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. 
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

60M, 2012

75.86 M, May 2013.

51.5M, Aug 2009

52.3M, Nov 2009

[QUOTE=MiniGeek;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. 
[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.) 
[quote=R.D. Silverman;142519]A pointless exercize.[/quote]
But a wellestablished tradition in these forums. No need to be a killjoy. 
1/19/2038

[quote=MiniGeek;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! 
Re. Predict M47
Do you mean the date of the 47th prime found (whatever the size) or the date of a new record prime?

[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: 
[QUOTE=Xyzzy;142539]1/19/2038[/QUOTE]Nice!
Paul 
20/12/2012 (European date)

[quote]Nice![/quote]
We were a bit off for M44… [url]http://www.mersenneforum.org/showthread.php?t=5201[/url] 
[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 
It was either that date or 12/21/2012.

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://imagephotos.linternaute.com/image_photo/550/autresanimauxaquatiquesmayotte11698089041139058.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=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://imagephotos.linternaute.com/image_photo/550/autresanimauxaquatiquesmayotte11698089041139058.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 
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 How I made: 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 
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.

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

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

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 minigeek, 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: 
[quote=uigrad;142935]... and send it to minigeek, 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). 
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? 
[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! 
[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: 
[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. 
[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 
[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 LevenbergMarquardt algorithm. Perhaps that will make your search easier. 
[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 69 mon MiniGeek 50,000,000 9/1/2009 uigrad 51,500,000 8/1/2009 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] 
88M, Nov 2011.

45M, next week.

[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: 
[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. 
[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 rereading you were proposing an even more bizarre explanation:) 
[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 rereading you were proposing an even more
bizarre explanation:)[/QUOTE]If it is something bizarre then that is definitely what I meant :wink: 
[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. 
54M, 14:25 CET, June 24, 2010

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 fourdigit 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 Mersenneprime exponents, not just two speciallypicked subsets) whose distribution is expected to be related to logarithms? Looking at all the known Mersenneprime exponents with 17 decimal digits (we don't yet have a complete census for 8decimaldigit 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, 12/38 = 32% start with "1", 7/38 = 18% start with "2", 4/38 = 11% start with "3". 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! 
[quote=cheesehead;147639]
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). 
59278411, some time mid2011

Things that make one go: hmm?

I predict M47 to be.... 43,112,609 :smile:
Perhaps me need a Predict M48 thread now 
[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 2^43,112,6091 is still said to be the 45th Mersenne prime found, though the same post talks also of 2^37,156,6671 . Tony 
[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 2^43,112,6091 is still said to be the 45th Mersenne prime found, though the same post talks also of 2^37,156,6671 . 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. 
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 69 mon MiniGeek 50,000,000 9/1/2009 uigrad 51,500,000 8/1/2009 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=MiniGeek;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. 
[quote=cheesehead;176243]Okay ...
I predict that M48 will be M(43,112,609) someday.[/quote] I predict it won't. Expected Mprimes lower than this is shrinking fast. 
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