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 2010-04-09, 17:14 #1 RichardB   Apr 2010 England 2×7 Posts Theory If the perfect numbers are all 2n-1x(2n-1) and all mersenne numbers are 2^n-1 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. :)
 2010-04-09, 17:33 #2 Mini-Geek 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 p-1 0's, (which is a direct result of the form being $(2^p-1)*(2^{p-1})$) but unfortunately this doesn't help any more than noting that all Mersenne numbers (not only the primes, but all numbers 2^n-1) in binary are 11...11 with p 1's (which is a direct result of the form being $2^p-1$). 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 Mini-Geek on 2010-04-09 at 17:40
2010-04-09, 18:23   #3
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

2×5,657 Posts

Quote:
 Originally Posted by Mini-Geek All perfect numbers in binary are indeed 11...1100...00 with p 1's following by p-1 0's, (which is a direct result of the form being $(2^p-1)*(2^{p-1})$) but unfortunately this doesn't help any more than noting that all Mersenne numbers (not only the primes, but all numbers 2^n-1) in binary are 11...11 with p 1's (which is a direct result of the form being $2^p-1$).
Correction: all even perfect numbers have that form.

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

2010-04-09, 22:12   #4
Jens K Andersen

Feb 2006
Denmark

2×5×23 Posts

Quote:
 Originally Posted by RichardB If the perfect numbers are all 2n-1x(2n-1) and all mersenne numbers are 2^n-1 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. " ?
Only few of the Mersenne numbers are prime numbers, and only the prime Mersenne numbers lead to a perfect number. The computational challenge is to determine which of the Mersenne numbers are prime. With the best known methods it can take weeks or months to test a single Mersenne number that hasn't been tested before. And the estimated chance that the tested number turns out to be prime may be about 1 in 420000 (depending on the exact size and factorization effort).

 2010-04-10, 02:11 #5 RichardB   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 2010-04-10 at 02:12
2010-04-10, 14:13   #6
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

7·13·47 Posts

Quote:
 Originally Posted by RichardB 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.
http://www.mersenne.org/freesoft/
Here's the link for Mac OS X:
http://mersenneforum.org/gimps/Prime95-MacOSX-2511.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 Mini-Geek on 2010-04-10 at 14:14

 2010-04-10, 18:39 #7 RichardB   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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