Predict M48...

[Uncwilly]

Originally Posted by CRGreathouse

Is that true? In the last 10 years (3652 days) we have discovered 9 Mersenne primes.

Over the history of Gimps, the intervals between discoveries have averaged 378 days. The deviations from that have been on average 221 days.

[ATH]

GIMPS found 13 primes so there are 12 gaps. Maximum gap is 897 days, minimum gap 14 days and average gap 377,75 days.

As of today Apr 14th 2010 its 367 days since last prime, so still 11 days below average gap:

M(1398269) Nov 13 1996
M(2976221) Aug 24 1997 +284 days
M(3021377) Jan 27 1998 +156 days
M(6972593) Jun 1 1999 +490 days
M(13466917) Nov 14 2001 +897 days
M(20996011) Nov 17 2003 +733 days
M(24036583) May 15 2004 +180 days
M(25964951) Feb 18 2005 +279 days
M(30402457) Dec 15 2005 +300 days
M(32582657) Sep 4 2006 +263 days
M(43112609) Aug 23 2008 +719 days
M(37156667) Sep 6 2008 +14 days
M(42643801) Apr 12 2009 +218 days

[joblack]

Originally Posted by cheesehead

I am amused to see that the automated simulation of coin tosses at the side of that article repeatedly shows a blue:red ratio that is closer to 55/45 than 50/50.

As far as I know it hasn't been proven that the random distribution of primes (and especially Mersenne primes) is correct?

[Primeinator]

Originally Posted by joblack

As far as I know it hasn't been proven that the random distribution of primes (and especially Mersenne primes) is correct?

I do not think it has been proven for Mersenne primes. Furthermore, I think there is a fairly decent amount of evidence suggesting otherwise. Look at this graph: http://primes.utm.edu/notes/faq/NextMersenne.html

[axn]

Originally Posted by Primeinator

Furthermore, I think there is a fairly decent amount of evidence suggesting otherwise. Look at this graph: http://primes.utm.edu/notes/faq/NextMersenne.html

What of it? What part of the graph suggests it is not a random distribution?

[cheesehead]

Originally Posted by axn

What of it? What part of the graph suggests it is not a random distribution?

Depends on meaning of "random" -- i.e., Poisson is not uniform (-- and also depends, in U.S. since late 1990s, on what the meaning of "is" is).

[Primeinator]

Originally Posted by axn

What of it? What part of the graph suggests it is not a random distribution?

Originally Posted by cheesehead

Depends on meaning of "random" -- i.e., Poisson is not uniform (-- and also depends, in U.S. since late 1990s, on what the meaning of "is" is).

It does depend on the definition of random. I apologize for not specifying. The aforementioned graph appears to follow a predictable pattern. In other words, there can be an expression given that approximates the location of the next Mersenne prime. The best-fit line seems to be very, very good and likely has a r value of very close to 1.

[axn]

Originally Posted by Primeinator

It does depend on the definition of random. I apologize for not specifying. The aforementioned graph appears to follow a predictable pattern. In other words, there can be an expression given that approximates the location of the next Mersenne prime. The best-fit line seems to be very, very good and likely has a r value of very close to 1.

The appearance of a pattern doesn't mean it is not random. Random != Chaos

Look at that graph again. Treat the first 39 points as one data set, and the last 8 points as another data set. Do a curve fit for them. You'll find that these gives significantly different patterns. Could you have predicted that?

That link you provided talks about modeling Mersenne primes using a Poisson process (and comes up with decent fit based on that). What is a Poisson process?

[cheesehead]

Originally Posted by axn

What is a Poisson process?

http://mathworld.wolfram.com/PoissonProcess.html

http://en.wikipedia.org/wiki/Poisson_process

[davieddy]

I have looked at the "expected new primes" < 79,300,000 for
April 2001,2004,2007 and 2010.
http://web.archive.org/web/*/http://...org/status.htm

From these figures, I deduce:

01 - 04 we expected 1.64 (found 2)
04 - 07 we expected 1.28 (found 4)
07 - 10 we expected 0.69 (found 3)

Note that expecting 0.69 corresponds to an even chance
of finding one or more.

I would guess that finding M48 before 2015 is a toss up.

David

[davieddy]

http://mersenneforum.org/showpost.ph...&postcount=182

This nice graphic indicates that it may well take 5 years for
the wavefront to advance by 20M (enough to give us a fighting
chance of finding M48).