Riemann Hypothesis
All non-trivial zeros of the Riemann zeta function have real part 1/2. If true, it pins down how regularly the prime numbers are distributed.
This problem has no runnable starter yet. Use the suggested experiments below as a starting point in the editor. Open the editor
Suggested experiments
-
Primes against x / log x
Count primes up to x with a sieve and compare π(x) with x / log x for growing x. See the prime number theorem in action.
Establishes: The values of π(x) for the x you computed.
Does not establish: Anything about the zeros of ζ(s) or about all x.
-
Locate zeros on the critical line
Evaluate the Riemann–Siegel Z function along the critical line and look for sign changes, which mark zeros. Compare with Odlyzko's published tables.
Establishes: Approximate zeros in the range you scanned, within floating-point accuracy.
Does not establish: That no zero lies off the line, even in that range, without rigorous error bounds.