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. 
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