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**SCRandom** The congruence $\displaystyle 2^{52532} \equiv 1 \bmod{52633}$ is true. Can you conclude that $\displaystyle 52633$ is a prime number?

Of course not: why would anyone conclude such a thing?? Of course, it's pretty easy to check directly that $\displaystyle 7\mid 52633$ , but even without this

we couldn't conclude that: for example, $\displaystyle 2^4=\!\!\!\pmod{15}$...can we conclude 15 is prime? $\displaystyle 2^6=1\!\!\!\pmod 9$...is 9 a prime?

About what you wrote below: " ...is in the format of FLT..." do you mean Fermat's Little Theorem? What is in this format??

Tonio

So would the answer be that since $\displaystyle 2^{52532} \equiv 1 \bmod{52633}$ is in the format for FLT then $\displaystyle 52633$ must be prime right?