20120128, 20:26  #1 
Apr 2010
Netherlands
17_{10} Posts 
A basic math question
I am looking into the math behind PSPPRP and other prime number finding projects. It is obvious that a lot of test candidates already have been eliminated. It's easy enough to figure out that all numbers dividable by 3 or 5 can easily be eliminated. Then in the past this project also did some sieve and eliminated even more test candidates.
Beyond that, are there more smart tricks that for example can easily exclude other numbers? Sorry in advance if this has been documented somewhere already, but it is hard to find stuff here on Mersenneforum. Last fiddled with by iconized on 20120128 at 20:39 
20120128, 21:01  #2  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
5,179 Posts 
Quote:
http://www.mersenne.org/various/math.php 

20120203, 00:01  #3 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
7·13·47 Posts 
There are various algebraic factorizations (applicable to some bases/k's, anyway; I'm not sure if PSP in particular benefits from them) that can eliminate numbers that don't have any small factors. An example of something like that are Aurifeuillian factorizations. While Aurifeuillian factorizations aren't useful for prime searching (they are useful for factoring), that's just an example.

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