- **Marin's Mersenne-aries**
(*https://www.mersenneforum.org/forumdisplay.php?f=30*)

- - **Trial factoring to > 2^77?**
(*https://www.mersenneforum.org/showthread.php?t=27160*)

Trial factoring to > 2^77?Nowadays people mainly do trial factoring in the two-k project (which I have very little interest), and GPU72 is releasing TF assignments to 2^76 and seems very reluctant to give any higher bounds. However, there are hundreds of thousands of unfactored exponents in the 107-119M range
. So I suggest doing trial factoring to higher than 2^77, starting from 107M. My reasons are as follows: 1. Currently most of the GIMPSChina members, such as arpcar, 1997rj7, Neutron3529 and I are doing wavefront factoring, but out throughput is rather small, so more help is welcome. 2. Even excluding SRBase and TJAOI, the trial factoring progress is currently at a rate of 1e8 GHZd/year, while the rate of PRP tests is at 5e7 GHZd/year. (If only half of the people focused on PRP wavefront, we would have done to 2^78.) And there are about 140,000 exponents waiting for TF, with approximately 140 GHZd per exponent, so they add up to 2e7 GHZd. These could be finished in less than a year. 3. Some ranges, like 108.3M, has 2098 unfactored exponents. If we do no more TF and use normal P-1 bounds (4% chance of a factor), Those ranges will eventually enter the two-k project. At that time, we could save no more PRP (maybe except for a few LL DCs) by finding a factor. It's definitely better to do it now. 4. Many people prefer TF over PRP on their GPUs for many reasons. Not only because TF earn credit faster, but it also takes up very little disk space (2MB) and writes checkpoints frequently (so less work lost) and easier to setup. If we only focus on recommended bounds, there will be a time when some people have to do TF far away from the wavefront or doing nothing at all. |

It'll be the best if other users have done the P-1 factoring from M107M to M119M first(B1=1,000,000 and B2=40,000,000 if possible), then ask the SRBase group to run every exponents up to 2^77 or 2^78.
The P-1 factoring are way faster in Prime 30.5 and 30.6 than ever before. The chance that they can score the F-PM1 is almost quadruple timewise higher than the TF from 2^76 to 2^78 per result entry. They can follow the minimum recommended P-1 bounds too, do in the order like M[M]120202123[/M] which I continued TheJudger's factoring for an aftermath upgrade. |

[QUOTE=tuckerkao;588647]It'll be the best if other users have done the P-1 factoring from M107M to M119M first(B1=1,000,000 and B2=40,000,000 if possible)[/QUOTE]
The bounds are a little high, though. [QUOTE=tuckerkao;588647]The chance that they can score the F-PM1 is almost quadruple timewise higher than the TF from 2^76 to 2^78 per result entry[/QUOTE] Not that high. It's about 0.04/(2/78) = 1.56 times higher. However, with TF done to 2^78, one need smaller P-1 bounds to reach desired probability, thus saving more CPU time. Taking [M]M109999993[/M] for example: If it has been TFed to 2^76, then run P-1 with B1=700000 and B2=26000000, we get 65.9117% probability. If it has been TFed to 2^77, then to get ~65.9117% probability, we only need to run B1=400000 and B2=10000000, getting 65.9167% probability and saving 7.4GHZdays per exponent. |

[QUOTE=Zhangrc;588653]The bounds are a little high, though.
Not that high. It's about 0.04/(2/78) = 1.56 times higher.[/QUOTE] It's a little high with the trial factoring up to 2^76 but not too high for 2^78. The quadruple chance is when running with the larger P-1 bounds. The higher trial factoring depth should be balanced with the larger P-1 bounds. I'm running P-1 with B1 = 1,000,000 and B2 = 40,000,000 with TFs up to 2^78 all the time. If I want my TFs to go up to 2^79, then B1 = 1,600,000 and B2 = 65,000,000. When work the TFs up to 2^80, B1 = 1,900,000 and B2 = 90,000,000. |

