The Pólya conjecture is a conjecture made by George Pólya in 1919.

Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. Pólya conjecture).

(See for example the Pólya conjecture, the Mertens conjecture and the Skewes' number.)

As shown in the cases of the Pólya conjecture, the Mertens conjecture and the Skewes' number, sometimes a conjecture's only counterexamples are found when using very large numbers.

In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors.