20051222, 21:53  #1 
Jun 2004
2^{2}·3·5 Posts 
Are M41,42,43 too close to each other?
around 24M, 26M, and 30M(?)
I read an article about prediction of the next Mersenne prime, which said, on average, P_(n) ~ 1.47576P_(n1) http://primes.utm.edu/notes/faq/NextMersenne.html 
20051222, 22:23  #2 
Aug 2002
Termonfeckin, IE
2^{4}·173 Posts 
"on average"
nuff said! 
20051222, 22:38  #3  
Jun 2004
3C_{16} Posts 
Quote:
I checked all Mesenne primes (142, and a guessed 43), it seems Pn/Pn1~1.5 is ok over the entire sequence, but some numbers (2or3) are clustered together. So, I think, M44 (very likely the 1st 10M digits number) probably is far away from M40, 41, 42, and 43 (forming a cluster), and makes a longer expectation of all GIMPSers Last fiddled with by nngs on 20051222 at 22:41 

20051222, 22:43  #4 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
"nuff" means "enough".
The point is that the estimate of Pn/P{n1}~1.5 holds on average  if you look at a very long sequence of Mersenne primes, the mean value of the ratios of exponents will be about 1.5. But this does not say anything at all about local behaviour of the sequence. It is perfectly possible that some Mersenne primes are close together, or that there is a long stretch with no Mersenne primes. Alex 
20051222, 22:49  #5  
Jun 2004
2^{2}·3·5 Posts 
Quote:


20051223, 00:26  #6  
Dec 2003
Hopefully Near M48
3336_{8} Posts 
Quote:


20051223, 10:25  #7 
Jul 2004
Potsdam, Germany
3×277 Posts 
That's basically correct  but IMHO, it's similar to "heads or tails". There, you also only have 2 extremes with nothing inbetween (assuming the coin doesn't fall on the thin side), but everyone talks about a 5050 chance. Changing the structure of the coin modifies the probability...

20051223, 10:48  #8  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
26476_{8} Posts 
Quote:
Paul 

20051224, 00:50  #9  
Jul 2004
Potsdam, Germany
3·277 Posts 
Quote:
Could you describe your opinion a little more explicit? 

20051224, 10:38  #10  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
26476_{8} Posts 
Quote:
I was afraid that the thread would degenerate into yet another discussion of the unsolvable three sided coin problem and was suggesting that we not go there. Paul Last fiddled with by xilman on 20051224 at 10:38 

20051224, 11:59  #11 
Jul 2004
Potsdam, Germany
1477_{8} Posts 
I have seen it, but I'm afraid it's too long ago.
I remember the killer rabbit, though. Last fiddled with by Mystwalker on 20051224 at 12:00 
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