Predict M49...

[gd_barnes]

Originally Posted by gmn17

I have done somye excel and mathematica analysis and get a 99.2% chance that the next exponent is in the 50,000,000-53,000,000 range. See files attached. and the 50th in the 64,000,000-66,000,000 range. SO check these ranges thorougly
Thanks,
Gregory

Originally Posted by VBCurtis

Perhaps my sarcasm meter is broken, but a 0.8% chance of a prime in 50M-53M sounds about right, given that some tests have already been completed. You sure you didn't forget a "1 - x" term in there somewhere?

A 99% chance? I'll settle for the under at 50% odds- if there is no prime, I win; if a mersenne prime is found in that range, you win. If your spreadsheet is correct, I am offering you 1-1 odds on a 992-8 favorite.

Gotta go with Curtis on this one. A 99.2% chance of prime for such a small n-range is ridiculous. 0.8% chance sounds reasonable to me. Would you care to wager either Curtis or me on this at even money?

My prediction: There will be only one more Mersenne prime for n<100M and it will be > 4 years before it is found.

[Dubslow]

Originally Posted by gd_barnes

My prediction: There will be only one more Mersenne prime for n<100M and it will be > 4 years before it is found.

That's a suitably general prediction that I agree with.

[aketilander]

Rules
1. We compete in two categories “Time” and “Exponent”.
2. No more than three active guesses at the same time per user in each category is allowed. If someone have more than three guesses the oldest is automatically invalid.
3. Old guesses can always be replaced by new ones.
4. Vague guesses are adjusted if possible.
5. The ones who are closest on the day before the find of next Mersenne prime wins the category.

Time-table
If the time given is a period (like a month or year) the guess is adjusted to be in the middle of this period.
 
2013-02-12 (”February 12, 2013”) petrw1 (on 2013-02-06)
2013-12-15 (“December 2013”) firejuggler (on 2013-02-05)
2014-12-31 (”by the end of 2014”) NBtarheel (on 2013-02-06)
2015-06-14 (”6/14/2015”) axn (on 2013-02-06)
2015-07-15 (“around July 2015”) ixfd64 (on 2013-02-05)
2015-09-15 (”in September 2015”) Brian-E (on 2013-02-06)
2015-11-15 (”in november 2015”) ATH (on 2013-02-06)
2016-07-15 (”in July 2016”) dabaichi (on 2013-02-06)
2017-01-15  (“in January 2017”) Batalov (on 2013-02-06)
2017-02-07 (“4 years time is a sensible (and sustainable) guess”) davieddy (on 2013-02-07)
2017-08-21 (“ August 21, 2017”) philmoore (on 2013-02-06)
2019-05-15 (”in May 2019”) ewmayer (on 2013-02-07)
2019-08-15 (“August 2019”) prime95 (on 2013-02-06)
2052-06-30 (“in year 2052”) aketilander (on 2013-01-26)
 
Undecided
(“it will be > 4 years before it is found”) gdbarnes (on 2013-02-07)
Dubslow agrees with gdbarnes (on 2013-02-07)

Exponent-table
If a span of exponents is given (like between 50M and 60M) the guess is adjusted to be in the middle of this span.
 
37150000 (”In the range 37.1M-37.2M”) Brian-E (on 2013-02-06)
49532123 (”49532123”) petrw1 (on 2013-02-06)
50498885 (“between M47 and M48”) firejuggler (on 2013-02-05)
51500000 (“in the 50,000,000-53,000,000 range”) gmn17 (on 2013-02-06)
52125000 (”maybe around 52 125 000” firejuggler (on 2013-02-05)
64500000 (“between 64M and 65M”) firejuggler (on 2013-01-26)
64500000 (”~64,500,000”) NBtarheel (on 2013-02-06)
66370000 (“66.37M range”) ixfd64 (on 2013-02-05)
67464577 (”67,464,577”) ATH (on 2013-02-06)
68407583 (”68407583”) axn (on 2013-02-06)
70120000 (”70.12M range”) dabaichi (on 2013-02-06)
76706041 (”M76706041”) philmoore (on 2013-02-06)
85734367 (”~85734367”) Batalov (on 2013-02-06)
88291201 (”88291201”) ewmayer (on 2013-02-07)
88300000 (“~88,300,000”) prime95 (on 2013-02-06)
176863549 ("M176,635,549") aketilander (on 2013-01-26)
 
Undecided
(“only one more Mersenne prime for n<100M”) gdbarnes (on 2013-02-07)
Dubslow agrees with gdbarnes (on 2013-02-07)

[davieddy]

Originally Posted by ewmayer

Combining the well-known --George "by a nose" algorithm, Crank (p-1) Smoothness^TM and my innate raving optimism, I predict

88291201, in May 2019.

Assuming Chalsall pulls his finger out, the date is at least compatible with the exponent.

D

[Flatlander]

61.5M, late 2013.
(Then the four years of wilderness.)

[davieddy]

Originally Posted by gd_barnes

My prediction: There will be only one more Mersenne prime for n<100M and it will be > 4 years before it is found.

Originally Posted by Dubslow

That's a suitably general prediction that I agree with.

Both vague and plausible.

D

[Uncwilly]

79399909 on 2/13/2015

[WOKIDNAPS]

64,499,971 MARCH 31, 2013

[prgamma10]

79865251, Febuary 2016.

[davieddy]

I realise that the thread (and its predecessors) is open to hunorous predictions.
But if you see the last few posts in "Predict M48" Jasong proposed the sensible idea of offering a reason for your guess.

Laughing aside, I use these as a guide:

Gambler's Fallacy
Poisson
Wagstaff

BTW Caldwell seems to think (log2 + log6)/2 is negligible compared to log(exponent). I make it ~7%

David

[aketilander]

Originally Posted by davieddy

offering a reason for your guess.

The ones who like to give reasons may do so of course, but surely anybody can guess with or without reason.

I based my guess on Lenstra–Pomerance–Wagstaff conjecture

According to the conjecture an estimate of the numbers of M(p) between M(p) and M(10*p) are 5.92

So I wanted to find the largest known relative "gap" between the exponents of M#n and M#(n+1). I found this between M#12 and M#13, that is p=127 and p=521

521/127 = 4.10

Of course if the distribution of Mp:s is a true poisson distribution the relative "gaps" can be of any size, but I wanted to base my guess on the largest "gap" so far seen.

Since M#47 was the largest known Mp at the time of my guess, it is close to 4.1 * p of M#47.

The time when we would find M48 (I did my original guess before it was found) was based on an estimation of the speed which the "wave" of LL advances, about 3M a year.

What I want/wanted to do with my guess was to show that it might take a very, very long time before we see a new Mp.

I am very, very surprised that we/GIMPS have found so many Mp:s, much more then would be expected according to the Lenstra–Pomerance–Wagstaff conjecture, so that I even start to doubt the conjecture?!

As RDS pointed out my way of thinking is "senseless numerology", but this is how I arrived at my guess.

Well, now I only stick to my original guess even though M48 has been found and change it to be for M49 instead.