Probabilistic number theory

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Probabilistic number theory is a subfield of number theory, which uses explicitly probability to answer questions of number theory. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables. This however is not an idea that has a unique useful formal expression.

The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the most intense periods of investigation in analytic number theory. The Erdős-Wintner theorem on additive functions was a foundational result.