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Old 2003-08-19, 05:49   #1
hyh1048576
 
Jun 2003

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Default Does Prime95 has a list of primes inside it???

I'm wondering this because when trying to write a math program, I came across some trouble. :(

Does Prime95 has a list of primes inside it???(If so, it will be quite large :? ) When we try to factor a Mersenne number Mp, how does the program know all the primes(<2^67 or 2^66) with the form 2kp+1? or it first find them out, then try to factor Mp? :? ;) :?
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Old 2003-08-19, 06:29   #2
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A simple sieve suffices for generating a list of primes.
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Old 2003-08-19, 07:51   #3
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From http://www.mersenne.org/math.htm

Quote:
One very nice property of Mersenne numbers is that any factor q of 2P-1 must be of the form 2kp+1. Furthermore, q must be 1 or 7 mod 8. A proof is available. Finally, an efficient program can take advantage of the fact that any potential factor q must be prime.

The GIMPS factoring code creates a modified sieve of Eratosthenes with each bit representing a potential 2kp+1 factor. The sieve then eliminates any potential factors that are divisible by prime numbers below 40,000 or so. Also, bits representing potential factors of 3 or 5 mod 8 are cleared. This process eliminates roughly 95% of potential factors. The remaining potential factors are tested using the powering algorithm above.
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Old 2003-08-19, 20:19   #4
Prime95
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Trif is correct, prime95 does not have a list of primes inside it.
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Old 2003-08-20, 09:24   #5
smh
 
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Quote:
Originally Posted by Prime95
Trif is correct, prime95 does not have a list of primes inside it.
I thought prime95 does have a list with all known mersenne primes inside?
(Yes, i know this is not what the original question is about)

On 04 Sep 1996, 1 day after M1257787 was announced (which was found a couple of months earlier) Luke Welsh wrote to the mersenne mailing list:

Quote:
....... I somehow kept in under my hat. George used
my machine as a backup site, so I had all of the source and HRF
databases. When I started to work a little on the factoring routines,
I noticed a small file called 'primes'. It had 34 entries.

--Luke
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Old 2003-08-20, 13:38   #6
Prime95
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Yes, prime95 has a list of all known Mersenne primes in it.

Luke was refering to backups of the master database. For a time, I zipped up the master database for backup on his computer.
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