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-   -   (Preying for) World Record P-1! (https://www.mersenneforum.org/showthread.php?t=27406)

 James Heinrich 2021-12-16 17:28

[QUOTE=Prime95;595280]Can the P-1 probability calculator be changed to allow more than 95 bits of TF?
Or even better, estimate the proper TF value given the amount of ECM that's been done?[/QUOTE][QUOTE=kruoli;595383]Take the estimated T-Level that is already on your site, then calculate T-level/log10(2). This is your value.[/QUOTE]The calculator will now accept either TF bitlevel [i]or[/i] ECM T-Level as input. If the latter it will be converted to equivalent TF bitlevel.

 lisanderke 2021-12-16 18:17

[URL]https://www.mersenne.ca/exponent/5003[/URL]
[URL="https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=33&b1=5000000000&b2=4.4190835712423E%2B15"]https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=33.639&b1=5000000000&b2=4.4190835712423E%2B15[/URL]
Do these values make sense? This is an example of stage 2 completed on 30.8b5

 firejuggler 2021-12-16 18:44

What do you consider a low exponent?
Because today, I found a rather big one.
[M]M8538269[/M] has a 129.728-bit (40-digit) factor: [url=https://www.mersenne.ca/M8538269]1127043861162808113814773315610463390639[/url] (P-1,B1=1000000,B2=330325710)

 lisanderke 2021-12-16 18:50

[QUOTE=firejuggler;595400]What do you consider a low exponent?
Because today, I found a rather big one.
[M]M8538269[/M] has a 129.728-bit (40-digit) factor: [URL="https://www.mersenne.ca/M8538269"]1127043861162808113814773315610463390639[/URL] (P-1,B1=1000000,B2=330325710)[/QUOTE]
Congratulations! Anything below Co-factor PRP FTC-wavefront is a low exponent to me :smile:

 Prime95 2021-12-16 18:53

[QUOTE=lisanderke;595393]
Now what amazes me the most is that for some reason, assignments of the second kind got MORE credit given. [/QUOTE]

Coincidence. The explanation is the larger exponents used a larger FFT length and thus deserved more credit.

Here's some good news. You can check if your save files are good. Create a worktodo.txt entry with a slightly larger B1 and no known factors. Let 30.7b9 run that and see if it finds some or all of the known factors. I think you'll find you're in good shape.

Example: Pminus1=N/A,1,2,5003,-1,200000999,200000999

 Prime95 2021-12-16 18:55

[QUOTE=firejuggler;595400]What do you consider a low exponent?
Because today, I found a rather big one.[/QUOTE]

I think of low as sub-100K. Maybe sub-1M.

Nice find, BTW! I'm a little jealous.

 charybdis 2021-12-16 18:59

[QUOTE=lisanderke;595397][URL]https://www.mersenne.ca/exponent/5003[/URL]
[URL="https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=33&b1=5000000000&b2=4.4190835712423E%2B15"]https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=33.639&b1=5000000000&b2=4.4190835712423E%2B15[/URL]
Do these values make sense? This is an example of stage 2 completed on 30.8b5[/QUOTE]

Note that many if not all exponents in this range have likely had far more ECM than has been reported. For example, this number has a known 44-digit factor found by ECM, and it's very unlikely that the reported t33.6 would have found this. See [URL="https://www.mersenne.ca/exponent/5333"]M5333[/URL] for a more extreme example.

Looking at the sizes of the [URL="https://www.mersenne.ca/userfactors/ecm/1/rexponent"]known factors[/URL], I'd say all exponents up to ~7500 have probably had at least a t45 (maybe even t50) from Ryan Propper. Ryan doesn't seem to have done any work from 7700-10000 so if I were you I'd focus your efforts there.

 lisanderke 2021-12-16 19:03

1 Attachment(s)
[QUOTE=Prime95;595403]Coincidence. The explanation is the larger exponents used a larger FFT length and thus deserved more credit.

Here's some good news. You can check if your save files are good. Create a worktodo.txt entry with a slightly larger B1 and no known factors. Let 30.7b9 run that and see if it finds some or all of the known factors. I think you'll find you're in good shape.

Example: Pminus1=N/A,1,2,5003,-1,200000999,200000999[/QUOTE]
Aha, that explanation is a relief.

I used the following worktodo entry as suggested: Pminus1=N/A,1,2,5903,-1,200000999,200000999
Copied save file for 5903 from 30.8b5 to 30.7b9. And Prime95 turned it into a 'bad' save file.

 lisanderke 2021-12-16 19:11

[QUOTE=charybdis;595405]Note that many if not all exponents in this range have likely had far more ECM than has been reported. For example, this number has a known 44-digit factor found by ECM, and it's very unlikely that the reported t33.6 would have found this. See [URL="https://www.mersenne.ca/exponent/5333"]M5333[/URL] for a more extreme example.

Looking at the sizes of the [URL="https://www.mersenne.ca/userfactors/ecm/1/rexponent"]known factors[/URL], I'd say all exponents up to ~7500 have probably had at least a t45 (maybe even t50) from Ryan Propper. Ryan doesn't seem to have done any work from 7700-10000 so if I were you I'd focus your efforts there.[/QUOTE]

Thank you for the insights! Before I move on from the 5k range, though, let me try wrap my head around this:
Let's assume B1=4e12 (as suggested by Zhangrc, no clue what the runtime for B1 would be) and B2=800K times 4e12, and T-level = 50, we have this calculation [URL="https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=50&b1=4000000000000&b2=3.2E%2B18"]https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=50&b1=4000000000000&b2=3.2E%2B18[/URL]
That seems a lot of effort for a very low chance of finding a factor.

 charybdis 2021-12-16 19:34

[QUOTE=lisanderke;595408]Thank you for the insights! Before I move on from the 5k range, though, let me try wrap my head around this:
Let's assume B1=4e12 (as suggested by Zhangrc, no clue what the runtime for B1 would be) and B2=800K times 4e12, and T-level = 50, we have this calculation [URL="https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=50&b1=4000000000000&b2=3.2E%2B18"]https://www.mersenne.ca/prob.php?exponent=5003&ecmtlevel=50&b1=4000000000000&b2=3.2E%2B18[/URL]
That seems a lot of effort for a very low chance of finding a factor.[/QUOTE]

Indeed it is. When this much ECM has already been run, it is more efficient to run further ECM rather than P-1 if your aim is solely to find factors. Of course you can only find a record P-1 factor by running P-1 :wink: but I'd still advise you to focus on ranges that Ryan hasn't targeted or you may not find factors at all.

 charybdis 2021-12-16 19:38

[URL="https://www.mersenne.ca/exponent/5231"]M5231[/URL] is a good example of a potential huge P-1 factor having already been found by Ryan using ECM.

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