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Equivalent Form of the Riemann Hypothesis

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The famous Riemann hypothesis is equivalent to the following not-so-famous conjecture:

              For every N ≥ 100, | log( lcm(1, 2, …, N) ) – N | ≤ 2 log(N) √N.

Here “lcm” stands for “least common multiple” and “log” means natural log.

Source: Andrew Granville’s chapter on analytic number theory in Princeton Companion to Mathematics.


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