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Mertens Conjecture
Statement
The Mertens conjecture, now refuted, posited that for all integers n>1, left bracketing bar M(n) right bracketing bar
Solution
False
Formal statement
for all _(n, n element Z ∧ n>1) left bracketing bar sum_(k=1)^nμ(k) right bracketing bar
History
formulation date | 1885 (141 years ago) formulator | Thomas Jan Stieltjes status | refuted proof date | 1985 (100 years later) (41 years ago) provers | Andrew Odlyzko | Herman J.J. te Riele
Associated equation
left bracketing bar sum_(k=1)^nμ(k) right bracketing bar
Current evidence
The value of the smallest counterexample is still unknown but known to exceed 1×10^14.