Probabilistic number theory

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (August 2017) (Learn how and when to remove this message)

In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions. 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 periods of investigation in analytic number theory. Foundational results include the Erdős–Wintner theorem and the Erdős–Kac theorem on additive functions.