OP-5741Status unassessedNumber theory

Irrationality of the Riemann zeta value at 5

TheoremDB P8362 · Candidate awaiting source review

Inferred from the community field; finer classification has not been reviewed.

Source candidate · not reviewedAs of 2026-09-08Source & evidence ↓

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Problem statement

The Riemann zeta function is defined for a complex number $s$ with real part greater than $1$ by

\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}.

A real number is said to be irrational if it cannot be expressed as a ratio of two integers. Prove that $\zeta(5)$ is irrational. Equivalently, prove that there exists an irrational number $x$ such that $\zeta(5) = x$ .

Lean 4

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Formal statement

Lean 4

theorem irrational_five : ∃ x, Irrational x ∧ riemannZeta 5 = x

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

This record is in the source backlog; its novelty and unresolved status have not passed source review.

References

[1]TheoremDB P8362 link
[2]Source formal statement (not locally verified) link

Recorded progress

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Machine attempts

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Discussion

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