{"id":"prime-arrangements-factorial-decomposition","text":"The answer to Prime Arrangements equals `factorial(prime_count) * factorial(non_prime_count) mod 10^9+7`, because primes must occupy prime indices and non-primes must occupy non-prime indices — two independent permutation groups.","truth_value":"IN","source":"entries/2026/06/06/prime-arrangements-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"prime-arrangements-factorial-decomposition","truth_value":"IN","reason":"premise"}]}}