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I do not think that 1 tells anything if p is a prime. I am not sure what it is really referring to. I think it is referring to 2
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mistrjirka authored Jun 8, 2024
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Expand Up @@ -16,7 +16,7 @@ $$
a^{p-1} \equiv 1\ (\texttt{mod }p).
$$

If $(1)$ holds for all numbers $a$, it is highly probable that $p$ is prime.
If $(2)$ holds for all numbers $a$, it is highly probable that $p$ is prime.
This probabilistic primality test is known as the *Fermat Primality Test*. Note, the
*Carmichael numbers*, which are composite yet pass the test for all $a$ relatively prime to the
respective number, are avoided when testing your implementation of this task.
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