Possible error in MR test

[Bogdan Opanchuk]

The decomposition function for MR, rewrite() reads:

fn rewrite(candidate: &BigUint) -> (u64, BigUint) {
    let mut d = candidate - 1_u32;
    let mut trials = 0;

    while d.is_odd() {
        d >>= 1;
        trials += 1;
    }

    (trials, d)
}

It seems that it should be while d.is_even() instead (otherwise it always returns trials = 0, and perhaps that's why miller_rabin() sets trials to at least 5), but if I make that change is_prime_tests() fails. The strange thing is that those tests fail because the MR test fails, but the Lucas test still passes - but that may be an effect of #16? I am not sure how those test numbers were obtained, perhaps you can shed some light on it.

[Bogdan Opanchuk]

Another strange moment is the following line in miller_rabin():

for _ in 1..trials - 1 {

trials here is such that candidate = odd_number * 2^trials (or at least it should be in a MR test; miller_rabin() sets it to at least 5, which obscures the bug). But with the limit set this way, test only goes up to odd_number * 2^(trials-1), so one check is skipped. As a result some of the strong pseudoprimes from https://oeis.org/A001262 are classified as primes (the first one being 3277, if force setting of trials to 5 is removed).