF column will show TFs below 2^67.
Thanks for cranking out all the maintenance and updates!