factorint variation?

[Phil Carmody <thefatphil@yahoo.co.uk>]

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.)

Phil

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