PRP-VDF and the impact on DC's

[kriesel]

From https://www.mersenne.org/report_milestones/

Progress toward next GIMPS milestones (last updated 2022-05-21 15:15:10 UTC, updates every 15 minutes)

    All exponents below M(60670541) have been tested and verified.
    All exponents below M(108938483) have been tested at least once.

    Countdown to first time checking all exponents below 109 million: 1
    Countdown to first time checking all exponents below 110 million: 4 953 (258 available)

    Countdown to verifying all tests below 61 million: 560 (278 available)
    Countdown to verifying all tests below 62 million: 7 539 (5 437 available)

    Countdown to verifying all tests below M(74207281): 223 473
    Countdown to verifying all tests below M(77232917): 278 647
    Countdown to verifying all tests below M(82589933): 377 318

~399 days (1.093 years) since https://mersenneforum.org/showpost.p...8&postcount=43
Progress to Mp#49* (311767-223473)/399 = 221.3/day; ~1010 days to go (~2.77 years estimated, ~Feb 24 2025)
Progress to Mp#50* (367387-278647)/399 = 222.41/day; ~1253 days to go (~3.43 years estimated, ~Oct 25 2025)
Progress to Mp#51* (466099-377318)/399 = 222.51/day; ~1696 days to go (~4.64 years estimated, ~Jan 11 2027)

Acceleration confirmed, but only of order 3%. (221.3/214.2 - 1 = 0.0331; 222.41/215.9 - 1 = 0.0302; 222.51/216.5 - 1 = 0.0278)

(Date computations via
https://www.timeanddate.com/date/duration.html
https://www.timeanddate.com/date/dateadded.html)

[Uncwilly]

But those primes and the exponents below them were tested without VDF's.

I had noticed that the rate of DC's has been dropping in the past few weeks. I don't have the data at hand at the moment. I have been tracking the the total of the Composite/DC and Status Unproven LL/PRP from 0 through the 149M range. With the VDF's the gap between the 2 has been closing. But over the las few weeks the rate has been slowing. The projected completion date has moved out about 2 years.

I think it might be time to reassess how fast a machine has to be to get FTC's. If it is not an automated process, it should be updated every 6 months or so.

[slandrum]

People get interested when major milestones are close. Right now there are no major milestones that are close so it looks like some interest is moving elsewhere. We're also coming into the summer slowdown.

I see a lot of interest in factoring and PRP-CF these days - a year ago few of my CERT assignments were PRP-CF, now I get a lot of them every day.

[kriesel]

Originally Posted by Uncwilly

But those primes and the exponents below them were tested without VDF's.

Of course. The acceleration anticipated that I was responding to was shift of some workers from LL first test to LL DC. That is necessarily about already-LL-first-tested exponents. The first PRP first tests were ~77.5M and up. So PRP, much less the later advent of PRP proof generation via VDF is for higher exponents than Mp#50* and to a large degree above Mp#51*.

As for seasonal effects, the latest sample period of 399 days is 1.093 years so should wash out the seasonal effects somewhat.