An absolute Fermat pseudoprime, also known as a Carmichael number, is a composite number which passes the Fermat test for any base a s.t.
(a,N) = 1.
How many values of a are necessary to determine the primality or compositeness of those N in the trial range
which are not absolute Fermat pseudoprimes?
still havent totally got it.
why did the question ask "how many values of a" ?
i tried to make a program like this,
Step 1: filter out those prime N by trial division, then filter those N with least prime factor > 100.
S2: find the GCD of all a from 2 to N-1 and each N.
S3: filter those a, with GCD > 1.
S4: find with the rest of a .
if all of them =1 , then N is a carmichael.
i thought you mean, in S2, we only need to find GCD of all a from 2 to 100?
is that what you meant?