P-1 on Fermat numbers - Page 5

cxc · 2023-06-21, 12:04

As I thought it would be better and more useful to try P–1 on one of the Fermat numbers (\(F_{12}\)), and obtain a result before posting again, I am happy to confirm GIMPS is now accepting P–1 results via manual testing. (In fact this seems to have been enabled as of June 16.) No accepted work credit in GHz-days, but you can’t have everything.

Andrew Usher · 2023-06-24, 12:27

Yes, I see. James wouldn't reply to me about it, but evidently the point was made. Now the main purpose of this thread is mostly done - at least if Batalov can submit those results (or better) for F21-29. A few more remarks for this thread:

- If you can run Mlucas, the minimum memory that would be required for F31 and F32 should be satisfied by 16 and 32 GB allocated, respectively. One still can't assume everyone can get that on the machines they have.

- One Fermat factor, historically, was found by P-1. On the authority of Sam Wagstaff (and I had guessed it previously), the 5th factor of F12 was found by P-1 (stage 1 only) though it's not very smooth: this was in 1986, slightly before ECM would have found it otherwise. I imagine the discoverer also tested F11 and if he'd run any Stage 2 at all, the smaller of the two ECM factors of that would have been found.

- On the other hand 14 factors have been found by ECM, including that one - 2 of F11 (fully factored by luck), 3 of F13, and one each for 10, 12, 14-19, and 22. This looks to be a win for ECM, but consider the relative time spent on the two!

2023-06-21, 12:04	#45
cxc "Catherine" Mar 2023 Melbourne 5·11 Posts	P-1 on Fermat numbers As I thought it would be better and more useful to try P–1 on one of the Fermat numbers (\(F_{12}\)), and obtain a result before posting again, I am happy to confirm GIMPS is now accepting P–1 results via manual testing. (In fact this seems to have been enabled as of June 16.) No accepted work credit in GHz-days, but you can’t have everything. Attached Thumbnails

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2023-06-24, 12:27	#46
Andrew Usher Dec 2022 3×13² Posts	Yes, I see. James wouldn't reply to me about it, but evidently the point was made. Now the main purpose of this thread is mostly done - at least if Batalov can submit those results (or better) for F21-29. A few more remarks for this thread: - If you can run Mlucas, the minimum memory that would be required for F31 and F32 should be satisfied by 16 and 32 GB allocated, respectively. One still can't assume everyone can get that on the machines they have. - One Fermat factor, historically, was found by P-1. On the authority of Sam Wagstaff (and I had guessed it previously), the 5th factor of F12 was found by P-1 (stage 1 only) though it's not very smooth: this was in 1986, slightly before ECM would have found it otherwise. I imagine the discoverer also tested F11 and if he'd run any Stage 2 at all, the smaller of the two ECM factors of that would have been found. - On the other hand 14 factors have been found by ECM, including that one - 2 of F11 (fully factored by luck), 3 of F13, and one each for 10, 12, 14-19, and 22. This looks to be a win for ECM, but consider the relative time spent on the two!