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Prime Number Theorem


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For a positive real number x, let π(x) be the number of primes less than or equal to x. The Prime Number Theorem says that, as x,In other words, for large values of x, π(x) is approximately equal to x/ln x. This gives, in a sense, an idea of what proportion of integers are prime. Proved first in 1896 by Jacques * Hadamard and Charles De La * Vallée-Poussin independently, all proofs are either extremely complicated or based on advanced mathematical ideas.

Subjects: Mathematics.


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