20100409, 17:14  #1 
Apr 2010
England
2×7 Posts 
Theory
If the perfect numbers are all 2^{n1}x(2^{n}1) and all mersenne numbers are 2^n1 and there is a clear (admittedly on and off) binary pattern for perfect numbers (110, 11100, 111110000) why is there so much trial and error as I am told "The chance that the exponent you are testing will yield a Mersenne prime is about 1 in 421010. " ?
Sorry I don't understand and thanks in advance for any replies. :) 
20100409, 17:33  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
7×13×47 Posts 
All perfect numbers in binary are indeed 11...1100...00 with p 1's following by p1 0's, (which is a direct result of the form being ) but unfortunately this doesn't help any more than noting that all Mersenne numbers (not only the primes, but all numbers 2^n1) in binary are 11...11 with p 1's (which is a direct result of the form being ).
Since all Mersenne numbers (and so all potential Mersenne primes) in binary are 11...11, and all associated potential perfect numbers are 11...1100...00, this is essentially a useless observation. We still need to determine if the Mersenne number is prime. Last fiddled with by MiniGeek on 20100409 at 17:40 
20100409, 18:23  #3  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×5,657 Posts 
Quote:
It is not yet known whether any odd perfect numbers exist. Many mathematicians appear believe that they do not exist. Some mathematicians believe they may exist. What is known is that if they do exist, they must be at least several hundred decimal digits long and that their prime factorization is severely constrained. The last constraint, a very particular prime factorization, is also true for even perfect numbers, of course. Paul 

20100409, 22:12  #4  
Feb 2006
Denmark
2×5×23 Posts 
Quote:


20100410, 02:11  #5 
Apr 2010
England
2×7 Posts 
OK thanks everyone :) got it
Just a quickie, can I take the 100 cpu limit off the program, I have a dual core (200 cpu points) iMac so it could run alot faster. Last fiddled with by RichardB on 20100410 at 02:12 
20100410, 14:13  #6  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
7·13·47 Posts 
Quote:
You can get it from this page: http://www.mersenne.org/freesoft/ Here's the link for Mac OS X: http://mersenneforum.org/gimps/Prime95MacOSX2511.zip Once you're running a version that supports multiple cores, it should automatically configure itself to run on all available cores. If not, go to Test > Worker Windows and configure it there. You'd want to run 2 worker windows, with each using one core. Last fiddled with by MiniGeek on 20100410 at 14:14 

20100410, 18:39  #7 
Apr 2010
England
2×7 Posts 
Thanks, found it, I was a bit confused with all the menus, I had looked in preferences and 'CPU' option windows.

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