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Number Theory Open

Riemann Hypothesis

Do all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2? The hypothesis governs the finest distribution of the prime numbers.

Impact
98 /100
Funded
$24,150
Donors
428
Of goal
60%

Why this matters

Primes are the atoms of arithmetic. The Riemann Hypothesis is the single statement that would lock in the sharpest known error terms for counting primes, with deep ties to random matrix theory, quantum chaos, and analytic number theory at large.

What a solution unlocks

  • Optimal prime-counting error bounds
  • Stronger results across L-functions and automorphic forms
  • New bridges between number theory and mathematical physics

Downstream impact

A proof would immediately strengthen dozens of conditional theorems in analytic number theory and clarify the statistical behavior of primes at scales relevant to cryptography and pure mathematics alike.

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