[Mission Accomplished] Let's finish primality verification through Mp#48*, M(57 885 161)
From [URL]https://www.mersenne.org/report_milestones/[/URL]
(last updated 20210311 23:30:07 UTC, updates every 15 minutes) All exponents below 54 480 799 have been tested and verified. Countdown to verifying all tests below 55 million: 40 (2 available) Countdown to verifying all tests below 56 million: 2 600 (1 737 available) Countdown to verifying all tests below M(57 885 161): 20,643 (A RadeonVII running relatively current gpuowl can chew through these at a rate of ~3.54 per day, as LL DC, or PRP with proof generation) 20643 * ~112 GHD adds up though. It could use any help from the PRPCFDC team that becomes available, now that that effort is wrapping up. People running Google Colab and feeling the pinch of the 15GB Google drive limit for larger exponents could help too. The odds of completing verification through M([M]57885161[/M]) and settling if it is indeed Mp#48 this year are good. Verification milestones have averaged progress of 4M per year the past few years. It's been over 8 years since its discovery. A little extra push should get the verification done in time for George's year end vacation (and the next prime discovery?) 
[QUOTE=kriesel;573453]It could use any help from the PRPCFDC team that becomes available, now that that effort is wrapping up.[/QUOTE]I have 8 workers comprising around 20 cores doing DCs'. Some are a little beyond the range because of some targeted work and reboots while I have not been able to touch the machines. But they will slowly move back down to the lower Cats.

From [URL]https://www.mersenne.org/report_milestones/[/URL]
(last updated 20210316 11:30:06 UTC, updates every 15 minutes) All exponents below 54 480 799 have been tested and verified. Countdown to verifying all tests below 55 million: 35 Countdown to verifying all tests below 56 million: 2 343 (1 581 available) Countdown to verifying all tests below M(57 885 161): 19 918 Relative to post 1, 4.5 days, 2064319918 = 725; 161.11.../day. An optimistic extrapolation indicates ~ 124 days (4 months) to go. Approximately late July 2021. (Optimistic for at least these reasons: as p increases, each is more work, estimated as about 7% more effort per exponent for 57.88M compared to 56M; as a milestone is approached, more of the DC effort lands above the milestone, lowering rate of exponents/day below the milestone; to the extent that effort is a function of school or vacation schedules, summer can show lower throughput; to the extent effort is affected by air conditioning cost, summer can have lower throughput) 
ID type of work please? TIA.

[QUOTE=kriesel;573834]From [URL]https://www.mersenne.org/report_milestones/[/URL]
as a milestone is approached, more of the DC effort lands above the milestone, lowering rate of exponents/day below the milestone; [/QUOTE] This reason is going to be the big one that the estimate is optimistic 
And, waiting for stalled exponents to expire and reissue. Some have no expiration date at all, and [URL="https://www.mersenne.org/assignments/?exp_lo=54634339&exp_hi=57885161&execm=1&exfirst=1&exp1=1&extf=1&excert=1"]ETAs of months or years[/URL]. (Click on ETA (days) twice to see that.) Something will need to be done about that.

Expiration dates for the assignments currently not showing an expiration will get attached as soon as they move about halfway into cat 1. Any exponent that's been assigned for over 360 days will instantly expire when that happens. If you notice right now, every double check assignment below 56000000 has an expiration date on it.
Waiting for years for an exponent to expire is really a nonissue. Cat 1 is never fully assigned, every day the range for cat 1 moves and more old assignments pick up their expiration dates. The assignments that will hang around the longest are the ones that are checking in every day/week/month, but are making hopelessly slow progress, so they won't expire until their full 360 days has run out and they've moved sufficiently far into cat 1 or even into cat 0. 
From [URL]https://www.mersenne.org/report_milestones/[/URL]
Progress toward next GIMPS milestones (last updated 20210417 13:30:06 UTC, updates every 15 minutes) All exponents below 55 133 759 have been tested and verified. Countdown to verifying all tests below 56 million: 917 (373 available) Countdown to verifying all tests below 57 million: 6 708 (3 751 available) Countdown to verifying all tests below M(57 885 161): 15 132 Relative to [URL="https://mersenneforum.org/showpost.php?p=573834&postcount=3"]post 3[/URL] status, 32 days 2 hours, 1991815132=149.17/day So, at least 101.4 days to go estimated, approximately 27 July 2021, and that is optimistic for several reasons previously stated. Probably by at least a month. 
My estimate is that all exponents below Mp#48 will be cleared approximately 4 months after it moves into cat 1 DC range. Unless someone at some point starts poaching lagging assignments, there will be some cat 2 assignments that will have to age out completely and expire and get reassigned and cleared.
It's going to take some time for that to happen, the upper bound of cat1 is currently 57109304. This puts the likely date sometime after September. 
[URL]https://www.mersenne.org/report_milestones/[/URL]
[CODE]Progress toward next GIMPS milestones (last updated 20210515 20:30:06 UTC, updates every 15 minutes) All exponents below 55 645 729 have been tested and verified. All exponents below 102 717 821 have been tested at least once. Countdown to first time checking all exponents below 103 million: 3 Countdown to first time checking all exponents below 104 million: 1 813 (5 available) Countdown to verifying all tests below 56 million: 93 Countdown to verifying all tests below 57 million: 2 380 (1 064 available) Countdown to verifying all tests below M(57 885 161): 9 456 Countdown to verifying all tests below M(74 207 281): 304 382 Countdown to verifying all tests below M(77 232 917): 359 929 Countdown to verifying all tests below M(82 589 933): 458 642[/CODE] 
I'm also working on it, currently doing LLDC's in the 5711XXXX range with my Ryzen 7 3700X CPU!

I borged a new machine (one that I should have done months ago). It is set to do DCs.

Make sure that the assignments are in the range up to M57 885 161, as the server may already output higher ranges.

