Predict M52

[ATH]

Originally Posted by kriesel

It's a record I expect to be exceeded repeatedly going forward. I made an extrapolation in late 2018 of completion of first testing to exponent 1G by around 2170 (152 years from 2018, ~148 years from now). There's an estimated 6 Mersenne primes to be found in that span. So that suggests an average around 25 years between future Mp discoveries below 1G exponent.

This estimate is not proven and we had 13 between 10⁷ and 10⁸, so who knows how many there will be.

[kriesel]

Originally Posted by ATH

who knows how many there will be.

No one, yet. But after over almost all of recorded history, of the discovered Mp count lagging the Wagstaff conjecture's implications for count versus search limit, since Mp#51 was found a few years ago, for a change we're a bit ahead of the conjecture's forecast. It seems a bad bet to expect the extremely productive run of the past 2 decades to continue despite the data below 10⁷ indicating a lower mean rate vs. log(exponent). I've not seen any rumored theoretical basis for a change in slope above some exponent. Earlier there were ~2:1, 3.5:1 and 4:1 intervals that were empty.

Possibly of interest: last paragraph of the "dubious claims" post, George's Wagstaff conjecture run post, number of Mersenne primes versus search limit (with Wagstaff conjecture and DC limit also plotted)

[tuckerkao]

Originally Posted by kriesel

I hope to see at least one more Mp discovered in my lifetime. If one is located near 1.47576 x 82.6M ~122M, reaching and finding it may only take a few more years from now. I'd be happy to be shown unduly pessimistic in regard to time required to find Mp52* or Mp53*.

Unless someone has already reached the retiring age now. Most of the users here should be the well beings up to at least year 2029~2032.

[tuckerkao]

Originally Posted by ATH

Here is the list using the agreed upon discovery dates, and today July 30th we reached the previous record gap of 1331 days, so tomorrow will be a new record This is not a record we want to beat.

I'm willing to wait until Sep 23, 2022 to solidly declare victory over Post #199 of this thread.

[Uncwilly]

Originally Posted by tuckerkao

I'm willing to wait until Sep 23, 2022 to solidly declare victory over Post #199 of this thread.

"Declare victory over Post#" How do declare victory over a post? Is a post an opponent?
If you are concerned about the content of the post, my statement at that time was exactly correct in that there was still a long way to go to declare it the longest gap. Since that post, there has been over a year and 3 months. That is not a small amount of time, when talking about gaps in MP discovery in the computer era.

[Dr Sardonicus]

Originally Posted by tuckerkao

I'm willing to wait until Sep 23, 2022 to solidly declare victory over Post #199 of this thread.

This makes less than no sense. The lengthening time since the last discovery of a Mersenne prime is in no way a "victory" for anyone, especially you.

I would say the longest gap during the GIMPS project is between the discovery of the exponent 42643801 giving M46 (June 12, 2009) and 43112609 giving M47 (August 23, 2008). The larger of the two was discovered first, so that's -293 days. Using 4-byte two's complement integers, that's 2^32 - 293 = 4294967003 days.

Your basic claim (in post #214 to this thread) is

Originally Posted by tuckerkao

I'm still believing the next Mersenne Prime will be in the M168,xxx,xxx region, if so, then the longest gap will be possible.

Have all exponents between 82,589,933 and 168,000,000 been eliminated as candidates? Not even close.

In fact, not all the exponents between 57,885,161 and 74,207,281 have been double-checked. (I don't think any additional exponents less than 82,589,933 yielding Mersenne primes will be discovered)

The GIMPS milestones include "All exponents up to xxxxxxxxx have been tested at least once." At present, "xxxxxxxx" is nowhere near 168,000,000. It's not even close to 117,000,000 which had already been suggested in this post (#188 to this thread) as a possible upper bound for the next Mersenne prime exponent.

AFAIK you have not contributed to the effort of testing exponents between 82,589,933 and 168,000,000 in order to validate the part of your claim that no exponents yielding Mersenne primes exist in that range.

Nor have you found an exponent in your pet range which yields a Mersenne prime. You have, however, eliminated a number of candidates in your pet range by finding factors.

[retina]

Originally Posted by Dr Sardonicus

You have, however, eliminated a number of candidates in your pet range by finding factors.

I find this to be a useful contribution.

I don't see any reason to discourage people to test whatever exponents that want. Just because some people are hyper-focussed on the leading edge stuff doesn't make it the only thing we should care about. Nor does it mean any other testing not currently advancing their goals is worth anything less.

Go for it tuckerkao, keep testing your exponents. Good luck.

[kriesel]

Originally Posted by Dr Sardonicus

Have all exponents between 82,589,933 and 168,000,000 been eliminated as candidates? Not even close.
...
AFAIK you have not contributed to the effort of testing exponents between 82,589,933 and 168,000,000 in order to validate the part of your claim that no exponents yielding Mersenne primes exist in that range.

It's easy enough to check.
I find 40 verified PRP first tests by tuckerkao between 82M and 169M, and 1 unverified:
https://www.mersenne.org/report_prp/...=tuckerkao&B1=

and one unverified LL first test: https://www.mersenne.org/report_ll/?...=tuckerkao&B1=
Most are in 168-169M. But ten of those verified PRP run by tuckerkao are 103.x M, as is the sole LL first test.
(Didn't find anything under drsardonicus or slight variations though. Maybe running under a different alias, or a different work type?)

[Dr Sardonicus]

Originally Posted by retina

<snip>
I don't see any reason to discourage people to test whatever exponents that want. Just because some people are hyper-focussed on the leading edge stuff doesn't make it the only thing we should care about. Nor does it mean any other testing not currently advancing their goals is worth anything less.
<snip>

I'm not trying to discourage anyone from working on the Project. What I am trying to discourage is making ludicrous, nonsensical, incoherent claims about their preferences and their work.

Originally Posted by kriesel

<snip>
easy enough to check.
I find 40 verified PRP first tests by tuckerkao between 82M and 169M, and 1 unverified:
<snip>
Most are in 168-169M. But ten of those verified PRP run by tuckerkao are 103.x M, as is the sole LL first test.<snip>

I stand corrected. He's tested 10 exponents in that range.

[tuckerkao]

Originally Posted by kriesel

It's easy enough to check.
But ten of those verified PRP run by tuckerkao are 103.x M, as is the sole LL first test.

When people contribute to the frontwave, their efforts tend to be forgotten faster and easier once the milestone passes through that area unless the total contribution is as massive as Ben Delo's.

[chalsall]

Originally Posted by tuckerkao

When people contribute to the frontwave, their efforts tend to be forgotten faster and easier once the milestone passes through that area unless the total contribution is as massive as Ben Delo's.

It takes valuable time to interact with you... And... You are, as usual, incorrect.

Every effort is valued. And recorded.

Every test reduces the entropy slightly.

You and yours introducing noise into these serious exercises is just something we have grown used to dealing with.

Thanks for being part of the equation so we can prove we have filtered out the noise.

Quick question: Do you and yours get paid by the hour, the day, or the job?