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 Mini-Geek 2008-09-14 18:30

Predict M47

Well, I know we don't know the identities of M45 and M46 yet, but we know we have two primes, so we might as well get M47 guesses out there.

Predict the exponent and/or the date it will be found.

I'll guess 50M in September 2009.

 henryzz 2008-09-14 18:48

by the way things have gone for the last few mersenne primes i reckon its going to be in september or late august in 1 or 2 years time

 davieddy 2008-09-14 20:56

60M, 2012

 MooooMoo 2008-09-14 21:11

75.86 M, May 2013.

51.5M, Aug 2009

 ATH 2008-09-15 08:47

52.3M, Nov 2009

 R.D. Silverman 2008-09-15 12:00

[QUOTE=Mini-Geek;142426]Well, I know we don't know the identities of M45 and M46 yet, but we know we have two primes, so we might as well get M47 guesses out there.

Predict the exponent and/or the date it will be found.

I'll guess 50M in September 2009.[/QUOTE]

A pointless exercize.

 Andi47 2008-09-15 12:04

[QUOTE=R.D. Silverman;142519]A pointless exercize.[/QUOTE]

This thread is not intended to be something like "exact maths", it is a [i]game[/i] just for fun.

(and fun is often pointless, but it's funny.)

 davieddy 2008-09-15 12:37

[quote=R.D. Silverman;142519]A pointless exercize.[/quote]
But a well-established tradition in these forums.
No need to be a killjoy.

 Xyzzy 2008-09-15 14:37

1/19/2038

 Raman 2008-09-15 14:45

[quote=Mini-Geek;142426]Well, I know we don't know the identities of M45 and M46 yet, but we know we have two primes, so we might as well get M47 guesses out there.

Predict the exponent and/or the date it will be found.

I'll guess 50M in September 2009.[/quote]

I suspect that the Mersenne Primes will be so [B]densely[/B] located in these ranges and higher. So, around only 50 million or slightly less than that within the next 6 to 9 months is thus my estimate!

 Flatlander 2008-09-15 14:49

Re. Predict M47

Do you mean the date of the 47th prime found (whatever the size) or the date of a new record prime?

 Mini-Geek 2008-09-15 14:57

[quote=Flatlander;142541]Do you mean the date of the 47th prime found (whatever the size) or the date of a new record prime?[/quote]
Technically, "M47" would mean the 47th Mersenne prime, regardless of the discovery order, but I mean the 47th Mersenne prime to be discovered (i.e. guessing an "M47" value below a known Mersenne prime is allowed), regardless of it being the true M47 (and, therefore, assuming no other primes are discovered larger than M46, the world record) or not.
I think we can all figure out the 47th prime pretty easily, it's the 47th Mersenne prime that's a bit more difficult. :wink:

 xilman 2008-09-15 15:23

[QUOTE=Xyzzy;142539]1/19/2038[/QUOTE]Nice!

Paul

 ET_ 2008-09-15 15:37

20/12/2012 (European date)

 Xyzzy 2008-09-15 16:43

[quote]Nice![/quote]
We were a bit off for M44…

 xilman 2008-09-15 17:34

[QUOTE=Xyzzy;142559]We were a bit off for M44…

[url]http://www.mersenneforum.org/showthread.php?t=5201[/url][/QUOTE]Sure, but at least I recognize the significance of that date.

Paul

 Xyzzy 2008-09-15 19:27

It was either that date or 12/21/2012.

 T.Rex 2008-09-15 19:32

We need a poll

We need a poll with a dozen of years. So that anyone can guess and we'll have a global view of all guesses.
My guess is: M47 will be found before end of 2010.
And the 100M prime will be found around 2020 (I previously said 2023. Changed my mind) and it will be M50 or M51. [URL="http://en.wikipedia.org/wiki/Poisson_distribution"]Poisson[/URL] told me ! And I believe in [URL="http://image-photos.linternaute.com/image_photo/550/autres-animaux-aquatiques-mayotte-1169808904-1139058.jpg"]Poisson[/URL]. Don't you like "[URL="http://primes.utm.edu/notes/faq/NextMersenne.html"]Poisson[/URL]" ?
Bad we are not 1rst of April...
Tony

 xilman 2008-09-16 07:47

[QUOTE=T.Rex;142593]We need a poll with a dozen of years. So that anyone can guess and we'll have a global view of all guesses.
My guess is: M47 will be found before end of 2010.
And the 100M prime will be found around 2020 (I previously said 2023. Changed my mind) and it will be M50 or M51. [URL="http://en.wikipedia.org/wiki/Poisson_distribution"]Poisson[/URL] told me ! And I believe in [URL="http://image-photos.linternaute.com/image_photo/550/autres-animaux-aquatiques-mayotte-1169808904-1139058.jpg"]Poisson[/URL]. Don't you like "[URL="http://primes.utm.edu/notes/faq/NextMersenne.html"]Poisson[/URL]" ?
Bad we are not 1rst of April...
Tony[/QUOTE]As they say, one man's fish is another man's poisson...