[QUOTE=moebius;578509]Make sure that the assignments are in the range up to M57 885 161, as the server may already output higher ranges.[/QUOTE]
I put it to DC, what ever the server will give it. It is proving itself now with Cat 4's. I expect in 3 or 4 weeks it will be in the Cat 2 or 1 range. Since it is a borg, I will not babysit it too much. 
[B]From [URL]https://www.mersenne.org/report_milestones/[/URL]
[/B] [B]Progress toward next GIMPS milestones [I](last updated 20210615 14:00:07 UTC, updates every 15 minutes)[/I][/B] [LIST][*] All exponents below [COLOR=blue]55 916 617[/COLOR] have been tested and verified.[*] All exponents below [COLOR=blue]103 313 627[/COLOR] have been tested at least once.[*] Countdown to first time checking all exponents below 104 million: [URL="https://www.mersenne.org/assignments/?exp_lo=103313627&exp_hi=104000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]91[/URL] [COLOR=black](2 available)[/COLOR][*] Countdown to first time checking all exponents below 105 million: [URL="https://www.mersenne.org/assignments/?exp_lo=103313627&exp_hi=105000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]9 265[/URL] [COLOR=black](7 420 available)[/COLOR][*] Countdown to verifying all tests below 56 million: [URL="https://www.mersenne.org/assignments/?exp_lo=55916617&exp_hi=56000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]21[/URL][*] Countdown to verifying all tests below 57 million: [URL="https://www.mersenne.org/assignments/?exp_lo=55916617&exp_hi=57000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]565[/URL][*] Countdown to verifying all tests below M(57 885 161): [COLOR=blue]3 560[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]295 610[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]351 080[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]449 789[/COLOR][/LIST] 
[QUOTE=Uncwilly;578512]I put it to DC, what ever the server will give it. It is proving itself now with Cat 4's. I expect in 3 or 4 weeks it will be in the Cat 2 or 1 range. Since it is a borg, I will not babysit it too much.[/QUOTE]
Make sure that your account is set to get smallest exponents :) 
[QUOTE=Zhangrc;581055]Make sure that your account is set to get smallest exponents :)[/QUOTE]I currently have 11 DC assignments in Cat 0 or Cat 1. I know what I am doing.

Projection for showing MP48* is MP48
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Based on the previous few months countdown of remaining exponents to DC to 56M to zero today, and the current remaining count for Mp48*, an estimate is computed which yields ~20211007.

[QUOTE=kriesel;582097]Based on the previous few months countdown of remaining exponents to DC to 56M to zero today, and the current remaining count for Mp48*, an estimate is computed which yields ~20211007.[/QUOTE]
There is the effect of Cat 2, then Cat 1, and then Cat 0 limits passing the milestone. And then there is the effect that as the exponents to achieve the milestone gets below say 20, there can be more intense activity than when it was 150 to go. 
By using the history of reaching the 56M milestone, I believe most if not all those effects are well allowed for. The last bit might see a little more aggressive approach because of the priority of Mp48* over a minor 1M milestone. That would have the effect of moving the completion date earlier than the projection, and indicates the odds of reaching it this year are excellent. Any slowdown of completion rate due to run time scaling is modest compared to the calendar margin. (57885161/56M)^2.1 ~ 1.072. It is potentially offset by increased interest or additional DC signups or hardware upgrade easily. If it is not offset at all, it amounts to ~7.2% of 3.4 months = about a week later. That still leaves more than 2.5 months margin to complete it this year. Completing 58M this calendar year seems very likely, and 59M a moderate possibility.
But you know what an estimate is. It's a value we use, with caution, even though we know it is wrong. 
2000 exponents to go until Mp48 is confirmed.

[QUOTE=Uncwilly;581056]I currently have 11 DC assignments in Cat 0 or Cat 1. I know what I am doing.[/QUOTE]
I have 10 that are being worked on or in queue. Should pick up another 1 or 2 soon. 
Basis of estimate
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Here is a screen capture of the LibreOffice formulas and input data used to compute the Oct 7 estimate.

