20120221, 01:11  #1 
Feb 2012
Athens, Greece
2F_{16} Posts 
Distribution of Mersenne primes before and after couples of primes found
I made some nonscientific quick observations re the grandscale distribution of found primes amongst all the tested exponents, paying particular attention to two M primes being found in consecutive millionexponents (e.g. 42M and 43M, M for millionexponents) and the gaps between the other primes before and after the prime couples: (when I say 'prime' I mean 'Mprime', M for Mersenne)
This list starts at the 0M range of exponents and goes up to 43M:
In the 0M range there're 33 Mersenne primes, and 2 in the 1M range. I regard these as 'lone primes' (X). Then there is one prime in 2M and another one in 3M, I regard these as a 'couple' (XXX). For the next two millionranges (4M and 5M) there is no Mprime, so I regard these as a 'gap' (O), which in this case it is a doublegap (O:2). So here's the list of gaps before and after each prime couple:
So the 'beforegap' prior to the second 'couple' is 3 (21M, 22M and 23M because the first prime of the couple is in 24M) and the 'aftergap' is 4. The 'beforegaps' so far have a sequence of (0, 3, 4) while the 'aftergaps' so far have a sequence of (2,4). The question is what would we expect the 'aftergap' after the third and last (so far) 'couple' to be? Could we expect 6? (so the next 'lone Mprime' would be in 50M), 8? (next 'lone' in 52M), or something else? Last fiddled with by emily on 20120221 at 01:12 
20120221, 01:37  #2  
If I May
"Chris Halsall"
Sep 2002
Barbados
2×5,431 Posts 
Quote:
Given fifty throws of a fair coin which shows up heads, what are the odds of the next throw being tails? 

20120221, 02:11  #3  
"Bob Silverman"
Nov 2003
North of Boston
1110101001000_{2} Posts 
Quote:
sample from a given density function. Indeed, learn what a density function is. Go learn some statistics and probability theory. Learn what conditional probability is. Study Bayes' Theorem. Come back here after you have done so. I don't know who you are or what your background is. But your post consists of jumbled numerology, nonsense, and nothing else. 

20120221, 02:35  #4 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1C35_{16} Posts 
@OP: RD Silverman is quick to jump on new guys. OTOH, if you show a willingness and competence (he is very big on competence) to learn what he's talking about, then you should get along just fine.
Many, many hours by many people have been put into studying the stats. As more of a "lightreading" suggestion, try http://primes.utm.edu/notes/faq/NextMersenne.html and http://primes.utm.edu/mersenne/heuristic.html . These two pages mention many of the things that RDS is talking about, and if you're not put off by it, then take his suggestion and read up (the "heavier reading") on those things. If you are put off by it (as I was, I hate statistics) then it's better to leave the thread alone, because the Math forum has literally the most knowledgeable mathematicians in the world lurking around. (I mean, e.g., this. "Of this vicinity" means "active posters on this forum".) Last fiddled with by Dubslow on 20120221 at 02:36 
20120221, 03:01  #5  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{4}×3^{3}×5^{2} Posts 
Quote:
You also might try some light reading over at the MersenneWiki.org 

20120221, 06:55  #6 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2×283 Posts 
Poisson Distribution
Well we might add that there are strong arguments in favor of the distribution of Mersenne Primes is a Poisson Distribution, but there is no proofs as yet.

20120221, 11:04  #7 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 

20120221, 11:22  #8  
Feb 2012
Athens, Greece
47 Posts 
Quote:
I said it's nonscientific, didn't try to present it as anything other than some quick nonscientific observations. But I was stupid to post it on this forum where the discussion is apparently on a higher level. Thanks for the suggestions. Oh and yeah, ofc I know this is a problem that very knowledgeable people are trying to solve for a very long time and still nobody knows for sure how the primes are distributed... Sigh...! 

20120221, 12:28  #9  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 
Quote:
It doesn't matter that the observations are not scientific. What matters is that they were made in the first place. Making these 'observations' violates some very basic fundamental principles and theorems in probability and statistics. In particular: FUTURE EVENTS ARE NOT DEPENDENT ON PAST EVENTS in this domain. Learn what "independence" means. What you did was like walking into a medical convention and announcing "I don't know anything about cellular chemistry, but I have some nonscientific observations about how to cure cancer". You violated principles that are taught in the very first day of any class on statistics and probability. 

20120221, 18:42  #10 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Unfortunately, it is a subtle difference that most people don't make on first thought. Many of the residents here have learned the difference, and now hopefully OP has learned the difference.

20120221, 20:39  #11 
Feb 2012
Athens, Greece
47 Posts 
My CapsLock key is mapped to the XWindows keyboard language layout switch and I avoid using allcaps because most people equate it with yelling which tends to make them feel upset.
But there's no need to continue discussing something that isn't of interest to the Maths forum. Last fiddled with by emily on 20120221 at 20:50 
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