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A good place to look is Granville’s paper “Harald Cramér and the distribution of primes numbers.” It is on Granville’s website here. He brings in Cramér’s work starting on the bottom of page 19. The reason Cramér deserves to have this probabilistic model for the primes named after him is that he went much further than anyone before him in exploring ...


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As Professor K. Conrad mentions, the short answer to this question is NO. Around 1792 Gauß already knew that the "frequency [of the primes] is on the average inversely proportional to the logarithm, so that the number of primes below a given bound $n$ is approximately equal to $\int \frac{1}{\log n} \, dn,$ where the given logarithm is understood to be ...


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