Equivalence · version 1
Earlier version 1. View current version 3 →
RH holds if and only if π(x) = Li(x) + O(√x log x) as x → ∞, where π counts primes and Li denotes the logarithmic integral.
An equivalent formulation of the same canonical question.
Open
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Bombieri · official RH description · §II, p. 4, equation π(x) = Li(x) + O(√x log x) →
Observed Oct 10, 2026
In this problem · publication v3 · Selected context
Equivalent formulation · Open
The equivalence is established; the displayed asymptotic error assertion itself is unproved. The prime number theorem alone gives a weaker error guarantee.
Relationship not independently reviewed. This concerns its use in this problem.
RH is equivalent to the square-root-scale error term for counting primes.
paraphrase · No upstream full text or code is republished by this record.
Enrico Bombieri · Published
Official Clay exposition. Historical results and approaches must not be read as current record bounds.
Source revision: official-description. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Official description PDF: official-description. External source evidence; no OpenMath execution or independent reproduction is attached.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Open
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Observed Oct 10, 2026 · Source passage →