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Results tagged with prime-number-theorem
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user 1004
The Prime Number Theorem is a theorem that describes the distribution of the primes. It says that the number of primes less than or equal to a real number $x$ is asymptotic to $\frac{x}{\ln x}$.
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Upper bounds for the sum of primes up to $n$
It is not difficult to calculate upper bounds on $s(n)$ from bounds on the prime counting function $\pi(n)$. Just use integration by parts,
$$
s(n) = \int_0^n x\,d\pi(x) = n\pi(n) - \int_0^n\pi(x)\,dx …
- 17.1k