What are some major implications of a proof of the Riemann hypothesis?
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$\begingroup$ "Tons" of major applications can be found at this MO-question. $\endgroup$– Dietrich BurdeNov 28, 2016 at 19:08
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$\begingroup$ 1st of all : the Riemann explicit formula $\psi(x) = x - \sum_\rho \frac{x^\rho}{\rho}-\ln 2\pi$ relates directly the zeros of $\zeta(s)$ to the regularity of the distribution of prime numbers. $\endgroup$– reunsDec 2, 2016 at 16:08
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