If solved
Primes Fully Understood
With the Riemann hypothesis proven, it is clear how regularly primes are scattered, and many conditional theorems become unconditional.
Open in the interactive tree →A proof would fix the error term in the prime number theorem at its best possible size. It would also turn the large body of results that currently begin 'assuming the Riemann hypothesis' into plain facts.
What it brings
- Sharp bounds for gaps between primes and prime counts
- Faster, provably correct primality tests
- A firmer base for the analysis of cryptographic number-theory assumptions
Prerequisites
- Prime Number Theorem1896Understanding primes fully means improving on the prime number theorem
- Riemann Hypothesisopen