At 06:19 PM 1998/10/21 EDT, [EMAIL PROTECTED] wrote:
> Hi:
>10/22/1998
>
> I was looking at the available ranges to test Mersenne primes and I noticed
> the range included exponents which by definition cannot yield primes.
>
> I looked at some Mersenne htmls and didn't see any mention of even
> number exponents excluded from the search.
>
> if the exponent, n, is an even number integer then 2^n is a square and
>2^n-1
> is factorable by:
> ((2^n)1/2 -1) ((2^n)1/2 +1) = 2^n-1
>
> Example ...
>
> 2^10 = 1024
> (2^10)1/2 = 32
>
> so:
> (2^10) - 1 = 1023
> ((2^10)1/2) -1 = 31
> ((2^10)1/2) +1 = 33
> 31(33) = 1023
Only exponents which are primes are represented in the database which
either primenet or your own manually administered prime95 draw exponents
to factor or Lucas-lehmer test. Furthermore, the exponents in the
database have already been tested for prime factors up to 2 to some power
between 48 and 60 or so. They are tested up to about an optimal level
where the odds of finding a factor by going higher are outweighed by
the amount of time it would take, versus getting (an almost conclusive)
yes-or-no answer on primality by doing the more time consuming Lucas-
Lehmer test. The factoring makes use of knowledge of the special form
of possible factors of mersenne numbers (which are q=2kp+1 where
p is the prime exponent and k= a positive integer; they are also
q=8n+1 or 8n-1 where n is a positive integer).
> My computer is a pentium 133, 64mb ram , 2gig hd, MS95, math coprocessor.
> Could I contribute to the prime search?
Sure. Download the software and read the readme file to get started.
You'll want the prime95 software.
> Regards,
>
> Jim Broadhurst
> aiseki@aol,com
