The "chinese remainder" prime-test  :
$\qquad \small \text{ if } 2^n-1 \equiv 1 \pmod n \qquad \text{ then } n \in \mathbb P $
fails first time at n=341 . That was one of the things that really made me thinking when I began hobbying with number-theory in a more serious way...

The "Chinese remainder" prime-test:

$$ \text{if } 2^n - 1 \equiv 1 \mod n \text{ then } n \in \mathbb{P} $$

fails first time at $n=341$. That was one of the things that really made me thinking when I began hobbying with number-theory in a more serious way...