This is practical when the number of remaining exponents below a milestone is < ~200.

Go to

https://www.mersenne.org/assignments...tf=1&exfirst=1
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 2021-08-21; by 2021-09-21.

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 ~ 2021-09-30, 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

https://www.mersenne.org/M57817769 which last updated 2021-08-19 and has 35 days remaining. Corresponding to reaching Mp#48* by ~ 2021-10-01.

That is very close to the 2021-10-07 date estimated in June, 2021-10-05 estimated 11 August, or 2021-10-04 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

https://www.mersenne.org/report_milestones/
**Progress toward next GIMPS milestones ***(last updated 2021-08-21 14:15:08 UTC, updates every 15 minutes)*
- All exponents below 56 917 213 have been tested and verified.
- All exponents below 104 244 157 have been tested at least once.
- Countdown to first time checking all exponents below 105 million: 35
- Countdown to first time checking all exponents below 106 million: 4 390 (2 510 available)
- Countdown to verifying all tests below 57 million: 7
- Countdown to verifying all tests below M(57 885 161): 107
- Countdown to verifying all tests below 58 million: 138
- Countdown to verifying all tests below 59 million: 4 326 (2 752 available)
- Countdown to verifying all tests below M(74 207 281): 278 624
- Countdown to verifying all tests below M(77 232 917): 334 160
- Countdown to verifying all tests below M(82 589 933): 432 867