Predict M52

[chalsall]

Originally Posted by R.D. Silverman

Yet you presume to make unjustified pronouncements. What compels you to do so?

To annoy you...

As I said, I /don't/ understand the maths. But my meta understanding, based on what has been written here by those who do understand the underlying ***theory***, is we've seen more MPs than expected. This might just be outliners. Or...

And, to put out there... Those who are theorists keep saying we should find about 1 factor every "bit level" TF'ed (e.g. 1/77 when going from 76 to 77). And yet, the empirical data suggests it's closer to 1/100.

[kriesel]

Originally Posted by Uncwilly

I did my own calc...
took difference between successive values
took the mean
added the mean to the value calculated for 82589933 (M51)
converted the resultant value back into the value for p.

Thanks for the clarification.
I suggest that ratio, not difference, would be the way to go.
And it's fairly moot, since all prediction methods for where is the next Mersenne prime are in practice no better than throwing darts blindfolded.

[kriesel]

Originally Posted by chalsall

my meta understanding, based on what has been written here by those who do understand the underlying ***theory***, is we've seen more MPs than expected.

But not many more. And probability theory tells us that some deviation from the "expected" rate is likely. Fairly flip a coin 60 times. There's a chance you'll get 30 heads, 30 tails. There's a considerable chance you'll get something different.

Those who are theorists keep saying we should find about 1 factor every "bit level" TF'ed (e.g. 1/776 when going from 76 to 77). And yet, the empirical data suggests it's closer to 1/100.

1/100 IS "about 1/bit-level". https://www.mersenne.org/various/math.php

Checking my own last 297 TF bit level results, over 72-76 bits, for an assumed average x=73.5 level,
1/x=0.136 x 297 = 4.04 factors expected. And I have 4 factors found. It's a small sample and could easily have been unlucky at 2 or lucky at 6 found. One of those found was in the first 25 results. These were produced mostly by new presumably reliable hardware. There are few error checks in TF. False factors will get detected at the server, but computation errors that lead to missing factors may go undetected.

[chalsall]

Originally Posted by kriesel

But not many more. And probability theory tells us that some deviation from the "expected" rate is likely.

I understand that. And I know that it is /most likely/ just a blip in the data.

But... We're getting more data every few years. And the theorists must always be willing to examine compelling empirical data. They have been known to occasionally be incorrect on some matters...

[dcheuk]

Originally Posted by kriesel

Why? Best heuristics say there are only about 6 left to find in p<10⁹, which will take many decades to search completely. https://www.mersenneforum.org/showpo...5&postcount=11

https://www.mersenne.org/primes/ contains many waits of 5+ years, and some longer than a century.

Sorry I didn't mean to start an argument, stressful times.

Hopefully we will see a prime by this Christmas.

[LaurV]

Originally Posted by dcheuk

Hopefully we will see a prime by this Christmas.

Only if all travel bans are lifted. Otherwise, George may decide to stay home...

[dcheuk]

Originally Posted by LaurV

Only if all travel bans are lifted. Otherwise, George may decide to stay home...

Lol

[Uncwilly]

I just noticed that is guess just got passed:

Uncwilly	12/29/2018	89999999	4/15/2020

The date guess is close to when the last value below that was finished.

Oh, BTW, Ken has found a factor or completed a first time check on every guess in this thread.

[kriesel]

Originally Posted by Uncwilly

BTW, Ken has found a factor or completed a first time check on every guess in this thread.

The ongoing effort has covered a lot more than the scope of this thread's exponent guesses.

Another possible game is to make guesses as to when the remaining dubious claims or last M50 guess standing may fall. I won't participate, partly because I know the estimated schedules for some of these. See https://www.mersenneforum.org/showpo...04&postcount=5
To spice it up a bit, you could add the requirement for some of the larger ones that the guesser must still be alive to win, or allow that guesses can be passed on to an heir, perhaps only above a certain exponent size.
But don't wait too long, or there will be fewer to choose from.

[Uncwilly]

Originally Posted by Uncwilly

I just noticed that is guess just got passed:

Uncwilly	12/29/2018	89999999	4/15/2020

Enough time has passed. I will now supplant that with 100002751 on October 6 2020

[dannyridel]

111906173 on Jan.2nd, 2021.