proposed
reason
Candidate claim vc_f7a87c42fff52207 imported from artifact packet cap_61973ee16b553d57
finding type
open_question
proposed confidence
0.99
confidence basis
agent-imported candidate claim; reviewer acceptance required
frontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewadd a finding
acceptedErdős Problem #1141 has status 'disproved (lean)'. Statement: Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2 < n$? In [Va99] it is asked whether $968$ is the largest integer with this property, but this is an error, since for example $968-9=7\cdot 137$. The list of $n$ satisfying the given property is [A214583] in the OEIS. The largest known such $n$ is $1722$. The answer is negative: [APSSV26b] proves a stronger finiteness theorem, deducing it from Pollack [Po17]. Oriike [Or26] formalised the deduction in Lean. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A214583.
- id
- vpr_4402372c6101ea2c
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-05-30
- findings
- +1
- state
- null → abccd53f
accept gate
1 of 4 on record- —
- signature
- reviewer:erdos-db-trust · no key registered on this bundle
- ✓
- chain
- null → abccd53f
- —
- witness
- no verifier attachment on record for this target
- —
- grade
- in state · unreviewed
timeline
- 2026-05-30proposeproposed · finding.addagent:erdos-spine-ingest
vpr_4402372c6101ea2cCandidate claim vc_f7a87c42fff52207 imported from artifact packet cap_61973ee16b553d57 - 2026-05-30acceptfinding.assertedreviewer:erdos-db-trust
null→abccd53fvev_09a54246fda19749Candidate claim vc_f7a87c42fff52207 imported from artifact packet cap_61973ee16b553d57
provenance
proposed by
agent:erdos-spine-ingest
actor type
agent
created at
2026-05-30
target type
finding
affected
inspect finding →Erdős Problem #1141 has status 'disproved (lean)'. Statement: Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2 < n$? In [Va99] it is asked whether $968$ is the largest integer with this property, but this is an error, since for example $968-9=7\cdot 137$. The list of $n$ satisfying the given property is [A214583] in the OEIS. The largest known such $n$ is $1722$. The answer is negative: [APSSV26b] proves a stronger finiteness theorem, deducing it from Pollack [Po17]. Oriike [Or26] formalised the deduction in Lean. Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A214583.
vf_7d8cb8ee64887166Diff
Read-only frontier; diff not recomputed.
Review chain
- 01requestopen review →
Change request
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
- 02packetopen the campaign →
Diff packet
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
- 03checksinspect checks →
Check output
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
- 04reviewread queue →
Reviewer decision
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
- 05acceptedinspect events →
Accepted event
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.