20141204, 10:24  #1 
"M49"
Dec 2014
Austria
30_{8} Posts 
Another interesting pattern of Mersenne exponents: they are prime!!!!1111
Mersenne prime exponents (except 2 and 3) follow this "pattern", or however you may call it.
There are 2 strands, the 5strand and the 7strand. (6n1 and 6n+1) Furthermore there are 8 "starting numbers", 4 for each strand. Starting numbers for 5strand: 5=1*61 17=3*61 107=18*61 756839=126140*61 Starting numbers for 7strand: 7=1*6+1 13=2*6+1 19=3*6+1 2281=380*6+1 The Mersenne exponents can be described as: p_{5}^{i}=p_{5}^{0} + 24*n_{i} p_{7}^{i}=p_{7}^{0} + 24*n_{i} My questions: 1) Are there more than these 8 "starting numbers"? 2) If question 1 can be answered with YES, how many exist? 3) Where are more, in the 5strand or in the 7strand? IMHO they are exactly 50% in the 5strand (1 mod 4) and 50% in the 7strand (3 mod 4). Have a look to the attached graphic and let´s discuss it! Last fiddled with by ProximaCentauri on 20141204 at 10:38 
20141204, 10:45  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:
The "pattern" you think you see is a delusion. Try reading some books on number theory. Read Sam Wagstaff's paper on the distribution of Mersenne primes. It would answer your "50% is 5strand" nonsense. Oh. And stop inventing your own terminology (e.g. "strands") It is one hallmark of a crank. Use standard terminology. Finally, with respect to your "IMHO", mathematics is not done by opinion. Noone cares about your opinion. You clearly do not know enough math to be allowed to have an "opinion". 

20141204, 11:21  #3  
"M49"
Dec 2014
Austria
11000_{2} Posts 
Quote:
Dear R.D. Silverman If you would have read my posting carefully you would have realized that I was not talking about MersennePrimes and their distribution but about the exponents yielding these Mersenneprimes! Instead of trying to answer one or more of my questions, you started insulting me. Don´t worry, I already read the paper of Sam and I also know very well about the distribution of MersennePrimes, but that does´t answer my question about the exponents, which my posting was about! Unless you don´t have an own opinion about it, please do me a favor and stay out of this discussion! Thanks! Last fiddled with by ProximaCentauri on 20141204 at 11:27 

20141204, 11:39  #4 
Feb 2010
Sweden
173 Posts 
What you post is an open question, since there are many prime numbers of a form 6*n1 or 6*n+1. How many of these are Mersenneprime exponents is ongoing project in any Mersenne prime search project (such as GIMPS). Did you notice the size of the gaps between your members of a chain?

20141204, 12:12  #5  
"M49"
Dec 2014
Austria
18_{16} Posts 
Quote:
However, what´s interesting is: What makes these 8 numbers (if they are complete) so unique? 517107756839 (5strand acc. to my new terminology) 713192281 (7strand acc. to my new terminology) Are they the building blocks of MersennePrimes? Are they already complete? Of course, the gaps (multiples of 24 added to the starting number to yield a new Mersenne prime exponent) are going bigger and bigger, as the Mersenne Primes do! That´s normal and no surprise! This discussion is about these starting numbers, as I call them, and maybe someone can answer me, but I doubt! Last fiddled with by ProximaCentauri on 20141204 at 12:29 

20141204, 12:42  #6  
"Forget I exist"
Jul 2009
Dumbassville
10000011000000_{2} Posts 
Quote:
just double checking if the raised number are supposed to be exponents if so it generalizes to: Quote:
Quote:
Quote:


20141204, 12:46  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:
I do not have "opinions" about math. Despite my trying to tell you that math is not done by "opinion", you refuse to learn. I believe your claim about reading Wagstaff's paper to be a lie based on the level of mathematical maturity exhibited by your posts, I apologize for suggesting that you read it. I doubt that you would understand it. The distribution of Mersenne primes says EVERYTHING about the distribution of the exponents. You would realize this instantly if you knew some math. (hint: think about logarithms). I will answer your question about distribution of the exponents. The density function is the logarithmic density of a Poisson distribution, (assuming the standard arguments about the distribution of the Mersenne primes themselves). Something you have to realize is the DunningKruger effect. One part of it is the inability of someone to recognize expertise in others. You claim that I did not read your posting carefully. I suggest that you consider the possibility that some people here know so much more about the subject than you do that it is obvious when you are prattling. 

20141204, 12:48  #8  
Nov 2003
1D24_{16} Posts 
Quote:


20141204, 13:06  #9 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 

20141204, 13:21  #10  
"M49"
Dec 2014
Austria
2^{3}·3 Posts 
Quote:
All I did was asking some questions which you could not answer. But it´s okay, i know number theory is a tough and dangerous ground to move. A Poissondistribution statistically tells you where to search for a needle in a haystack! With other words: You know nothing where to search! Come back to me when you have an idea on my starting numbers! 

20141204, 13:24  #11 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 

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