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.

[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 (~2021-10-03)

7 are updating currently and ETA is sooner than expiration, with last ETA 2021-09-22 in this group, latest expiration 27 days, so if one stops updating it might take until ~2021-10-13 to reissue and ~2021-10-20 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 ~2021-09-29.

Completion of verification to Mp#48* is the last of those dates, probably by 2021-10-03, maybe as late as ~2021-10-20 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 Cat0-capable systems: 6 days start to finish.

To get to greenskull's revised estimate ~2021-11-16, we'd need an additional stall on such an exponent following, or a very slow execution for a Cat0-qualified 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 2021-09-15 clears in a day; lowest remaining exponent becomes [M]57256631[/M], delta 33,040
[M]57256631[/M] 69.9% 20 3 2021-09-16 clears in a few days; lowest remaining jumps to [M]57555247[/M], delta 298,616
[M]57514837[/M] 8.7% 27 0 2021-09-15 clears in a day; has no effect on lowest remaining exponent
[M]57555247[/M] 9 6 2021-09-16 clears in 6 days
[M]57641957[/M] 86.7% 3 6 2021-09-14 expires & reissues in a few days[/CODE]

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 2021-09-16)
[M]57256631[/M] 79.4% 20 2 2021-09-17 clears in 2 days; lowest remaining jumps to 57555247, delta 298,616
[M]57514837[/M] 8.7% 27 -1 2021-09-15 overdue; user contacted by PM to investigate; may have no effect on lowest remaining exponent
[M]57555247[/M] 8 5 2021-09-16 clears in 5 days
[M]57641957[/M] 91.3% 2 5 2021-09-14 expires & reissues in 2 days
[M]57650269[/M] 72.3% 2 12 2021-09-15 not progressing, expires & reissues in 2 days, completes ~2021-09-26[/CODE][M]57256631[/M] completing 2021-09-19 along with [M]57514837[/M] would make [M]57555247[/M] lowest remaining then, which would put that (date,lowest-remaining) point left of both green curves of the previous post.
Not a miracle, just normal progress.

[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 y-axis later to max it out at the total count of unfactored in the range.

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 2021-09-18
[M]57514837[/M] cleared 2021-09-18
[M]57555247[/M] 0.9% 26 3 2021-09-18 now lowest unverified exponent (delta 298516 since 2021-09-17); clears ~2021-09-24
[M]57641957[/M] cleared 2021-09-18
[M]57650269[/M] 72.3% 0 12 2021-09-15 not progressing, expires & reissues within a day, clears ~2021-09-26
[M]57727781[/M] 97.4% 2 -1 2021-09-17 completes or reissues by 2021-09-20; completes by ~2021-09-27
[M]57728663[/M] 29.7% 2 -17 2021-08-04 expires and reissues 2021-09-20, completes ~2021-09-27
[M]57730297[/M] 81.6% 2 -6 2021-09-06 expires and reissues 2021-09-20, completes ~2021-09-27[/CODE]

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.

In tracking the 56M verification milestone, it went from 21 remaining, to 0, in ~12.3 days.
(At 2021-06-15 14:00:07 21 left; 2021-06-27 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]. 2021-09-19 + 12d = 2021-10-01. Greenskull would have us believe along with him that somehow for no reason given that this time will be markedly different; 2021-11-16 is 46 days later, nearly 5-fold 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.