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[B]From [URL]https://www.mersenne.org/report_milestones/[/URL]
[/B] [B]Progress toward next GIMPS milestones [I](last updated 20210811 16:15:11 UTC, updates every 15 minutes)[/I][/B] [LIST][*] All exponents below [COLOR=blue]56 606 299[/COLOR] have been tested and verified.[*] All exponents below [COLOR=blue]104 125 811[/COLOR] have been tested at least once.[*] Countdown to first time checking all exponents below 105 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104125811&exp_hi=105000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]94[/URL][*] Countdown to first time checking all exponents below 106 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104125811&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]6 689[/URL] [COLOR=black](4 722 available)[/COLOR][*] Countdown to verifying all tests below 57 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56606299&exp_hi=57000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]25[/URL][*] Countdown to verifying all tests below M(57 885 161): [URL="https://www.mersenne.org/assignments/?exp_lo=56606299&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]196[/URL][*] Countdown to verifying all tests below 58 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56606299&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]261[/URL][*] Countdown to verifying all tests below 59 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56606299&exp_hi=59000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]5 397[/URL] [COLOR=black](3 216 available)[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]280 826[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]336 300[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]435 008[/COLOR][/LIST]Updated projection to determination of MP#48* as Mp#48 or not by exhaustive DC to that exponent level is ~20211005, slightly earlier than the projection posted in late June. 
[QUOTE=kriesel;585415]
Updated projection to determination of MP#48* as Mp#48 or not by exhaustive DC to that exponent level is ~20211005, slightly earlier than the projection posted in late June.[/QUOTE] My prediction is November 22, 2021 95%, ±82 days 50%, ±25 days Let's see :) 
An alternate way of estimating DC completion to Mp#48*
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This is practical when the number of remaining exponents below a milestone is < ~200.
Go to [URL]https://www.mersenne.org/assignments/?exp_lo=56917213&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1[/URL] Then sort by estimated completion date. Then from the end of the list, latest estimated completion, consider that those with expiration date sooner than ETA will be reassigned if not completed before expiration. Find the latest such expiration by moving back up the list from the end. At the moment that's 57864227, 25 days from now. There are currently 107 left below Mp#48*. So that will be a Cat 0 DC upon expiration. Cat 0 typically will complete within 7 days of assignment. (I expect reassignment to be swift, therefore negligible.) So this initial approach predicts completion to Mp#48* by 25 + 7 = 32 days from 20210821; by 20210921. Next, review the list for others that expire later than that, not currently updating. There are a few now up to 34 days and showing no current updating. These will add up to 34  25 = 9 more days to the estimate, or ~ 20210930, assuming no further updating or completion occurs before expiration. There are a few with expiration dates further out, but these are currently updating. Except for [URL]https://www.mersenne.org/M57817769[/URL] which last updated 20210819 and has 35 days remaining. Corresponding to reaching Mp#48* by ~ 20211001. That is very close to the 20211007 date estimated in June, 20211005 estimated 11 August, or 20211004 estimated 21 August, that were based on the 56M milestone trajectory and remaining # of exponents to Mp#48* versus date/time. I believe the method of relying for projection fitting on the lowest unverified exponent over time is using an inferior metric, both because in a sense it depends at any point in time upon only a single exponent's state, and because those are consistently exceptional, laggard exponents. It does not reflect the progress made upon the many other exponents that also must be cleared to reach a milestone. In the extreme case, the lowest unverified exponent could remain fixed for its entire expiration period, up to ~60 days before completion or reassignment, if it is assigned as a cat 1 DC as part of a group of >200 remaining, to a system that begins it and then ceases transmitting updates or making sufficient progress, until it is the last remaining below the milestone. Unlikely, but possible. From [URL]https://www.mersenne.org/report_milestones/[/URL] [B]Progress toward next GIMPS milestones [I](last updated 20210821 14:15:08 UTC, updates every 15 minutes)[/I][/B] [LIST][*] All exponents below [COLOR=blue]56 917 213[/COLOR] have been tested and verified.[*] All exponents below [COLOR=blue]104 244 157[/COLOR] have been tested at least once.[*] Countdown to first time checking all exponents below 105 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104244157&exp_hi=105000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]35[/URL][*] Countdown to first time checking all exponents below 106 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104244157&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]4 390[/URL] [COLOR=black](2 510 available)[/COLOR][*] Countdown to verifying all tests below 57 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56917213&exp_hi=57000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]7[/URL][*] Countdown to verifying all tests below M(57 885 161): [URL="https://www.mersenne.org/assignments/?exp_lo=56917213&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]107[/URL][*] Countdown to verifying all tests below 58 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56917213&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]138[/URL][*] Countdown to verifying all tests below 59 million: [URL="https://www.mersenne.org/assignments/?exp_lo=56917213&exp_hi=59000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]4 326[/URL] [COLOR=black](2 752 available)[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]278 624[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]334 160[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]432 867[/COLOR][/LIST] 
I took a whack at estimating when the exponents up to 57885161 would all be doublechecked in [url=https://www.mersenneforum.org/showpost.php?p=512300&postcount=3064]this March 31, 2019 post[/url]. My guess, based on simple extrapolation of thencurrent progress, was about two and a half years from then. The responses (thanks to all!) [and which you can see by clicking on [u] Newer milestone thread[/u] at top right of the single post view] indicated that my guess was not unreasonable.
One thing that has changed since then is that firsttime LL testing is no longer routine. Instead, PRP testing which can be verified relatively cheaply is the order of the day. 
[QUOTE=Dr Sardonicus;586254]I took a whack at estimating when the exponents up to 57885161 would all be doublechecked in [URL="https://www.mersenneforum.org/showpost.php?p=512300&postcount=3064"]this March 31, 2019 post[/URL]. My guess, based on simple extrapolation of thencurrent progress, was about two and a half years from then. The responses (thanks to all!) [and which you can see by clicking on [U] Newer milestone thread[/U] at top right of the single post view] indicated that my guess was not unreasonable.
One thing that has changed since then is that firsttime LL testing is no longer routine. Instead, PRP testing which can be verified relatively cheaply is the order of the day.[/QUOTE]Well done. 2.5 years from 20190331 is 20210930. Very good agreement with most recent estimates. 20211122 is the outlier. (This reminds me of a combustion model discussed decades ago in one of my advanced engineering classes. It incorporated so many independent simplifying assumptions, over two dozen. that their errors canceled well and it was quite accurate in most cases.) PRP first testing began at p~75.5M so was not a factor in reaching 57885161 in first tests. PRP/GEC/proof can be used in place of LL DC and essentially eliminates the possibility of need for TC then. That favors earlier completion dates for DC to 57885161. TC would probably add only a few days to completion date. From [URL]https://www.mersenneforum.org/showpost.php?p=512475&postcount=3072[/URL] posted 2 April 2019: "I expect that ll tests below 47 mio will be verified on 21 April 2019 ±45 days 48 mio  on 19 July 2019 ±45 days 49 mio  on 14 October 2019 ±45 days 50 mio  on 07 January 2020 ±45 days." Actual milestone dates: 47 20190407 14 days 48 20190905 +49 days 49 20191119 +36 days 50 20200223 +47 days ±45 days (~95% confidence) indeed. Although it didn't make much sense applying 45 days to 21 April 2019 in a 2 April 2019 post. 
[QUOTE=kriesel;586257]
Actual milestone dates: 47 20190407 14 days 48 20190905 +49 days 49 20191119 +36 days 50 20200223 +47 days ±45 days (~95% confidence) indeed. Although it didn't make much sense applying 45 days to 21 April 2019 in a 2 April 2019 post.[/QUOTE] You're right. But all this was made by eye, with no particularly careful calculations. And, it seems, this is even my very first post, which I made, when I still did not fully understand where I ended up :) 
All exponent below 57M have been verified.
I predict that we'll finish the verification of M57885161 in about a month, probably before 20211001. 
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I will correct my last prediction regarding All tests below M57885161 by 6 days,
from (November 22, 2021) to (November 16, 2021) ±25 days (50% probability tube). [ATTACH]25548[/ATTACH] Acceleration of All tests verification has been observed since August 19. If it stays at the current level, then there are chances that the kriesel's prediction regarding October 6 will turn out to be correct. 
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History extrapolation from 56M method: currently indicating ~20210925 (which inherently includes allowance for number of exponents/day completing declining over time)
Alternate method update: part one, of those exponents currently updating server, and not indicating expiration before estimated completion, latest estimated completion is 20210920; part two, laggards not currently updating, likely to expire, latest expiration date 18 days = Sep 26, + ~7 days for reassign & complete = 20211003. Completion is expected by about the later of the two parts' date estimates, 20211003. Chun sung soo has 9 not updating out of 32 remaining. 
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What we have at the moment.
[ATTACH]25638[/ATTACH] I'm still sticking to my early prediction – November 16, 2021 ±25 days. Maybe I will slightly correct it, but later, when I will more reliably understand the microtrend within the macrotrend. 
On a related topic:
I was wondering how the spread of PRP with cert is impacting the DC vs FTC balance. So I went and pulled a bunch of old work distribution files from Archive.org. I initially grabbed 1 a month for the last year or so and less frequent back to the end of 2015. I summed the factored, the verified, and those with only a FTC from 0M to (but excluding) 150M. That revealed a decided and dramatic change in exponents that only had FTC and no DC in 2020 first up then down. We hit a peak on or about 19 August 2020 of 843737 FTC's awaiting verification. As of 13 September 2021 we are at 778878, down 64859 from the peak. A rough projection puts this gap closing around 2031AD I will be gathering more data before releasing a graph of this. There is a huge inflection in the count of verified exponents at the same point that the FTC's peaked. 
I note that the [url=https://www.mersenne.org/assignments/?exp_lo=57223591&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1]Countdown to verifying all tests below M(57 885 161)[/url] has 25 "D" (LL Doublecheck) assignments. On August 21 there were 107 such assignments, according to [url=https://mersenneforum.org/showpost.php?p=586192&postcount=26]this post[/url]. Of the 25 assignments now remaining, 12 have [i]negative[/i] ETAs (in days); that is, they are "past due." They are overdue by from 13 to 50 days.
Of the 12 "overdue" assignments, 7 are assigned to the same user. Those 7 are overdue by 14, 18, 21, 22, 26, 30, and 39 days. 
The one 'overdue' at 50 days is 99.5% done, I have hope.

