Phil Carmody on Sun, 21 Dec 2003 23:06:07 +0100

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factorint variation?

In situations that I encounter every day (as I hunt for 
factors and prime numbers every day) is that of finding 
factors with special forms (of numbers with special forms).

In particular, working with cyclotomic numbers and Lucas
sequences, I encounter the situation where all factors 
will be of the form 2kn+/-1 (+1 common, -1 very rare) for
some fixed (e.g. in factors of polcyclo(n)), and k variable.

Is there any way to either 
- get factorint to accept a parameter representing n 
(maybe Mod(1,n)?) in order to speed up any trial-division, 
P-1, and possibly Rho?
- create a new function with the specific job of just 
finding small factors with this modular rule.

The kinds of numbers I'm looking at are quite large, and 
therefore the majority of the cracking will be done with 
GMPECM, but it's nice to have at least p<10^10 all flushed 
out before I crank out that sledgehammer. (Mainly as I 
don't like the way GMPECM will stop as soon as it finds 
the first factor.)


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