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 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.

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