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[QUOTE=Dr Sardonicus;587980]On August 21 there were 107 such assignments, according to [URL="https://mersenneforum.org/showpost.php?p=586192&postcount=26"]this post[/URL].[/QUOTE]And both exponents identified as limiting in that post have been verified.
Looking at it again today, at 25 remaining, as 3 groups, sorted by estimated completion: 14 are not updating for over a week, with latest expiration in 10 days M[M]57836003[/M]; these will complete, or reissue, in 10 days or less, & if reissued, likely complete in ~17 days or less (~20211003) 7 are updating currently and ETA is sooner than expiration, with last ETA 20210922 in this group, latest expiration 27 days, so if one stops updating it might take until ~20211013 to reissue and ~20211020 to complete; that's unlikely because it's ATH's M[M]57514837[/M] and he's reliable; also Syntony is crushing the next longest expiration 22 days with 2 days to go on M[M]57779987[/M]; 4 are recently or currently updating but ETA is later than expiration, expiring within 6 days; reissue and completion by ~20210929. Completion of verification to Mp#48* is the last of those dates, probably by 20211003, maybe as late as ~20211020 if we get an unlucky stall among the several now updating with ETAs of 6 days or less or a reissued exponent. AndersM's assignment of [M]57555247[/M] is indicative of speed of Cat0capable systems: 6 days start to finish. To get to greenskull's revised estimate ~20211116, we'd need an additional stall on such an exponent following, or a very slow execution for a Cat0qualified system, and no poaching in response. The lowest 5 remaining exponents are [CODE]exponent stage exp ETA last update Probable course [M]57223591[/M] 90.3% 20 0 20210915 clears in a day; lowest remaining exponent becomes [M]57256631[/M], delta 33,040 [M]57256631[/M] 69.9% 20 3 20210916 clears in a few days; lowest remaining jumps to [M]57555247[/M], delta 298,616 [M]57514837[/M] 8.7% 27 0 20210915 clears in a day; has no effect on lowest remaining exponent [M]57555247[/M] 9 6 20210916 clears in 6 days [M]57641957[/M] 86.7% 3 6 20210914 expires & reissues in a few days[/CODE] 
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Current situation.
Just in case, I made two quadratic approximations  green curves. First one with the previous kriesel's prediction 03 Oct 2021, the second one without that prediction. [ATTACH]25670[/ATTACH] It seems to me that we will definitely fly far past October 03, but apparently within the limits of my red dotted tube. Unless, of course, a miracle happens :) I am still sticking to my early prediction Nov 16, 2021. 
From [URL]https://www.mersenne.org/assignments/?exp_lo=57256631&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1[/URL] near time of posting:
[CODE]exponent stage exp ETA last update Probable course ([M]57223591[/M] cleared 20210916) [M]57256631[/M] 79.4% 20 2 20210917 clears in 2 days; lowest remaining jumps to 57555247, delta 298,616 [M]57514837[/M] 8.7% 27 1 20210915 overdue; user contacted by PM to investigate; may have no effect on lowest remaining exponent [M]57555247[/M] 8 5 20210916 clears in 5 days [M]57641957[/M] 91.3% 2 5 20210914 expires & reissues in 2 days [M]57650269[/M] 72.3% 2 12 20210915 not progressing, expires & reissues in 2 days, completes ~20210926[/CODE][M]57256631[/M] completing 20210919 along with [M]57514837[/M] would make [M]57555247[/M] lowest remaining then, which would put that (date,lowestremaining) point left of both green curves of the previous post. Not a miracle, just normal progress. 
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[QUOTE=Uncwilly;587925]On a related topic:
... I will be gathering more data before releasing a graph of this. There is a huge inflection in the count of verified exponents at the same point that the FTC's peaked.[/QUOTE] Here is the graph. The straight line is just an eyeball fit of the slope. The trend line will get better as more data is added over time. I will adjust the yaxis later to max it out at the total count of unfactored in the range. 
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From [URL]https://www.mersenne.org/assignments/?exp_lo=57000000&exp_hi=57885161&execm=1&exfirst=1&exp1=1&extf=1[/URL] near time of posting, 20 remain. Some recent completions, and the lowest 5 remaining:
[CODE]exponent stage exp ETA last update Probable course [M]57256631[/M] cleared 20210918 [M]57514837[/M] cleared 20210918 [M]57555247[/M] 0.9% 26 3 20210918 now lowest unverified exponent (delta 298516 since 20210917); clears ~20210924 [M]57641957[/M] cleared 20210918 [M]57650269[/M] 72.3% 0 12 20210915 not progressing, expires & reissues within a day, clears ~20210926 [M]57727781[/M] 97.4% 2 1 20210917 completes or reissues by 20210920; completes by ~20210927 [M]57728663[/M] 29.7% 2 17 20210804 expires and reissues 20210920, completes ~20210927 [M]57730297[/M] 81.6% 2 6 20210906 expires and reissues 20210920, completes ~20210927[/CODE] 
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Kriesel's prediction of the high jump came true.
[ATTACH]25701[/ATTACH] But usually, after each such jump, we observe a protracted decline in growth dynamics. I admit that the cherished moment may come somewhere in the middle between our predictions, but I don’t undertake to assert this reliably yet, therefore I leave my previous prediction in force. 
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In tracking the 56M verification milestone, it went from 21 remaining, to 0, in ~12.3 days.
(At 20210615 14:00:07 21 left; 20210627 21:30:09 0 left; UTC I believe, not that it matters in computing a delta) Today, there are 20 remaining in verification up to [URL="https://www.mersenne.org/report_exponent/?exp_lo=57885161&exp_hi=&full=1"]Mp#48*[/URL]. 20210919 + 12d = 20211001. Greenskull would have us believe along with him that somehow for no reason given that this time will be markedly different; 20211116 is 46 days later, nearly 5fold longer from now than the previous experience (12+46)/12 ~4.83, or maybe reaching Mp#48* comes in the middle, only ~2.5 times longer than the previous experience. The current lowest unverified exponent, [M]57555247[/M], has made progress consistent with completion in ~5 more days. That will be another ~100K jump, leaving only ~230K to go on exponent value. There is acceleration at the end partly because reissued assignments are all Cat0 to known fast reliable systems. A given span of say 250K in exponent value gets more thinly populated with remaining exponents over time, making larger deltas of lowest remaining exponent value more likely, and smaller ones less likely. The average delta between sorted remaining exponent values is now over 16,500. As intermediate exponents complete, the deltas between their remaining neighbors increase. Linear extrapolation does not allow for the acceleration that's known to occur, both observed empirically and for known good reasons/mechanisms including those built into the assignment rules. As in chess and other situations, in GIMPS milestone approach, the end game is not like the mid game. 
[QUOTE=kriesel;588164]As in chess and other situations, in GIMPS milestone approach, the end game is not like the mid game.[/QUOTE]And not all of the pieces are on the table.