Paul

 nngs 2008-09-16 18:10

1 Attachment(s)
My prediction of M45 was quite off ([url]http://mersenneforum.org/showpost.php?p=130178&postcount=174[/url]), and didn't even have a chance to predict M46 (my prediction of M46 surely
would be even more off if I give a try).

Now is my prediction of M47:

M47 exponent is around 90087850.
1 sigma range of this prediction is between 69,814,566 and 116,248,250

I assume [TEX]$\log_2(\log_2(M_{\rm n}))$[/TEX] depends on n as [TEX]A+B\times n+C\sin(D\times n+E)[/TEX]

The best fit using all 46 known mersenne primes is:
A=1.1253235 +/- 0.125
B=0.55185022 +/- 0.00484
C=0.68753629 +/- 0.0850
D=0.29490442 +/- 0.00560
E=-3.2489748 +/- 0.149

Attached figures is the best fit curve verus 46 data points

 ixfd64 2008-09-16 18:12

I predict that "M47" will be discovered early this December, and it will be in the 45M range. That's right - three new Mersenne primes in the same year.

 T.Rex 2008-09-16 19:18

[QUOTE=nngs;142758]I assume [TEX]$\log_2(\log_2(M_{\rm n}))$[/TEX] depends on n as [TEX]A+B\times n+C\sin(D\times n+E)[/TEX]

The best fit using all 46 known mersenne primes is:
A=1.1253235 +/- 0.125
B=0.55185022 +/- 0.00484
C=0.68753629 +/- 0.0850
D=0.29490442 +/- 0.00560
E=-3.2489748 +/- 0.149
[/QUOTE]Interesting. How did you find A, B, C, D and E ?

The theoretical (but not yet proved !) Poisson's slope is : [TEX]1/e^\gamma= 0.5614594...[/TEX]
So, your B is not so far.

Tony

 nngs 2008-09-16 20:19

[QUOTE=T.Rex;142782]Interesting. How did you find A, B, C, D and E ?

The theoretical (but not yet proved !) Poisson's slope is : [TEX]1/e^\gamma= 0.5614594...[/TEX]
So, your B is not so far.

Tony[/QUOTE]

I use a [URL="http://www.ittvis.com/ProductServices/IDL.aspx"]IDL[/URL] route called LMFIT. Here is the first sentence in LMFIT help:

[QUOTE]The LMFIT function does a non-linear least squares fit to a function with an arbitrary number of parameters. [/QUOTE]

If I use A+B*n only (which will give me B=0.561...), the residuals show a sinusoidal pattern. So I add a sine term in my guess function.

 petrw1 2008-09-16 22:49

Well, breaking from the mathematically sound 2^n intervals, I charted the number of MPs by 10^n digits:
0 = 7 (for 10^0 digits there are 7 MPs)
1 = 5
2 = 6
3 = 8
4 = 5
5 = 6
6 = 7
7 = 2 (so far)

Again, based on unsound principles, excluding the first interval, I see a pattern (5,6,8,5,6,'7'). So, it would suggest there is one more MP at 10^6 digits. But with all the focus on larger ranges it could be a while before that range clears so I am guessing it will be in the 29M range but not found until November 2009.

 Primeinator 2008-09-17 05:56

I predict M47's exponent will be approximately 47,300,000 and will be discovered in October of next year.

 Uncwilly 2008-09-17 17:59

I have started tabulating the data. I am up to date at this point.

 R. Gerbicz 2008-09-17 18:49

Never. There is no more Mersenne prime, the list is complete.

[quote=Uncwilly;142931]I have started tabulating the data. I am up to date at this point.[/quote]

Once we get a few more, we could make a chart, and send it to mini-geek, so that he can update his post.

"All mersenne primes have been found" is a valid guess, so there should be a bucket for that. In fact, I would say that as of right now, Gerbicz is currently the leading contender in this contest :smile:

 Mini-Geek 2008-09-17 19:25

[quote=uigrad;142935]... and send it to mini-geek, so that he can update his post.[/quote]
Only mods can edit posts after 1 hour, so someone else will have to put it up on the first post, if a chart is made (I think that's a good idea).

 petrw1 2008-09-17 19:28

To the contrary could there be MORE than expected?

I started monitoring the "pretty colorful stats report" almost 3 years ago (Oct 25, 2005).
At the time there were 42 known primes and 2.64 "Expected New Primes" for an expected total between 44 and 45.

Not quite 3 years later we are at 46 known primes and it still reports 1.77 expected for an expected total NOW closer to 48 ... 3 more than expected 3 years ago.

