Riesel Problem — open problem in number theory

Riesel Problem

It is conjectured that the integer k = 509203 is the smallest Riesel number, that is, the first n such that a(n) = -1 is 254602.

From the catalogue. Imported from The Formal Conjectures Authors (Google DeepMind and contributors) (Apache-2.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim. A Lean proof is checked against the statement below by the Lean kernel; a curator confirms before the problem counts as resolved.

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Cite

@misc{cairn-oeis-108129,
  title        = {Riesel Problem},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/oeis-108129}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-29}
}

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Claims

Verified

Disputed

Refuted

On the literature board

The problem

The question

It is conjectured that the integer $k = 509203$ is the smallest Riesel number, that is, the first $n$ such that $a (n) = - 1$ is $254602$ .

Riesel problem: let $k = 2 n - 1$ ; then $a (n)$ is the smallest $m \geq 1$ such that $k \cdot 2^{m} - 1$ is prime, or $- 1$ if no such prime exists.

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.OEIS.«108129».

theorem conjecture :
    a 254602 = -1 ∧ (∀ n : ℕ, 1 ≤ n ∧ n < 254602 → a n ≠ -1)

What counts as progress

A Lean proof of the pinned statement (or of its negation, for a yes/no question) — checked by the Lean kernel against the upstream statement; a curator confirms before the problem is marked resolved.
Partial results: special cases, weaker bounds, reductions — as verified claims.
Computations and numerical evidence with published code (reproducible).
Literature: the problem may have been solved or partly solved already. Report it as a literature claim.
A precise flaw in the formal statement (a misformalisation) — report it upstream too.

References

A108129

Source and licence

Imported from Formal Conjectures (OEIS), commit e6d1743831c2. Statements and descriptions © The Formal Conjectures Authors, Apache License 2.0; reformatted for this page.