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Now 19 left, average delta increased, max delta is ~172.5K. Judging from progress per exponent in the past 3 days, the lowest and highest remaining will complete within a day or two, the rest will probably expire and be reissued, by 5 days from now; add 7 days for run on fast Cat0qualified systems and we get a projection of 20211003 for completion of verification to Mp#48*. The possibility of stall and expiration without poach on any one or more of the ~17 reissued could delay that. It would take more than a startedandthenstalled 30 day expiration and a noprogressreported 10 day expiration on the same reissued exponent, and no poaches, to delay to 20211116, which is 44 days after 20211003.
The alternate method is in close agreement with the 56M historical analogy method which now gives 20211002. From [URL]https://www.mersenne.org/report_milestones/[/URL] [B]Progress toward next GIMPS milestones [I](last updated 20210921 12:45:12 UTC, updates every 15 minutes)[/I][/B] [LIST][*] All exponents below [COLOR=blue]57 555 247[/COLOR] have been tested and verified.[*] All exponents below [COLOR=blue]104 405 113[/COLOR] have been tested at least once.[*] Countdown to first time checking all exponents below 105 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104405113&exp_hi=105000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]3[/URL][*] Countdown to first time checking all exponents below 106 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104405113&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]265[/URL][*] Countdown to verifying all tests below M(57 885 161): [URL="https://www.mersenne.org/assignments/?exp_lo=57555247&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]19[/URL][*] Countdown to verifying all tests below 58 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57555247&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]26[/URL][*] Countdown to verifying all tests below 59 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57555247&exp_hi=59000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]2 354[/URL] [COLOR=black](1 665 available)[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]271 961[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]327 512[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]426 215[/COLOR][/LIST][QUOTE=kriesel;588164]or maybe reaching Mp#48* comes in the middle, only ~2.5 times longer than the previous experience.[/QUOTE]That ~2.5 longer should have been (4.83+1)/2 ~2.9 times as long. Also nearly 5fold longer should have been nearly 5fold as long. 
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Oh, no!..
[ATTACH]25734[/ATTACH] For me, the question remains  how assignments with long overdue deadlines will be processed. Will they be forcibly taken away from the previous owners. Whether they will be processed from scratch or from the point where everything stopped. If the latest date is October 10, then does this mean that the cherished date will not come earlier than this moment. 
[QUOTE=greenskull;588428]Will they be forcibly taken away from the previous owners.[/quote]When they expire, they get reassigned to someone else. If the slowpoke turns in the result before the other person does, oh well.
[QUOTE]Whether they will be processed from scratch or from the point where everything stopped.[/QUOTE]PrimeNet does not receive the interim files. The data transfer and storage are not currently worth it. So, the person with the new assignment has to start afresh. [quote]If the latest date is October 10, then does this mean that the cherished date will not come earlier than this moment.[/QUOTE]The slowest assignment that expires furthest in the future will then have to be reassigned and then run by who ever gets it. If that is a person that takes 10 days to complete such an assignment normally and their machine goes down for a few days over a long weekend, it may be 15 days after the current latest expiry. Or other things can happen.... 
Ok. Thanx!
This means there are rather big chances that my prediction will come true. 
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[QUOTE=greenskull;588428]Oh, no!..
[ATTACH]25734[/ATTACH] For me, the question remains  how assignments with long overdue deadlines will be processed. Will they be forcibly taken away from the previous owners. Whether they will be processed from scratch or from the point where everything stopped. If the latest date is October 10, then does this mean that the cherished date will not come earlier than this moment.[/QUOTE]Oh, yesss. A little late to be learning [URL="https://www.mersenne.org/thresholds/"]the rules[/URL] of operation for the system you've made predictions about. Don't know where you get October 10 from. Estimated completion, for an exponent that will expire and get reassigned far sooner, so the current estimated completion is irrelevant, perhaps. Run a line through the uppermost red x in your plot, at the slope of your red prediction line, and get ~Oct 5. Way outside +25 days from Nov 16. [QUOTE=greenskull;588433]Ok. Thanx! This means there are rather big chances that my prediction will come true.[/QUOTE] Um no. It means there are 17 small chances, for which multiple things would have to go your way to produce unexpectedly long delay. Nov 16 is far enough away that multiple successive assignments on the same exponent would need to expire before completion, and at least one of them would need to start reporting progress before stalling. That, after assignments go only to Cat0 qualified systems known reliable at not having expirations for the past 4 months. Read and understand the Cat0 assignment requirements. Plus it also requires that no one poaches the stalled exponent(s). An initial delay of a day or two or three from assignment to start of progress is normal in prime95 or mprime. See prime95's days of work to queue up setting in Options, Preferences. FYI there is hardware that can do such LLDC or the equivalent PRP/GEC/proofgeneration, in several HOURS. [CODE]20210316 09:37:08 asr2/radeonvii0 57034589 LL 0 loaded: 0000000000000004 20210316 09:37:51 asr2/radeonvii0 57034589 LL 100000 0.18%; 431 us/it; ETA 0d 06:49; 51ebf4cd88bbcb14 ... 20210316 16:27:55 asr2/radeonvii0 57034589 LL 57034587 100.00%; 453 us/it; ETA 0d 00:00; c6d59ecf237f149e 20210316 16:27:55 asr2/radeonvii0 waiting for the Jacobi check to finish.. 20210316 16:28:10 asr2/radeonvii0 57034589 OK 57000000 (jacobi == 1) 20210316 16:28:10 asr2/radeonvii0 {"status":"C", "exponent":"57034589", "worktype":"LL", "res64":"c6d59ecf237f149e", "fftlength":"3145728", "shiftcount":"0", "program":{"name":"gpuowl", "version":"v6.11364g36f4e2a"}, "user":"kriesel", "computer":"asr2/radeonvii0", "aid":"74720917554D8F6A27FABDFF1149FFC1", "timestamp":"20210316 21:28:10 UTC"}[/CODE]Actual duration 16:28:10  09:37:08 = 6:51:02 (h:mm:ss) Add ~2.7% or ~11 minutes for 57.75M: ~7 hours 2 minutes. 
[QUOTE=greenskull;588433]This means there are rather big chances that my prediction will come true.[/QUOTE]You can "help it along" towards reaching your predicted goal by grabbing the last reassigned exponent and [strike]running it slowly[/strike] making your best effort to complete it quickly. :razz:

