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-   -   Getting others to do the work on exponents I like (was: Trial Factoring Progress) (https://www.mersenneforum.org/showthread.php?t=26499)

tuckerkao 2021-02-16 06:39

Getting others to do the work on exponents I like (was: Trial Factoring Progress)
 
I found a factor between 2^74 and 2^75 for M168,377,329 several minutes ago -
[URL="https://www.mersenne.org/report_exponent/?exp_lo=168377329&exp_hi=&full=1"]https://www.mersenne.org/report_exponent/?exp_lo=168377329&exp_hi=&full=1[/URL]

M82,589,939 has a known factor too -
[URL="https://www.mersenne.org/report_exponent/?exp_lo=82589939&exp_hi=&full=1"]https://www.mersenne.org/report_exponent/?exp_lo=82589939&exp_hi=&full=1[/URL]

Any similarities can be observed between these 2 exponents?

Uncwilly 2021-02-16 06:51

They are both known composites. As are the bulk of all Mersenne Number.

tuckerkao 2021-03-03 03:43

I believe I have figured out the assignment system by the trial factoring within Category 2 and 3. After I manually submit the results between 2^74 to 2^76, someone like curtisc will start to test the exponent I want with a faster PRP result -
[URL="https://www.mersenne.org/report_exponent/?exp_lo=108377323&exp_hi=&full=1"]https://www.mersenne.org/report_exponent/?exp_lo=108377323&exp_hi=&full=1[/URL]

kriesel 2021-03-03 13:19

The P-1 factoring done on [URL]https://www.mersenne.ca/exponent/108377323[/URL] is quite inadequate. It looks like curtisc has systems with prime95 default memory settings preventing stage 2 P-1. Doing adequate bounds P-1 the first time is efficient; doing stage1 only first or probability-of-factor-per-cpu-hour first, with or without a followup second factoring to adequate bounds to retire the P-1 task, is not efficient. I'm running a cleanup P-1 on that exponent now, which will complete in about an hour.
If you want to primality test yourself those exponents you begin with TF, immediately after reporting the TF to adequate bounds, request a manual PRP assignment for the same exponent, then adequately P-1 factor it before beginning the primality test (PRP/GEC/proof).

tuckerkao 2021-03-06 03:10

It seemed like that the chance of finding a factor only dropped by 0.0794% for not doing the trial factoring from 2^77 to 2^78 after the adequate P-1 factoring conducted -
[URL="https://www.mersenne.ca/exponent/168374303"]https://www.mersenne.ca/exponent/168374303[/URL]

I finished the 2^78 bit on another exponent and didn't find a factor anyway, so unless someone really finds at least a factor between 2^77 to 2^80, I probably won't do the trial factoring further, just aiming for the direct PRP test.

axn 2021-03-06 03:55

[QUOTE=tuckerkao;573083]It seemed like that the chance of finding a factor only dropped by 0.0794% for not doing the trial factoring from 2^77 to 2^78 after the adequate P-1 factoring conducted -
[URL="https://www.mersenne.ca/exponent/168374303"]https://www.mersenne.ca/exponent/168374303[/URL][/quote]

No, it is 0.3868%, if we go by the calculation. However, I don't trust either of those numbers. I think empirically, it is more like 1%.

[QUOTE=tuckerkao;573083]I finished the 2^78 bit on another exponent and didn't find a factor anyway, so unless someone really finds at least a factor between 2^77 to 2^80, I probably won't do the trial factoring further, just aiming for the direct PRP test.[/QUOTE]

It seems like you're trying to rationalize not running deeper TF? I mean, it is your hardware, so do what you want, but you'll be better off in the long run by doing the recommended TF.

tuckerkao 2021-03-06 09:19

[QUOTE=axn;573085]No, it is 0.3868%, if we go by the calculation. However, I don't trust either of those numbers. I think empirically, it is more like 1%.[/QUOTE]
Your % is the chance that the trial factoring may find a factor between 2^77 to 2^78, but Viliam F found a factor in M107,373,143 which can also be found from the P-1 factoring -
[URL="https://www.mersenne.org/report_exponent/?exp_lo=107373143&exp_hi=&full=1"]https://www.mersenne.org/report_exponent/?exp_lo=107373143&exp_hi=&full=1[/URL]

So how likely will a factor between 2^77 to 2^78 skip the P-1 factoring check?

I ran the trial factoring from 2^77 to 2^78 for another exponent and that got my video card torched hot. I'd rather Viliam F perform this action if must needed.

axn 2021-03-06 10:15

[QUOTE=tuckerkao;573090]Your % is the chance that the trial factoring may find a factor between 2^77 to 2^78,[/QUOTE]
No, it isn't. The chance of a factor if you TF from 2^77 to 2^78 is 1/78 or 1.28%. The chance will be reduced if we're doing the TF after P-1, but it will still be closer to 1% rather than 0.07% which is just nonsense.

axn 2021-03-06 10:32

[QUOTE=tuckerkao;573090]So how likely will a factor between 2^77 to 2^78 skip the P-1 factoring check?[/QUOTE]

The P-1 probability at B1=1M, B2=40M with TF done to 2^77 is 4.3848. Same probability with TF done to 2^78 is 3.9980. Hence, the overlap of probability is 0.3868 (i.e. the probability that there is a factor that could be found by either P-1 or TF).

So probability that TF will find a factor after P-1 has completed is 1.28 (normal TF prob) - 0.3868 (overlap prob) = 0.895% (or about 70% of the normal TF prob). This is the correct probability.

tuckerkao 2021-03-06 11:11

Looks like this is a personal preference ratio and may depend on each individual PC machines. It takes me 16 straight hours to run a trial factoring from 2^77 to 2^78, finish a PRP of the exponent that size will take me 28 days nonstop.

I have the liquid cooling for CPU but not GPU, the GPU couldn't run at its full speed if it's overheating.

I don't know about the CPU and GPU speeds of Kriesel and Viliam's computers, but the ratio doesn't appear to save me time in the long run.

axn 2021-03-06 12:32

[QUOTE=tuckerkao;573096]It takes me 16 straight hours to run a trial factoring from 2^77 to 2^78, finish a PRP of the exponent that size will take me 28 days nonstop.[/QUOTE]
On what hardware?


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