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
A more rigorous statement is as follows.
Suppose we want to consider whether $n$ is prime. Let $W_n(b)$ be the statement that
$1 \leq b < n$,
$b^{n-1} \not \equiv 1 \bmod n$, or
there is some $i$ with $2^i \mid (n-1)$ and $1 < \gcd(b^{(n-1)/2^i} - 1, n) < n.$
If $W_n(b)$, then we say that $...