The Mertens conjecture (1897): |M(x)| < sqrt(x) for the Mertens function.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 3/5
Well-known 1897 conjecture implying the Riemann Hypothesis if true.
Attackability 1/5
Disproved nonconstructively via lattice reduction; no explicit witness is known even today.
- finite witness
- 1/5
- oracle cost
- 1/5
- freshness
- 1/5
- seedability
- 1/5
Confirmed resolution
counterexample by A. M. Odlyzko and H. J. J. te Riele on .
Disproved via lattice reduction on zeta zeros -- nonconstructively; no explicit counterexample is known even today, though one exists below 10^(6.9x10^39).
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.