Is this not mathematically significant enough to make one wonder if they are LESS rare than we thought?

 philmoore 2008-09-17 19:50

[QUOTE=petrw1;142937]Is this not mathematically significant enough to make one wonder if they are LESS rare than we thought?[/QUOTE]

Take a look at Chris Caldwell's updated graph at:
[url]http://primes.utm.edu/mersenne/heuristic.html[/url]
Note the last seven points - definitely a significantly tighter clustering than the clusterings at M21 through M23 and M24 through M26. Could be one of the following:

1) Purely a statistical deviation.
2) The beginning of a departure from the heuristic which has been pretty successful so far in characterizing the overall distribution of Mersenne primes.
3) Just the universe's way of encouraging us to continue searching for more Mersenne primes!

 Primeinator 2008-09-17 20:14

[QUOTE]2) The beginning of a departure from the heuristic which has been pretty successful so far in characterizing the overall distribution of Mersenne primes.[/QUOTE]

I'm hoping it is possibility number two. :cool:

 Mini-Geek 2008-09-17 20:20

[quote=philmoore;142939]1) Purely a statistical deviation.[/quote]
This one, IMHO. Assuming (the unproven statement that...) Mersenne primes are infinite (or that they're finite but the last one is very large), you'll eventually run into a group that are tightly bunched beyond normal statistical chance.

 T.Rex 2008-09-17 21:41

[QUOTE=nngs;142797]I use a [URL="http://www.ittvis.com/ProductServices/IDL.aspx"]IDL[/URL] route called LMFIT. [/QUOTE]Sems that this is not a free tool... I have some Math tool on my PC. I'll see if it can help.
[QUOTE]If I use A+B*n only (which will give me B=0.561...), the residuals show a sinusoidal pattern. So I add a sine term in my guess function.[/QUOTE]Nice. Bob (Silverman) should say that it is not Math, but maybe you should send an email to Chris Caldwell or to Mr Wagstaff. Why not. Though this Poisson' process does not really help to find the next Mersenne, it is interesting to do some guesses. It's like doing Physic: you observe phenomenons, you find a law that seems to be in accordance with the data, and then you analyse the consequences of the law, and search if it can help to guess other things, and if it continues to represent the reality...
Good !
Tony

 sylvester 2008-09-18 04:48

[QUOTE=T.Rex;142963]Sems that this is not a free tool...[/QUOTE]

From the name LMFIT one can make a guess that this was some implementation of the Levenberg-Marquardt algorithm. Perhaps that will make your search easier.

 Uncwilly 2008-10-09 20:16

[code]petrw1 29,000,000 11/1/2009
ixfd64 43,112,609 12/1/2008
Primeinator 47,300,000 10/1/2009
Raman 50,000,000 3/1/2009 <50mil or w/in next 6-9 mon
MiniGeek 50,000,000 9/1/2009
ATH 52,300,000 11/1/2009
davieddy 60,000,000 1/1/2012
MoooMoo 75,860,000 5/1/2013
nngs 90,087,850
henryzz 8/31/2009
ET 12/20/2012
Yzzyx 1/19/2038
Bob Silverman pointless[/code]

 XYYXF 2008-10-11 13:11

88M, Nov 2011.

 Damian 2008-10-11 19:40

45M, next week.

 davieddy 2008-10-13 14:47

[quote=Damian;145136]45M, next week.[/quote]
Nobody has returned a 44M test yet, so I don't see
who will discover 45M this week:smile:

 retina 2008-10-13 14:52

[QUOTE=davieddy;145271]Nobody has returned a 44M test yet, so I don't see
who will discover 45M this week:smile:[/QUOTE]Perhaps Damian meant M45 next week. As in, M47 will actually be the current M45 because two more primes less than the current M45 will be discovered next week.

 davieddy 2008-10-13 15:12

[quote=retina;145273]Perhaps Damian meant M45 next week. As in, M47 will actually be the current M45 because two more primes less than the current M45 will be discovered next week.[/quote]
You mean a dyslexic confusion between 45M and M45?

Edit: No. On re-reading you were proposing an even more
bizarre explanation:)

 retina 2008-10-13 15:35

[QUOTE=davieddy;145274]You mean a dyslexic confusion between 45M and M45?[/QUOTE]Could be dyslexia, or just a typo.[QUOTE=davieddy;145274]Edit: No. On re-reading you were proposing an even more
bizarre explanation:)[/QUOTE]If it is something bizarre then that is definitely what I meant :wink:

 ATH 2008-10-14 11:22

[QUOTE=davieddy;145271]Nobody has returned a 44M test yet, so I don't see
who will discover 45M this week:smile:[/QUOTE]

I got 46M exponent and I use "First time test"-option.

 mcduck 2008-10-14 20:22

54M, 14:25 CET, June 24, 2010

 Terrence Law 2008-11-03 02:35

Prediction for the Next Mersenne Prime

I predict that the next Mersenne prime will be around 95M, discovered in May 2011. The gaps between the recent Mersenne primes are short. There are four-digit Mersenne prime exponents which start with 2, 3 and 4.

