I've heard two conflicting stories on whether or not the Zeta function 100% accurately predicts where primes are.
So does It? Also, is there an error correction formula that makes it 100% accurate if it is not already?
2026-04-07 01:36:45.1775525805
Riemann Zeta function error %?
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The Riemann Zeta function is a huge topic in maths, but my understanding is that Schoenfeld (1976) showed that $\zeta$ can put a bound on the error of the prime number theorem with $$| \pi (x) - \text{Li}(x) | < \frac{1}{8\pi} \sqrt{x} \log(x)$$ Where $x \geq 2657$ and with $\pi(x)$ being the prime counting function.