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Understanding Riemann by aa.kzali1 is a document available to read on EtoBox.

Recall from Chapter 10 that a rough guess for an approximation to π(X ), the number of primes ≤ X, is given by the function X/ log(X ). Recall, as well, that a refinement of that guess, offered by Gauss, stems from this curious thought: the “probability” that a number N is a prime is proportional to the reciprocal of its number of digits; more precisely, the probability is 1/ log(N). This would lead us to guess that the approximate value of π(X ) would be the area of the region from 2 to X under

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aa.kzali1

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EN