Hmmm ... yes, a bit of similarity in runs of initial decimal digits:

...

607
1279
2203
2281
3217
4253
4423
9689

...

6972593
13466917
20996011
24036583
25964951
30402457
32582657
37156667
43112609
(?)

But why should that mean anything other than a coincidence within a larger demonstration of Benford's Law ([URL]http://mathworld.wolfram.com/BenfordsLaw.html[/URL] or [URL]http://en.wikipedia.org/wiki/Benford's_law[/URL]) over a set of numbers (_all_ known Mersenne-prime exponents, not just two specially-picked subsets) whose distribution is expected to be related to logarithms?

Looking at all the known Mersenne-prime exponents with 1-7 decimal digits (we don't yet have a complete census for 8-decimal-digit exponents), the counts by initial digit are:

1: 12

2: 7

3: 4

4: 3

5: 2

6: 3

7: 2

8: 3

9: 2

Of the 38 exponents in that range,

Compare that to the ideal Benford distribution of

30.1% "1"s,

17.6% "2"s, and

12.5% "3"s.

Pretty close for such a small sample (N = 38), eh? And -- Benford's Law comes with a logical mathematical explanation -- no guessing needed!

 davieddy 2008-11-03 07:27

Pretty close for such a small sample (N = 38), eh? And -- Benford's Law comes with a logical mathematical explanation -- no guessing needed![/quote]

And the Wagstaff conjecture makes Mersenne exponents an
ideal application for it does it not?

For a given number of digits, the expected number of
primes with exponent beginning with digit n is proportional to
log(n+1)-log(n).

 10metreh 2008-11-13 19:36

59278411, some time mid-2011

 Uncwilly 2009-06-06 16:31

Things that make one go: hmm?

 Primeinator 2009-06-06 17:15

I predict M47 to be.... 43,112,609 :smile:

Perhaps me need a Predict M48 thread now

 T.Rex 2009-06-06 18:18

[QUOTE=Primeinator;176228]I predict M47 to be.... 43,112,609 :smile:[/QUOTE]Nice guess !
I'm happy you follow the Math rules and not the GIMPS rules.
I mean: GIMPS gives number to Mersenne primes based on when they are found. So 2^43,112,609-1 is still said to be the 45th Mersenne prime found, though the same post talks also of 2^37,156,667-1 .
Tony

 joblack 2009-06-06 18:22

[quote=T.Rex;176236]Nice guess !
I'm happy you follow the Math rules and not the GIMPS rules.
I mean: GIMPS gives number to Mersenne primes based on when they are found. So 2^43,112,609-1 is still said to be the 45th Mersenne prime found, though the same post talks also of 2^37,156,667-1 .
Tony[/quote]

Don't have to be M47 ... there is enough free space for one or two others ;).

[quote=Primeinator;176228]I predict M47 to be.... 43,112,609 :smile:

Perhaps me need a Predict M48 thread now[/quote]Okay ...

I predict that M48 will be M(43,112,609) someday.

 Mini-Geek 2009-06-06 18:35

Here's all the guesses: (from Uncwilly's post on page 1)[code]petrw1 29,000,000 11/1/2009
ixfd64 [b]43,112,609[/b] 12/1/2008
Primeinator 47,300,000 10/1/2009
Raman 50,000,000 [b]3/1/2009[/b] <50mil or w/in next 6-9 mon
MiniGeek 50,000,000 9/1/2009
ATH 52,300,000 11/1/2009
davieddy 60,000,000 1/1/2012
MoooMoo 75,860,000 5/1/2013
nngs 90,087,850
henryzz 8/31/2009
ET 12/20/2012
Yzzyx 1/19/2038
Bob Silverman pointless[/code]I've bolded the closest guesses for n size and time, assuming this candidate is prime, and calling the discovery date when the computer reported it, not when a human noticed it. Congrats to ixfd64 and Raman for closest in size and time, respectively, assuming this is really prime.
By some measure, ixfd64's answer for size is now thought to be precisely correct, but I said:
[QUOTE=Mini-Geek;142542]Technically, "M47" would mean the 47th Mersenne prime, regardless of the discovery order, but I mean the 47th Mersenne prime to be discovered (i.e. guessing an "M47" value below a known Mersenne prime is allowed), regardless of it being the true M47 (and, therefore, assuming no other primes are discovered larger than M46, the world record) or not.
I think we can all figure out the 47th prime pretty easily, it's the 47th Mersenne prime that's a bit more difficult. :wink:[/QUOTE]
So I say he's only close, not precise.

 davieddy 2009-06-09 03:11