[QUOTE=tuckerkao;588654]
The higher trial factoring depth should be balanced with the larger P-1 bounds.[/QUOTE] Yes if you want to find more factors, no if you want to save more time. [QUOTE=tuckerkao;588654] I'm running P-1 with B1=1,000,000 and B2=40,000,000 with TF up to 2^78 all the time. [/QUOTE] You are referring to your 168,***,*23, I suppose? |

[QUOTE=Zhangrc;588655]Yes if you want to find more factors, no if you want to save more time.
[/QUOTE] The recommended TF depth is only 2^76 for exponents from M107M to M119M. It'll definitely cost a lot more time to go up to 2^78. I'm running P-1 on M[M]115173323[/M], the P-1 with B1 = 700,000 and B2 = 26,000,000 will only cost 8 hours on my machine. TF from 2^76 to 2^77 will cost 132.88 GHz days on GPU TF from 2^77 to 2^78 will cost 265.76 GHz days on GPU Ask ViliamF, he has a lot of more experience than I do, that was what he told me. Apply the corresponding higher P-1 bounds if raise the TF bits. |

[QUOTE=tuckerkao;588656]The recommended TF depth is only 2^76 for exponents from M107M to M119M[/QUOTE]
That's my point: They have all been done months before, and if we still focus on these "recommended" bounds, we might have nothing to do (TF at the PRP wavefront) in the future. |

[QUOTE=Zhangrc;588653]The bounds are a little high, though.
Not that high. It's about 0.04/(2/78) = 1.56 times higher. However, with TF done to 2^78, one need smaller P-1 bounds to reach desired probability, thus saving more CPU time. Taking [M]M109999993[/M] for example: If it has been TFed to 2^76, then run P-1 with B1=700000 and B2=26000000, we get 65.9117% probability. If it has been TFed to 2^77, then to get ~65.9117% probability, we only need to run B1=400000 and B2=10000000, getting 65.9167% probability and saving 7.4GHZdays per exponent.[/QUOTE] Maybe most users have better GPUs than CPUs. It'll cost me more time to run TFs from 2^76 to 2^77 for M107M to M119M than the difference between the larger and the normal P-1 bounds on my PC. However the GPU prices are skyrocketing recently, I'd rather to buy AMD Ryzen 5950X than Nvidia Geforce 3070 Ti if only 1 choice but not the other. [QUOTE=Zhangrc;588655]Yes if you want to find more factors, no if you want to save more time. You are referring to your 168,***,*23, I suppose?[/QUOTE] TFs from 2^76 to 2^78 of M168M are around 46% faster to finish than 2^76 to 2^78 of M115M. P-1 with B1 = 1,000,000 and B2 = 40,000,000 of M168M are 36% slower to complete than the same 2 bounds for M115M. |

[QUOTE=tuckerkao;588659]It'll cost me more time to run TFs from 2^76 to 2^77 for M107M to M119M than the difference between the larger and the normal P-1 bounds on my PC.[/QUOTE]
Me too. However we should compare the time of running TF and P-1 on the same GPU, not TF on GPU and P-1 on CPU. |

[QUOTE=Zhangrc;588660]Me too. However we should compare the time of running TF and P-1 on the same GPU, not TF on GPU and P-1 on CPU.[/QUOTE]
I always run TFs on my GPU and P-1 on my CPU simultaneously, so I get more works done on the same machine during the same day. It's impossible to only use GPUs to run P-1, it'll consume certain amount of CPU computations with GPUOwl as well. [QUOTE=Zhangrc;588653]The bounds are a little high, though. Not that high. It's about 0.04/(2/78) = 1.56 times higher.[/QUOTE] Maybe it's different in a lower range. That ratio seems to be more accurate in M168M, but then the total GHz days are not the same. I've gotten 4 F-PM1: M[M]168173323[/M], M[M]168830323[/M], M[M]168860123[/M], M[M]168926123[/M] so far. Only 1 factor from 2^76 to 2^77 M[M]168101891[/M] was reported from another user in the same range. |

[QUOTE=tuckerkao;588661]I always run TFs on my GPU and P-1 on my CPU simultaneously, so I get more works done on the same day.[/QUOTE]
Me too, that doesn't hurt your throughput. Would you like to help with some wavefront TF? |

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