🔗 Pólya conjecture

🔗 Mathematics

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. The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove.

The size of the smallest counterexample is often used to show how a conjecture can be true for many cases, and still be false, providing an illustration for the strong law of small numbers.