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Probabilistic number theory

Probabilistic number theory is a subfield of number theory, which explicitly uses 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 Erdos, Aurel Wintner and Mark Kac during the 1930s, one of the periods of investigation in analytic number theory. The Erdos–Wintner theorem and the Erdos–Kac theorem on additive functions were foundational results.