Probabilistic number theory

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Probabilistic number theory

Overview
Probabilistic number theory is a branch of number theory that uses probability to study integers and functions that take integer values. A key idea is that prime numbers can be viewed, in a meaningful way, like independent random variables. This is a powerful heuristic, but it isn’t a strict theorem.

Origins and key results
The field emerged in the 1930s within analytic number theory, led by Paul Erdős, Aurel Wintner, and Mark Kac. Important foundational results include:
- Erdős–Wintner theorem
- Erdős–Kac theorem (about additive functions)
- DDT theorem

See also
- Number theory
- Analytic number theory
- Areas of mathematics
- List of number theory topics
- List of probability topics
- Probabilistic method
- Probable prime

Further reading
- Gérald Tenenbaum (1995), Introduction to Analytic and Probabilistic Number Theory
- J. Kubilius (1964), Probabilistic methods in the theory of numbers

Note
The article is a stub and could be expanded with more details and inline citations.