20130211, 19:06  #1  
Feb 2013
2^{2}·7 Posts 
New around here
Hi 
So I just had a couple of questions in general, and I'll also dump a pattern I've seen up to 2^37. (After which I need a new computer or better prog skills.) First, I'm trying to wrap my head around why someone, or many now, have proven there are infinitely many primes, but why at the same time no one has figured out for sure if there are infinitely many Mersenne primes. Anyone speculate? If there were a proof, do you all think it would probably boost our ability to find more Mersenne's, or would just be something we already figured, but "ok that's nice to know." Second, I mostly just like playing around with patterns, and I'm a little more interested in that proof than finding big ones. This one seems a bit useless so I'll throw it on the pile here. Quote:
Probably just a stupid random pattern among a sea of prime randomness. Maybe you see something. Last, I couldn't really test further because up to now I've been doing the bulk of my work in R, which is probably funny to a lot of you. The next best thing I know is C, but there I only have survival C, like I only have survival french. Is the only way to go for this plain old programming languages, or are there software, and better yet, open source software that is good to use? best Last fiddled with by Andrew on 20130211 at 19:29 Reason: add a little thing 

20130211, 19:38  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 
Most "simple" proof of infinitudes of various forms of primes involve a product (plus or minus one) of the smaller examples of that form; that product (or the number above it) shares some properties of that form, whence you can conclude something about that number. Such a form does not occur dit products of Mersenne primes, so such a simplistic attack fails. I guess more advanced techniques also fail for whatever reason, though I can't comment on them. I can say that I would be shocked if an MP infinitude proof was practically useful.
As for arbitrary arithmetic, GMP (or MPIR) is your friend, especially regarding C/C++. Python offers "native" arbitrary precision integer arithmetic, though it uses GMP in the background (I think). 
20130211, 19:52  #3  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·3,313 Posts 
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if you work with R, you will find that Pari/GP is reasonably easy to learn, and it makes it very easy to prototype your ideas with any wanted precision. 

20130211, 20:16  #4  
Jun 2003
7·167 Posts 
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In my experience, people who can't express their ideas clearly rarely have clear ideas to express. Last fiddled with by Mr. P1 on 20130211 at 20:17 

20130211, 20:28  #5  
"Gang aft agley"
Sep 2002
2×1,877 Posts 
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20130211, 20:36  #6  
3·7·191 Posts 
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I started out knowing that Riemann proved that between K and 2K there is at least 1 prime number. So I just started playing with numbers where the Mersenne Number (not just the primes) was exactly in the middle of a K and a 2K. Actually, I put 2^P in the middle, not 2^P  1. It's not some big idea, just pattern searching. It turned out that [2^P  K] happened to be a prime number pretty frequently up to [P = 61] These are the numbers where [2^P  K] are prime: 3, 5, 7, 11, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347 And I didn't go to look back through all of them, but it appears at first glance the [2^P  K] and [2^N  1] are coprime. Again, it's not some big idea, just something I got sidetracked with, and thought was neat. [[***As a note, [2^N  K] and [2K  2^N] cannot be equal and still be integers, and hence with integer K, 2^N cannot be exactly in the middle. One of [2^N  K] and [2K  2^N] is odd and the difference is 1.***]] It's almost like a standard deviation kinda concept, is what [2^N  K] is... Dunno how much better I can do explaining, but it's not important. Sorry, I knew the first one wasn't a good effort of showing what I was thinking. Just lazy thinking... 

20130211, 21:04  #7  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
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20130211, 23:14  #8  
Jun 2003
1169_{10} Posts 
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20130211, 23:57  #9  
Feb 2013
28_{10} Posts 
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N stood for the exponent when 2^X  1 was not a prime exponent. And I beleive I used Pm to denote mersenne prime cases vs just mersenne numbers with a prime exponent. Just the n for a plain old Mersenne Number. And an example: 2*43 = 86 : 86  64 = 22 64  43 = 21 so, 43<<= 2164+22 =>>86 = 43*2 similarly 2*85 = 170 170128 = 42 128  85 = 43 85<<= 43128+42 =>>170 = 85*2 I'm looking at the left hand difference since it's odd. In this case, 43 and 21 Last fiddled with by Andrew on 20130211 at 23:58 

20130212, 03:50  #10  
Jun 2003
7·167 Posts 
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20130212, 04:27  #11  
Jun 2003
7·167 Posts 
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Another way is to exhibit an infinite set of numbers, and show that they are pairwise coprime. There are many such sets, for example the Fermat numbers. Last fiddled with by Mr. P1 on 20130212 at 04:28 
