20060915, 16:27  #45 
∂^{2}ω=0
Sep 2002
República de California
3·53·73 Posts 
Please Don't Flame each other over something this silly.

20060915, 19:42  #46 
"Phil"
Sep 2002
Tracktown, U.S.A.
10001011110_{2} Posts 
Ernst, it wasn't intended as a flame, I really just didn't understand what Phil was referring to. Thanks for the explanation, Drew.
I should teach probability sometime and learn the proper terminology, as my knowledge of it is more based on my experience in physics. However, there is an interesting point about Poisson processes, and that is the long tail that skews the mean to be considerably higher than the median. So if the mean ratio between successive Mersenne prime exponents is roughly 1.48 (assuming none have been missed less than the most recent), the median should be 1.48^(ln 2), or about 1.31. Someone please correct me if I have made a mistake, but it seems to me that we would expect the ratio to be less than this about half the time. Looking at the actual data, we see a median of about 1.41, but this may be somewhat skewed by the small exponents. If we consider only the Mersenne primes discovered by computer, the median is about 1.322, which is pretty close to the median of our guesses so far; I think wpolly's guess of M41991811 is the actual median (ratio of 1.29). So as a group, it looks like our guesses are fairly reasonable, although I detect a faint bias toward the "we're due for a big gap" way of thinking. 
20060915, 19:52  #47  
∂^{2}ω=0
Sep 2002
República de California
3·53·73 Posts 
Quote:
Quote:
Last fiddled with by ewmayer on 20060915 at 19:53 

20061120, 04:10  #48 
Nov 2006
SW Virginia USA
2 Posts 
45th MPE
from basic fit, "prediction" puts at 8.6E7 assuming no previous gaps

20061123, 02:20  #49 
Dec 2005
2×7 Posts 
Predict m45
I predict it will be less than 40,000,000 and found in September 2007
Last fiddled with by PrimeCrazzy on 20061123 at 02:21 
20061223, 15:19  #50 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
After consulting Chris Caldwell's page
"Where is the next Mersenne Prime" It seems there is a 50% chance that it will be less than 43,000,000. However, I don't think he has taken all the testing up to 37,000,000 which has been done since the page was last updated. David Eddy 
20061223, 17:21  #51 
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
Where is 45th Mersenne Prime
50% chance of it being less than 2^43,000,000
judging by Chris Caldwell's page "Where is the next Mersenne Prime" But I don't think it takes into account all the testing of exponents <37,000,000. David Eddy 
20070111, 07:57  #52 
Feb 2004
France
2×457 Posts 
Chris Caldwell's page URL.
Where is the next Mersenne Prime
Within figures 1 and 2, I see "waves" around the theoretical curve. Really clear for fig 2. It really does not look as random values above or below the curve. I guess there is a way to check if the values appear to be random or not. Who can provide the theory and do the computation ? T. Last fiddled with by T.Rex on 20070111 at 08:05 
20070111, 08:44  #53  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
of Mersenne primes is a "Poisson" process, i.e. random. For example, the discovery of M44 didn't alter the "expected" primes in each range of the status page at mersenne.org in the slightest. The "expected new primes" column on this page provides the easiest way to keep up to date on the probability (or lack of it!) of finding a new prime. If the expected number of primes in a range is x, then the probability of finding none is e^{x} David 

20070111, 08:55  #54 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
I do see what you mean about "waves" however.
My guess is that if you chose 44 mumbers at random between one and a thousand, then plotted them in order and drew the best fit straight line, you would see a similar effect. David 
20070111, 09:12  #55  
Jun 2005
2·191 Posts 
Quote:


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