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

hyh1048576 · 2003-08-19, 05:49

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? :? ;) :?

ColdFury · 2003-08-19, 06:29

A simple sieve suffices for generating a list of primes.

trif · 2003-08-19, 07:51

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.

Prime95 · 2003-08-19, 20:19

Trif is correct, prime95 does not have a list of primes inside it.

smh · 2003-08-20, 09:24

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

Prime95 · 2003-08-20, 13:38

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.

2003-08-19, 05:49	#1
hyh1048576 Jun 2003 64₁₀ Posts	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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2003-08-19, 06:29	#2
ColdFury Aug 2002 2⁶×5 Posts	A simple sieve suffices for generating a list of primes.

2003-08-19, 20:19	#4
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 2×53×71 Posts	Trif is correct, prime95 does not have a list of primes inside it.

2003-08-20, 13:38	#6
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 2×53×71 Posts	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.