[QUOTE=retina;588446]You can "help it along" towards reaching your predicted goal by grabbing the last reassigned exponent and [strike]running it slowly[/strike] making your best effort to complete it quickly. :razz:[/QUOTE]
I've already thought about it :) But I am more of an observer than a participant. And I am committed to the principles of fair play and noninterference. 
[QUOTE=kriesel;588443]A little late to be learning the rules of operation for the system you've made predictions about.[/QUOTE]
You are very strict with me. The game doesn't end there. And I am very good at long distances than at short ones. My earliest forecast, which I gave here on April 4, 2019, regarding the crossing of this level, was for September 12, 2021 ± 45 days: [url]https://mersenneforum.org/showpost.php?p=512565&postcount=12[/url] And I think we can already start predicting the next level. I suggested the method of scoring for predictions above: [url]https://www.mersenneforum.org/showpost.php?p=585848&postcount=3442[/url] 
[QUOTE=retina;588446]You can "help it along" towards reaching your predicted goal by grabbing the last reassigned exponent and [strike]running it slowly[/strike] making your best effort to complete it [B][I]quickly[/I][/B]. :razz:[/QUOTE][B][I]quickly[/I][/B] meaning here, at a rate consistent with his latest prediction that was based on more application of statistics than understanding. Assuming he both has at least one cat0 rated system and is lucky enough to draw on it one of the 8 exponents that get reassigned in the next 3 days, that is.

[QUOTE=greenskull;588455]And I am very good at long distances than at short ones.
My earliest forecast, which I gave here on April 4, 2019, regarding the crossing of this level, was for September 12, 2021 ± 45 days: [URL]https://mersenneforum.org/showpost.php?p=512565&postcount=12[/URL] [/QUOTE] which states in part: [QUOTE=greenskull;512565]We could estimate that all tests below M57885161 will be completed on 12 September 2021 ±45 days. [URL]https://ibb.co/b11f3tt[/URL] [B]Assuming the validity of my hypothesis, it can be assumed that at least 3 new Mersenne Prime numbers will be open by this date.[/B][/QUOTE]If that "open" meant found, your hypothesis would seem to be contradicted by the facts. The number of new Mersenne prime discoveries disclosed as occurring between 2018 Dec 8 and today remains zero. (It's unclear what that hypothesis is, or where it's clearly stated, if at all.) predicted at [URL]https://www.mersenneforum.org/showpost.php?p=512475&postcount=3072[/URL] [QUOTE]48 mio  on 19 July 2019 ±45 days 49 mio  on 14 October 2019 ±45 days 50 mio  on 07 January 2020 ±45 days.[/QUOTE](Not sure why you're using "mio" there; Google translate with language detect converts that to "my" in English. Nor what your native language may be. Not English, seems apparent. 49M would be pretty standard forum usage.) actual (delta days computed by [URL]https://www.timeanddate.com/date/duration.html[/URL]) 48M 20190905 +48 days (miss) 49M 20191119 +36 (hit at +80% of error bar value) 50M 20200223 +47 days (miss) +45 days is a 91 day wide target, rather broad as the side of a barn, for a process that TAKES ~91 days on average per million of milestone advance recently. (# of milestones by year: 2020: 5; 2019: 3; 2018:4; 2017: 4; etc [URL]https://www.mersenne.org/report_milestones/[/URL]) Note that the average error in your earlier predictions above was +43.7 days, quite close to the difference between our current projections for reaching Mp#48* of +46 days, and to the 45 day error bar value. IIRC you changed your estimation method since, and chose not to compensate for observed past consistent prediction bias demonstrated by 48M, 49M, 50M. The 20210912 old predicted date for Mp#48* has already passed. It would likely work out thanks to the broad error bar of +45 days, except for having replaced (repudiated) it repeatedly since with predictions months later in date predicted.:realitycheck::deadhorse: 
[QUOTE=kriesel;588472]Not sure why you're using "mio" there; Google translate with language detect converts that to "my" in English. Nor what your native language may be. Not English, seems apparent.[/QUOTE]
At least in German, this is an abbreviation of "million". But Google Translate is also correct if the Italian word is meant (at least if you checked for the word in isolation). When using the automatic language selection and "10 mio", it correctly translates as "10 millions" for me ([URL="http://translate.google.com/?sl=auto&tl=auto&text=10%20mio&op=translate"]example I used[/URL]). Somehow it still insisted that the original language was Italian, so maybe they use that abbreviation, too? 
[QUOTE=Uncwilly;588432]
Or other things can happen....[/QUOTE] :goodposting::popcorn: 
[URL="https://quoteinvestigator.com/2013/10/20/nopredict/"]Prediction is hard, especially about the future.[/URL]

[QUOTE=kriesel;588472]which states in part:
... later in date predicted.:realitycheck::deadhorse:[/QUOTE] I will read it when I take a vacation and have more spare time :) PS The forecast error is best taken into account depending on the distance from which the forecast was made. Since making a error for a couple of weeks from a distance of 1 year and from a distance of 1 month are completely different things. 
[QUOTE=greenskull;585849]My prediction is November 22, 2021
95%, ±82 days 50%, ±25 days Let's see :)[/QUOTE] There are only 17 outstanding exponents left until M[SUB]#48[/SUB] becomes official, so the prediction has been really accurate. Wouldn't it be easier if other users just run the PRP tests for these exponents, less likely to encounter the Gerbicz errors than the Jacobi errors. 
[QUOTE=tuckerkao;588522]Wouldn't it be easier if other users just run the PRP tests for these exponents, less likely to encounter the Gerbicz errors than the Jacobi errors.[/QUOTE]:picard:

[URL="https://www.mersenneforum.org/showpost.php?p=533167&postcount=5"]required reading[/URL]

[QUOTE=kriesel;588525][URL="https://www.mersenneforum.org/showpost.php?p=533167&postcount=5"]required reading[/URL][/QUOTE]
Encounter Jacobi errors in LL are much more likely than Gerbicz errors in PRP. Also the PRP certifications of those exponents won't take longer than 1 hour for most users. 
Methink encountering errors has nothing to do with what math you use to spot the error and to recover from that error. Errors pop up if you have shitty hardware, or try to push it too hard.

