Pólya's conjecture (1919): at least half the integers up to any bound have an odd number of prime factors.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 3/5
Classic 1919 conjecture on prime factor parity.
Attackability 3/5
Finite integer witness (near 9x10^8) with a computable but nontrivial oracle; famous for surviving massive numerical evidence.
- finite witness
- 5/5
- oracle cost
- 3/5
- freshness
- 1/5
- seedability
- 2/5
Confirmed resolution
counterexample by C. B. Haselgrove (existence), R. S. Lehman (explicit: n = 906,180,359) on .
Disproved nonconstructively in 1958; smallest explicit counterexample found 1960/1980. Verified for decades before failing.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
Confirmed
This entry no longer accepts claims or resolution reports.