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2008-04-14, 07:40   #27
gd_barnes

May 2007
Kansas; USA

29CC16 Posts

Quote:
 Originally Posted by gd_barnes OK, I will change your reservation from k=110M-111M to 110M-120M. I responded to your PM on the Riesel conjecture. The script on the input file would be the same except -1 instead of +1. Like the Sierp conjecture, only even k's need to be tested so no change there. But there is a slight change on the command line. Instead use: input.txt -f100 -l100k.txt -tp The -tp switch tells it to prove the primality of "-1" numbers vs. "+1" numbers. Good luck and thank you for attacking these huge bases! Gary

Quote:
 Originally Posted by Anonymous Actually, no. -tp signifies that PFGW should do an N+1 test (as opposed to an N-1 test with just plain -t), which can be used for numbers that an N-1 test can't prove primality for. (I've run into those occasionally.) Both N-1 and N+1 tests are not dependent on any form of number, so either should work for both +1 and -1 numbers.
Quote:
 Originally Posted by axn1 Actually, to successfully run an N+1 primality test, N+1 must be factored to atleast 33% of its length (meaning, if N is 100 digits, then at least 33 digits worth of prime factorization should be known). Vice versa for N-1. If the 33% factorization criteria is not met, then the test can't "prove" the primality. Since N+1 factorization of a "-1" number is trivial, it makes sense to use N+1 for "-1" (and N-1 for "+1" numbers).

As I stated originally for KEP's Riesel testing and without getting into the technical details of this; if you wish to prove the following:

Riesel numbers (-1) tests; use the -tp switch in PFGW

Sierpinski numbers (+1) tests; use the -t switch in PFGW

For all other forms, a good starting point it to try -tc, which effectively attempts to prove the number prime using both of the above but is very unlikely to do so if it is a random form.

For numbers with random forms and (I think) < 10000 digits, Primo is the best way that I know how to prove them.

Gary