Erdős #398 (Brocard), finite confirmation

Canonical assertion

for all 1 ≤ n ≤ 2000, n!+1 is a perfect square exactly for n ∈ {4,5,7}; every other n carries a quadratic-non-residue certificate. The conjecture over all n remains open.

Notation is rendered from the stored source. The pinned checkout remains the exact record.

Sourcemodel_output
Assertioncomputational
Evidence0 spans
Standingretracted

Scope and conditions

computational

Record vrc_b618c7104270ab85 (signed; recorded against the current head). Caveats: Finite confirmation over 1..2000; the general Brocard conjecture is open.. Artifacts: 1 hash-verified at propose.

Provenance summary

Source: record:vrc_b618c7104270ab85
Source type: model_output
Recorded: Jul 5, 2026, 10:55 PM
Updated: not recorded
Evidence spans: 0

Exact record identityFinding ID, frontier identity, and pinned Git source

Finding ID: vf_f1f82e1bb82742b2
Frontier: vfr_0a25edabc16db143
Commit: ce8ba7d934c848408e0d91caca39e938698e3fc7
Tree: 03f7371b496485f761f91961027fd48198dc7e93

Exact source and rootsGit ce8ba7d934c8 and content-addressed ledgers

Source identity

Commit: ce8ba7d934c848408e0d91caca39e938698e3fc7
Tree: 03f7371b496485f761f91961027fd48198dc7e93
Committed: 2026-07-20T19:20:20-04:00
Repository: Open source

Content roots

Event log: sha256:a06797bc0d1b0e3c88a2f97507fe0832661e3992d8df41187a0aa6d3ceee9bde
Snapshot: sha256:1faedc24f040a60a22177b456c74b969a61ce8836082297b1835797a57b4fa56
Proposals: sha256:e69b38037814f2e8ca826942cfc50ab370993889be2913cac1c0b3e77711160f
Actor registry: sha256:665f3e1c48f0a50fac949681c0af01bdd28de2991f2cdc5cc4cddbe69df6311b
Artifacts: sha256:3d58619c5cfb7e28de2f344476e35c9f0b80709c996b2a1bfdb2e11496f7e1da