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I was investigating primes with the property that the sum of the first $n$ primes is divisible by $p_n$. It turns out that these primes are extremely extremely rare. For primes less than $10^9$, I ...

The prime number theorem says on average we can find $\frac n{\log n}$ primes of magnitude $n$. Erdos-Kac law state a typical number of magnitude $n$ has $\log\log n$ primes. Somehow the fact $e^{\...