The board / number theory / #695
Erdős Problem #695
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(q_1 < q_2 < \cdots\) be a sequence of primes such that \(q_{i + 1} \equiv 1 \pmod{q_i}\). Is it true that \[ \lim_{k \to \infty} q_k^{1/k} = \infty? \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/695.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA061092
Original pageerdosproblems.com/695
Attempts
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Exact multiplier-cost reduction and independently verified sharp terminal-prime bounds for every prime-chain length 1 through 14; the uniform exceptional-path lemma needed for either asymptotic questi
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