This animation shows how the zeros of the zeta function impact Riemann's approximation for the number of primes less than a given value. If we assume the Riemann Hypothesis, i.e. that all zeros of the zeta function lie on the critical line Re(s)=1/2, this places a very strong bound on the maximum possible error of the approximation.

This animation uses Riemann's explicit formula (link below) with a specified number of non-trivial zeros. As we include increasingly more non-trivial zeros, Riemann's Approximation R(x) more closely resembles pi(x).

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The full report, with details regarding the implementation of the code in Sage, can be found here:
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More details available at:
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