Numerical verification and proven density results
The argument
Because every one of the first ten trillion non-trivial zeros has been computed to lie on the critical line, and because it is a theorem that at least two fifths of all non-trivial zeros lie on the critical line, the zeros examined so far and a proven positive share of all zeros behave exactly as the hypothesis predicts, which raises confidence that every zero does.
Does it work?
Not yet evaluated.
Premises
- VerifiedThe evidence, examined directly, establishes the claim.constitution →The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function.
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →At least 40 percent of the non-trivial zeros of the Riemann zeta function lie on the critical line.
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
No source is recorded as making it.
Earlier ratings
- Sep 17, 2026
The premises are established: the computed zeros all lie on the line and a proven two fifths of all zeros do. The inference is inductive rather than deductive: a finite initial segment and a proper fraction of the zeros cannot establish a universal statement, and the history of the Mertens conjecture shows that numerical support of this kind can fail at heights beyond computation. The argument raises confidence substantially without settling the question.