Saturday, December 01, 2018

[ambdtzgq] Precisely estimating the number of prime powers

How many numbers below a given upper bound are primes or prime powers? It's asymptotically the same as the number of primes, but can we be more precise?

This question might be slightly easier than coming up with approximations to the normal prime counting function which only counts first powers.  Possibly relevant: Chebyshev psi function, von Mangoldt function.

Inspired by Reed-Solomon codes and finite fields in general, which need an alphabet whose size is a prime or power of a prime.

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