Problem packetResearch packetR1203
Resolve the stated acceptance condition
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Attempt outcome: open strategy
Recorded scope: No scope is recorded.
Originating problem: Consecutive Primes in Arithmetic Progression
Authored record and scope
- Authored title
- Resolve the stated acceptance condition
- Record type
- attempt
- Stored status
- open_strategy
- Evidence grade
- self_reported
Work and source credit
- Recorded action
No action description supplied.
- Authored result summary
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Give a rigorous proof or counterexample that completely resolves this statement: Erdős Problem 141: For every integer \(k \geq 3\), does there exist a set of \(k\) consecutive primes in arithmetic progression? That is, for each \(k \geq 3\), does there exist a set \(s\) of natural numbers such that \(s\) forms an arithmetic progression of length \(k\) and consists of \(k\) consecutive primes?
- Reported outcome
No separate outcome supplied.
- Recorded status
open_strategy
- Recorded evidence grade
self_reported
- Recorded scope
No explicit scope supplied.
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2Authored explanation
Target the displayed statement directly. Give a rigorous proof or counterexample that completely resolves this statement: Erdős Problem 141: For every integer \(k \geq 3\), does there exist a set of \(k\) consecutive primes in arithmetic progression? That is, for each \(k \geq 3\), does there exist a set \(s\) of natural numbers such that \(s\) forms an arithmetic progression of length \(k\) and consists of \(k\) consecutive primes? Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.
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3Outcome
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Verification source: www.erdosproblems.com ↗, Editorial research route recorded 2026-07-31
4How it connects
Addresses
- claim
Recorded for
- problem
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}6Provenance
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