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The primes become more sparse in the integers as you go farther. For most reasonable definitions of the density of composite integers in the integers, the density would be 100%.

Iirc, it is believed that the number of primes less than n is O(n/log(n)), so primes/integers among the first n integers should go as O(1/log(n)), so goes to 0 as n goes to infinity.




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!




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