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Not just believed, pi(n) ~ n / log(n) is the prime number theorem.

I wasn't sure if the proof depended on the Riemann hypothesis or not.

So, I wasn't sure if it had been proven, or just proven given that assumption. So that's why I said that it was believed.

Riemann hypothesis gives better error estimates for the asymptotics in the prime number theorem.

Ah, alright, thanks!