Trial Divison Improvement
I also wanted to mention the trial division of numbers (of special forms) in PFGW for (a^nb^n)/(ab) (with prime n) for integer roots a, b should be reduced to only trial dividing numbers of the form 2kn+1 (or if it is faster, sieving values of 2kn+1 and then trial dividing). Although little interest is shown in finding prp factors of (a^nb^n)/(ab) other than the Mersenne Cofactors, I would strongly appreciate more and more searches for these factors from others. I am working hard at prp testing factors generalized base repunit forms, and a^nb^n where a = b+1 more specifically. Thanks if someone knows how to do the trial division of these forms.

From pfgwdoc.txt:
[code] f[percent][[{Mod_Expr}][{condition}[{condition}...]]] Modular factoring: f{801} uses only primes which are of the form k*801+1 f{632,1} uses only primes which are of the form k*6321 ** The {801} and the {632,1} are the optional {Mod_Expr} *** NOTE new code added to do both 1 and +1. the format would be f{801,+1} (the +1 MUST look just like that) f{256}{y,8,1) uses only primes which are of the form k*256+1 where the resultant primes are also of the form j*8+1 f{256}{n,8,1) uses only primes which are of the form k*256+1 where the resultant primes are not of the form j*8+1 f500{256}{y,8,1){y,8,7){n,32,1) uses only primes which are of the form k*256+1 where the resultant primes are also of the form j*8+1 but not j*32+1. There is also a 500% factoring level. f{8132}{y,8,1){f,8132} uses only primes which are of the form k*8132+1 where the resultant primes are also of the form j*8+1. Also, all factors of 8132 (2,19,107) are checked first. f{8132}{y,8,1){p,8133} uses only primes which are of the form k*8132+1 where the resultant primes are also of the form j*8+1. Also, ALL primes <= 8133 are checked first. Note this is also available within the ABC and ABC2 file formats, and within those formats, expressions can also be used. [/code] :rtfm: 
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