A little program in rust to brute-force disprove the Pólya conjecture
cargo test # runs tests
cargo run 450 # tests all numbers up through 450
You can disprove the conjecture by running
cargo run 1000000000 # one billion
On a 2021 M1 Macbook Pro, it took me 2h9m3s to output 906,150,257; the smallest number that disproves the conjecture.