(Preying for) World Record P-1!

[James Heinrich]

Originally Posted by Prime95

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?

Originally Posted by kruoli

Take the estimated T-Level that is already on your site, then calculate T-level/log10(2). This is your value.

The calculator will now accept either TF bitlevel or ECM T-Level as input. If the latter it will be converted to equivalent TF bitlevel.

[lisanderke]

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

[firejuggler]

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

[lisanderke]

Originally Posted by firejuggler

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

Congratulations! Anything below Co-factor PRP FTC-wavefront is a low exponent to me

[Prime95]

Originally Posted by lisanderke

Now what amazes me the most is that for some reason, assignments of the second kind got MORE credit given.

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]

Originally Posted by firejuggler

What do you consider a low exponent?
Because today, I found a rather big one.

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

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

[charybdis]

Originally Posted by lisanderke

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

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 M5333 for a more extreme example.

Looking at the sizes of the known factors, 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]

Originally Posted by Prime95

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

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]

Originally Posted by charybdis

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 M5333 for a more extreme example.

Looking at the sizes of the known factors, 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.

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 https://www.mersenne.ca/prob.php?exp...0&b2=3.2E%2B18
That seems a lot of effort for a very low chance of finding a factor.

[charybdis]

Originally Posted by lisanderke

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 https://www.mersenne.ca/prob.php?exp...0&b2=3.2E%2B18
That seems a lot of effort for a very low chance of finding a factor.

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 but I'd still advise you to focus on ranges that Ryan hasn't targeted or you may not find factors at all.

[charybdis]

M5231 is a good example of a potential huge P-1 factor having already been found by Ryan using ECM.