[QUOTE=tuckerkao;588526]Encounter Jacobi errors in LL are much more likely than Gerbicz errors in PRP. Also the PRP certifications of those exponents won't take longer than 1 hour for most users.[/QUOTE]
I would have guessed the opposite. On bad hardware, Gerbicz should catch [I]more[/I] errors than Jacobi (key word is [I]catch[/I]; the actual number of bad iterations should be roughly equal either way), but also have the ability to correct the bad iterations more efficiently (wrt granularity/frequency of checks and the probability of an error being caught), thus producing more reliable results. 
Lets hope it id before the new year, and i'll be happy.

[QUOTE=Happy5214;588566]Gerbicz should catch [I]more[/I] errors than Jacobi (key word is [I]catch[/I]; the actual number of bad iterations should be roughly equal either way), but also have the ability to correct the bad iterations more efficiently (wrt granularity/frequency of checks and the probability of an error being caught), thus producing more reliable results.[/QUOTE]Correct. [URL="https://en.wikipedia.org/wiki/Jacobi_symbol"]Jacobi symbol [/URL]check is done infrequently, only ~twice a day because it is computationally costly. Its detection rate is only ~50% of errors. If done after every LL iteration it would cost more than it might save, and still only detect ~75% of errors. For Mersennes it yields +1 or 1 IIRC; there are only 3 possible values in general, 1, 1, 0, so an error going undetected is quite probable. [URL="https://mersenneforum.org/showpost.php?p=465033&postcount=30"]This post[/URL] describing the Jacobi symbol check led to some quick implementation, and consideration of what other checks might be available.
[URL="https://www.mersenneforum.org/showpost.php?p=465431&postcount=88"]Robert Gerbicz' post[/URL] describing the check for PRP followed days later. Both Jacobi and GEC are typically applied by the software authors to use around 0.2% of computing time by default, with some user control for more or less cost & frequency. Gerbicz' check is highly effective, since it can return one of a great many values, and only one will match. Empirically, PRP/GEC has shown ~24ppm error in completed tests, ~800 times lower than LL. And some of that error count was from outside / after the GEC check, handling the final residue produced. Prime95 got hardened against that after some such errors were identified. See [url]https://www.mersenneforum.org/showpost.php?p=509940&postcount=4[/url] These numbertheory based checks are in addition to and independent of other inexpensive measures, such as roundoff magnitude checking, or sum of inputs vs. sum of outputs. 
15 left
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and M57747401 likely to complete within a day.
[QUOTE=firejuggler;588579]before the new year, and i'll be happy.[/QUOTE]Get ready to celebrate. 
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This is what we have at the moment:
[ATTACH]25749[/ATTACH] 
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[M]57747401[/M] done, lowest remaining unchanged. A fine example of how lowest remaining does not always reflect progress well, sometimes not at all. Smallest remaining delta just jumped from 32 to 340.

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12 DC to finish, and a cert. Certs typically complete within a day. One DC is a bit overdue for expiration and reassignment. The other 11 DC are all recently reassigned to Cat0qualified fast reliable systems, reporting in recently.
Estimated completions for those range from today 20210925 to 20211001. Average indicated ETA is ~3 days (20210928) The laggard for expiration and reissue likely expires and reissues today and completes by ~20211003. 
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12 (11 DC 1 cert) remain; 57760333 completed; smallest remaining delta 582, average 12905.

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10 DC and 1 lingering CERT remain; [M]57760673[/M] completed.

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Only 8 left now. How often are triplechecks required?

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That changed quickly. Lingering cert cleared, and 2 LL DC. MP#48* loses the * projected ~20211001 by alternate method.
Extrapolating a linear fit through the various projections from M56 history gives a solution for convergence (date of projection, matching date projected) as 20210930 02:45 UTC. [QUOTE=masser;588740]How often are triplechecks required?[/QUOTE]I don't recall there being any seen in previous final going to milestones. Cat0 qualified systems are prescreened to be fast and reliable for the previous 120 days. The strategic double and triple check thread sweeps the TC needs out of the way earlier. Overall, TC rate is ~24% per exponent, 12% per LL test. (Much higher if there's an error code recorded.) It varies depending on exponent size, system speed, whether the system has ECC ram, and whether it runs software with Jacobi check included. All 8 now remaining have nonzero shift count first LL tests with no error codes indicated. Chance of a TC being needed somewhere in the last 8 is slim but nonzero, ~12% chance or less of one TC, <2% of 2 or more. If whoever got a hypothetical TC had a Radeon VII they could move it and complete it in 7 hours. 
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[M]57797893[/M] completed.

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Probably two more clear in the next day; all by ~20211002. Average delta 25811.

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Two more will complete soon. All are progressing.

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What we have at the moment:
[ATTACH]25784[/ATTACH] Probably kriesel's forecast will be closer to the fact than mine. But it is not exactly :) 
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[QUOTE=greenskull;588889]Probably kriesel's forecast will be closer to the fact than mine. But it is not exactly[/QUOTE]Did anyone claim to be able to project the conclusion exactly? Given the quantizations of lowest exponent completed, number of exponents remaining, exponent ETAs, client reporting time interval, server view of state of completion of each exponent, and perhaps more, mathematical fits to the historical data, of linear equations that are analog models, will necessarily be inexact representations.
Transition from cat2 systems' assignments expiring to cat0 systems for reassigned exponents creates a substantial increase in slope of the number of remaining exponents versus time. A model that forces overall linear extrapolation on the nonlinear behavior inherent in the assignment rules does not represent that well. Currently it looks like ~20211002 conclusion with Syntony's assignment, although it could come sooner. 
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Last update.
[ATTACH]25788[/ATTACH] All hope for the slow computer OldQC of the user GrunwalderGIMP and Syntony's Kilderkin that process the data a teaspoon per hour :) 
[QUOTE=kriesel;588895]Currently it looks like ~20211002 conclusion with Syntony's assignment, although it could come sooner.[/QUOTE]That month looks like it will have the 58M DC and 105M FTC milestones too. There are a few assignments in the 105106 interval that [B][U]will[/U][/B] expire after October. George has a hold out too. Otherwise it [I]would[/I] be favourable for meeting the 106M milestone in October.

[QUOTE=greenskull;588896]Last update.
[ATTACH]25788[/ATTACH] All hope for the slow computer OldQC of the user GrunwalderGIMP and Syntony's Kilderkin that process the data a teaspoon per hour :)[/QUOTE] Thanks for making these graphs. I appreciate seeing the data presented this way. 
[QUOTE=Uncwilly;588897]George has a hold out too. [/QUOTE]
Thanks. The gpuowl python script thought the result was uploaded successfully. Resubmitted it manually. 
[QUOTE=Uncwilly;588897]That month looks like it will have the 58M DC and 105M FTC milestones too.[/QUOTE]Ben Delo has several nearing expiration with substantial progress made and no updates in nearly a month, in the 105M[URL="https://www.mersenne.org/assignments/?exp_lo=104815069&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]106M[/URL] range. It would be unfortunate for all that work to be lost.

