He ain't no Ramanujan

Your friend has written a program to check whether or not a number \(n\) is prime. It is very simple and works by checking if \(n\) is divisible by each number from 2 all the way to \(n-1\). When you see this, you curse your friend and tell him he's wasting time.

If your friend didn't want to waste time, what is (approximately) the biggest number that he needs to check before he can determine that any number \(n\) is prime?

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