{"schema":"https://assignee.net/schemas/math-result-v1","schema_version":"1.0","contract_version":"math-result-v1.0","schema_documentation":"https://assignee.net/schemas","changelog_url":"https://assignee.net/changelog","publisher":{"name":"Assignee Research","url":"https://assignee.net"},"result":{"id":"d177586b3b3d4762a3ca874038addcb6","problem_id":"d571909f-3a0e-4875-b12f-1a529fb1546d","problem_name":"Primes of form n^2+1 — density and distribution","domain":"Number Theory","statement":"Let P_N be the set of primes of the form n^2+1 for 1 <= n <= N. Let A_N be the count of such primes where the generator n is itself a prime number. The conjecture states that for all N >= 1000, the ratio of the density of 'prime-generated' primes to the total density of such primes exceeds the reciprocal of the natural logarithm of N. Specifically: A_N / |P_N| > 1 / ln(N). This suggests that prime generators are slightly over-represented among the solutions to n^2+1 being prime compared to the b","status":"falsified","url":"https://assignee.net/math#result-d177586b3b3d4762a3ca874038addcb6","doi":"10.5281/zenodo.20540615"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":3.32,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/d177586b3b3d4762a3ca874038addcb6/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/d177586b3b3d4762a3ca874038addcb6/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20540615","format":"text/html"}],"interpretation":"Computational evidence is not a formal proof. Formal verification is claimed only when public Lean4 source is attached.","limitations":["Python check code, local file paths, and private execution logs are not exposed in public manifests.","Computational evidence reports bounded search only and can be invalidated by later counterexamples.","Formal proof verification requires public Lean4 source; otherwise the record remains a proof attempt or report."]}