Abstract
If x > 0 let π(x) denote the number of primes not exceeding x. Then π(x) → ∞ as x → ∞ since there are infinitely many primes. The behavior of π(x)as a function of x has been the object of intense study by many celebrated mathematicians ever since the ighteenth century. Inspection of tables of primes led Gauss (1792) and Legendre (1798) to conjecture that π(x) is asymptotic to x/log x, that is
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© 1976 Springer Science+Business Media New York
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Apostol, T.M. (1976). Some Elementary Theorems on the Distribution of Prime Numbers. In: Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5579-4_5
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DOI: https://doi.org/10.1007/978-1-4757-5579-4_5
Publisher Name: Springer, New York, NY
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