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

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] 
The P1 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 P1. Doing adequate bounds P1 the first time is efficient; doing stage1 only first or probabilityoffactorpercpuhour first, with or without a followup second factoring to adequate bounds to retire the P1 task, is not efficient. I'm running a cleanup P1 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 P1 factor it before beginning the primality test (PRP/GEC/proof). 
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 P1 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. 
[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 P1 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. 
[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 P1 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 P1 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. 
[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 P1, but it will still be closer to 1% rather than 0.07% which is just nonsense. 
[QUOTE=tuckerkao;573090]So how likely will a factor between 2^77 to 2^78 skip the P1 factoring check?[/QUOTE]
The P1 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 P1 or TF). So probability that TF will find a factor after P1 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. 
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. 
[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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