[QUOTE=kriesel;588928]Ben Delo has several nearing expiration with substantial progress made and no updates in nearly a month, in the 105M[URL="https://www.mersenne.org/assignments/?exp_lo=104815069&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]106M[/URL] range. It would be unfortunate for all that work to be lost.[/QUOTE]
If they aren't completed within a couple days after they start processing, his exponents generally expire out. There's any of a number of possible reasons for it. I imagine sometimes he has something else he needs to direct some portion of his fleet of machines to do. You can find plenty of cases where his exponent expired out then he picked it up for assignment again and 2nd time around processed it to completion. 
Hi people.
Which exponents are left to verify M48? I can help in doublechecking. 
There are only three exponents left and those are all already assigned and being worked on, but you can of course help with verifying M49. :smile:

[QUOTE=slandrum;588957]You can find plenty of cases where his exponent expired out then he picked it up for assignment again and 2nd time around processed it to completion.[/QUOTE]Since Ben alone accounts for ~half of primality tests completed, Ben's scripts taking a second crack at the same exponent after an expiration is a coin toss. But the lost progress of the first expired attempt is still a regrettable loss.

[QUOTE=JCoveiro;588971]Hi people.
Which exponents are left to verify M48? I can help in doublechecking.[/QUOTE]You're weeks or months too late to this party. All: it's good practice to read before posting. See [URL]https://mersenneforum.org/showpost.php?p=588895&postcount=79[/URL], just 7 posts before the quoted post. Or use [URL]https://www.mersenne.org/report_milestones/[/URL] and the links that are those red numbers there, for periodically updated info, from which I have been regularly posting snapshots. I'm hopeful that people will respect this thread's secondary purpose, of documenting the natural progression to achieving a milestone, for future reference and consideration by anyone in making any future projections for future milestones. That means let the normal progression run its course following the well documented [URL="https://www.mersenne.org/thresholds/"]assignment rules[/URL], without poaching. 
Currently the PrimeNet server is projecting [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]20211002 conclusion[/URL].
But the assignment [M]57773081[/M] to AndersM on PC1 has not reported an update for 2 days. If it is stalled and not fixed and not poached it may take 24 days to expire and several more to reassign and complete, adding an unnecessary 4 additional weeks to reaching the 48* DC milestone. AndersM is not a valid userid for PM. AndersM has delivered recently; [M]57555247[/M] assigned 20210915 to AndersM [URL]https://mersenneforum.org/showpost.php?p=588135&postcount=41[/URL] reached 69.5% on 20210921 and was completed by 20210923 0:46. [URL]https://mersenneforum.org/showpost.php?p=588443&postcount=49[/URL] So wait a bit and see. 
Houston, We Have A Problem! :)

[QUOTE=greenskull;589030]Houston, We Have A Problem! :)[/QUOTE]AndersM? Is that you? I'd be happy to finish [URL="https://www.mersenne.org/M57773081"]that one[/URL] for you, as would some other forumites, if you've had some computer problems that prevent continuing it.

[QUOTE=kriesel;589044]AndersM? Is that you?[/QUOTE]
Of course it's not me. I like forecasting, and I have something to keep my Mac busy besides catching Mersenne numbers :) In this game, I am more of an observer than a participant. 
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[B][SIZE=3]From [URL]https://www.mersenne.org/report_milestones/[/URL][/SIZE]
[/B] [B]Progress toward next GIMPS milestones [I](last updated 20211001 12:45:11 UTC, updates every 15 minutes)[/I][/B] [LIST][*] All exponents below [COLOR=blue]57 747 433[/COLOR] have been tested and verified.[*] All exponents below [COLOR=blue]104 815 069[/COLOR] have been tested at least once.[*] Countdown to first time checking all exponents below 105 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104815069&exp_hi=105000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]2[/URL][*] Countdown to first time checking all exponents below 106 million: [URL="https://www.mersenne.org/assignments/?exp_lo=104815069&exp_hi=106000000&execm=1&exp1=1&extf=1&exdchk=1&excert=1"]91[/URL][*] Countdown to verifying all tests below M(57 885 161): [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]2[/URL][*] Countdown to verifying all tests below 58 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]5[/URL][*] Countdown to verifying all tests below 59 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=59000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]1 792[/URL] [COLOR=black](1 157 available)[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]269 860[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]325 389[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]424 092[/COLOR][/LIST][M]57747433[/M] (Syntony) ETA tomorrow, 60.6% complete [M]57773081[/M] (AndersM) ETA yesterday, hasn't updated since 20210927, 26% complete 
Perhaps somebody could get in touch with AndersM for a sitrep...

[QUOTE=kriesel;589133][*] Countdown to verifying all tests below M(57 885 161): [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=57885161&execm=1&exp1=1&extf=1&exfirst=1"]2[/URL][*] Countdown to verifying all tests below 58 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]5[/URL][*] Countdown to verifying all tests below 59 million: [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=59000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]1 792[/URL] [COLOR=black](1 157 available)[/COLOR][*] Countdown to verifying all tests below M(74 207 281): [COLOR=blue]269 860[/COLOR][*] Countdown to verifying all tests below M(77 232 917): [COLOR=blue]325 389[/COLOR][*] Countdown to verifying all tests below M(82 589 933): [COLOR=blue]424 092[/COLOR][/LIST][M]57747433[/M] (Syntony) ETA tomorrow, 60.6% complete
[M]57773081[/M] (AndersM) ETA yesterday, hasn't updated since 20210927, 26% complete[/QUOTE] Now we have verified that [URL="https://oeis.org/A279095"]A279095[/URL](29) = 1996040, since neither 57747433 nor 57773081 is == 1 mod 29, thus 57885161 is [B]proven[/B] to be the smallest prime p == 1 mod 29 such that 2^p1 is (Mersenne) prime. 
[QUOTE=Dr Sardonicus;589135]Perhaps somebody could get in touch with AndersM for a sitrep...[/QUOTE]Yes that might help. That would need to be someone like Madpoo or Prime95 that may have access to an email address, or forum ID != AndersM, for him.[QUOTE=kriesel;589003]AndersM is not a valid userid for PM.[/QUOTE]If not cleared soon it will also be delaying the [URL="https://www.mersenne.org/assignments/?exp_lo=57747433&exp_hi=58000000&execm=1&exp1=1&extf=1&exfirst=1&excert=1"]58M milestone[/URL] for which the server currently shows 4 left, projected conclusion 20211006.

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