The board / number theory / #472
Erdős Problem #472
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The initial segment \(q_0,\ldots,q_{m-1}\) is a strictly increasing sequence of primes.
The prime \(r\) is an eligible next term after \(q_{\mathrm{prev}}\).
After the initial segment, each term is the least eligible next prime.
Given a finite sequence of primes \(q_1<\cdots<q_m\), extend it by taking \(q_{n+1}\) to be the smallest prime of the form \(q_n+q_i-1\) for \(n\geq m\). Is there an initial sequence for which this process continues forever?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/472.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA389713
Original pageerdosproblems.com/472
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The seed \(3,5\) is exactly certified through \(10{,}000{,}000\) terms with \(q_{10^7}=437{,}662{,}243\) and sharp gap bound \(3270\) on that range; infinitude remains open because the required adapti
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