20120222, 21:27  #12 
"Phil"
Sep 2002
Tracktown, U.S.A.
2^{5}·5·7 Posts 
On the contrary, there is nothing wrong with making this sort of observation, people do it all the time. Casinos make a good living from people who think that they see a pattern in wins and losses that will enable them to predict when they are due for their next win. The problem here is that no one has ever proven that the distribution of Mersenne prime exponents is described by a Poisson distribution, that only appears to be the simplest explanation. However, because we know that the distribution of primes, or the distribution of Mersenne primes, is not truly random, we really cannot rule out the possibility that there is some underlying structure not yet discerned. The gaps and irregularities are certainly intriguing, but the central question is whether or not you would see similar sorts of gaps and irregularities in any randomly generated Poisson sequence. Have fun, Emily, and don't be too concerned by the comments of RDS; he's the forum's oldtime schoolteacher who raps your knuckles with a ruler when you give the wrong answer. Of course, to him, he's not rapping your knuckles, he's rapping your answer!

20120222, 21:54  #13  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
the structure. But that is not the issue here. The phrase "not truly random" is meaningless here because "truly random" has not been defined. If the gaps between Mersenne primes can be proven to conform to a Poisson process, then under any reasonable definition the gaps are 'truly random'. The next gap is unpredictable. Quote:
of presenting astrology at a physics convention. Her prose "was not even wrong". 

20120223, 00:53  #14  
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
2A8B_{16} Posts 
Quote:
Secondly, did not astrology (which should have been the proper term for astronomy) lead to astronomy? Just be cause it seemed to you to be astrology, does not mean that it is of no value as a step to learning for the presenter. It is the duty of the more knowledgeable, if and only if they choose to speak up, to shepherd the presenter to a position of knowledge, knowledge sufficient so that they understand why astrology is wrong. Part of this selfassigned duty is to present the teaching in such a way that the newbie does not become so offended that they shut down to instruction. I would ask Bob that he practice biding his time and let others the first couple of chances with newbies like Emily. 

20120223, 06:59  #15 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
10,891 Posts 
RDS is the one on the right:
http://xkcd.com/386/ 
20120223, 07:46  #16 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 

20120223, 10:04  #17  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
19×613 Posts 
Quote:
How would you go about proving that the gaps between Mersenne primes conform to a Poisson process? Note: I'm not asking for a proof (though one woud be wonderful), only for a sketch of how such a proof may be attempted. Last fiddled with by xilman on 20120223 at 10:06 Reason: Add last sentence / clarification 

20120223, 12:01  #18  
"ร
ke Tilander"
Apr 2011
Sandviken, Sweden
1066_{8} Posts 
Nature of Poisson Distributions?
Quote:
There is a proof that there are at least 1 prime between X and 2X. If the distribution of primes were a true Poisson Distribution there would be a very, very, very small porobability that there were 0 primes between X and 2X. So my question is: Is this not a proof that the distribution of primes is not a true Poisson Distribution only a distribution very similar to a Poisson Distribution? I suppose to a matematician this is a dumb question, but even though I would like to pose it and hopefully learn someting from the answer. 

20120223, 12:38  #19  
"Bob Silverman"
Nov 2003
North of Boston
1110101010100_{2} Posts 
Quote:
similar to those uses by Tau & Greene to prove that there are arbitrarily long AP's of primes. It might use analytic methods. Noone knows how to even approach such a proof. 

20120223, 12:42  #20  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
Contrawise: And if the distribution of primes was not a Poisson process then there would be a very small probability that there were 0 primes between X and 2X. Indeed. Since the probability is zero in either case your statement basically says nothing. Quote:
is illposed at best and nonsense at worst, especially since "similar to a Poisson Distribution" is meaningless. 

20120223, 12:50  #21 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
Without already knowing that fact, how many primes would you suppose there are between 1000 and 2000? None or a great deal? It's pretty obvious there'd be a great deal. The proof that this extends infinitely means it at least might not be a true Poisson distribution, but doesn't preclude it being extremely similar.

20120223, 13:33  #22  
"ร
ke Tilander"
Apr 2011
Sandviken, Sweden
566_{10} Posts 
Quote:


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