{"taskid":"59f8deca115aa901df74db204be5a398ecf47e17878fe23cbcb07e4df3ae59e0i0","node":"find364","result":{"type":"negative","from":1,"to":2000000000000000,"script":"search_ep364.py","log":"run.log","runtime_env":"python3 stdlib only (CPython >= 3.8, math.isqrt); no third-party packages, no randomness","method":"Complete enumeration, no structural assumptions. Every powerful number has a unique canonical form n = a^2*b^3 with b squarefree, so enumerating all such (b, a) pairs in a 10^12-wide chunk lists each powerful number exactly once. Chunks are sorted and scanned for adjacent runs; the last two elements of each chunk are carried over so consecutive pairs, distance-2 pairs and triples straddling chunk boundaries are detected. Cross-validated against a from-scratch trial-division brute force on [1, 200000] and against every published OEIS anchor below the bound (A060355 x 26, A076445 x 8; see crosscheck.log). Replay: unzip, then run 'python3 search_ep364.py --from <A> --to <B>', or 'python3 spec-ep364.py .' for the campaign verifier.","scan_summary":{"chunk_size":1000000000000,"chunks":2000,"powerfuls":97003419,"pairs_count":26,"distance2_count":8,"triples_found":0,"powerful_sum":"64700194590340627952451","powerful_xor":"0x639564a8db10f"},"anchors":{"sources":["OEIS A060355 (k such that k and k+1 are powerful), b-file","OEIS A076445 (smaller of a powerful pair differing by 2), b-file","Erdos Problem #364 page (T. F. Bloom), erdosproblems.com/364"],"pairs_expected_below_bound":26,"pairs_reproduced":26,"distance2_expected_below_bound":8,"distance2_reproduced":8,"check_script":"crosscheck_ep364.py"},"files":["search_ep364.py","run.log","README.md","spec-ep364.py","crosscheck_ep364.py","crosscheck.log","rehearsal.txt","sha256sums.txt"],"disclosure":"Honest scope: no exceedance claimed over published boundaries (unverified exhaustive to 10^22; conditional ~7.38*10^28 per erdosproblems.com/364 via OEIS A076445; kernel-certified below 10^14 per arXiv:2609.25011). This record covers [1, 2*10^15): a self-contained, replayable-from-chain exclusion whose pair/distance-2 lists match the published OEIS entries exactly. Result: no triples of consecutive powerful numbers in [1, 2*10^15).","hash":"d7998c66e3e20aafd4bc97270b475e715fd1f3383acd7b52b01661167f4fdcd1"},"hash":"814306f11a670dfb9c9ed93a7d549676e7a60b7186de74e66230e69be9036d5b","contentType":"application/json;utf-8","attachment":"metafile://80d5301f73f9ccc4ab34986a52ba5a62dda44fb0f91507e7fefb3e7b1b0c8db0i0","childids":[]}