The Mertens conjecture, now refuted, posited that for all integers n>1, left bracketing bar M(n) right bracketing bar

False

for all _(n, n element Z ∧ n>1) left bracketing bar sum_(k=1)^nμ(k) right bracketing bar

formulation date | 1885 (140 years ago) formulator | Thomas Jan Stieltjes status | refuted proof date | 1985 (100 years later) (40 years ago) provers | Andrew Odlyzko | Herman J.J. te Riele

left bracketing bar sum_(k=1)^nμ(k) right bracketing bar

The value of the smallest counterexample is still unknown but known to exceed 1×10^14.

refuted conjectures | solved mathematics problems