Hello,

I tried looking at classes of numbers that I believe would
be pseudo-prime free when tested against the base that makes
up each different class of numbers.

Let R = k *b^n +(b-1); the multiplier 'k' is an odd natural
number; the base 'b' is a small enough prime number; and the
exponent 'n' is also prime, but much larger of course.

The first such instance/class would be a Proth number.

My conjecture:
iff b^(R-1) ==1 (mod R), then 'R' is prime, without encoun-
tering the pseudo-prime effect when tested against the same
base 'b' that makes up the number; I believe this to be true
based simply on the construction of the number.

When I found PRP candidates using PFGW, I called the Brillhart-
Lehmer-Selfridge primality test, and it chose the same base
and only said that the number was again... PRP and didn't say
... Done.(if composite) or ... is prime!(in so many seconds).

Could the PFGW program be flawed in this respect ???

Bill