{"taskid":"08cac496dfa93874dd7d16893038da16b0d2dbc92f844d09512ca0cc78c03b46i0","node":"t47","claimid":"ba2824f9efaf3f80817204d335173dfbd11a32907ab78e1e263da0abc0270f59i0","result":{"type":"triage","conjecture":47,"judgment":{"well_defined":true,"well_defined_reason":"判定对象明确：对每个充分大的偶数 n（∃N∀偶n≥N），存在 [n]={1,...,n} 的置换 π 使所有 i 的 π(i)+i 均为素数——量词结构明确，π 与素数谓词均有标准数学定义，无歧义。","finitely_refutable":false,"finitely_refutable_reason":"本命题为 ∃N∀n≥N 的渐近存在形式：单个乃至有限多个偶数 n 的无解结果不能证伪——失败实例可能全部低于阈值 N，证伪需证明失败 n 无界（无穷多）。故不可有限证伪。bounded 表 n∈[4,64] 全部 exists:true，为支持性数据，既不构成证伪也不构成证明。","known_conflict":"none","difficulty":3,"importance":3},"route":"bounded-search","bounded":{"params":{"n_range":[4,64],"parity_note":"π(i)+i 为素数需 i 与 π(i) 奇偶相反（和为偶数只能为 2，即 i=π(i)=1），故 π 须为奇偶反转双射；偶数 n 时偶数位×奇数值、奇数位×偶数值各构成 n/2 对 n/2 的二部图完美匹配。"},"table":[{"n":4,"exists":true,"pi":[4,3,2,1]},{"n":6,"exists":true,"pi":[6,5,4,3,2,1]},{"n":8,"exists":true,"pi":[6,5,2,1,8,7,4,3]},{"n":10,"exists":true,"pi":[10,9,4,3,8,7,6,5,2,1]},{"n":12,"exists":true,"pi":[12,11,8,7,6,5,10,9,4,3,2,1]},{"n":14,"exists":true,"pi":[12,11,14,13,8,7,10,9,2,1,6,5,4,3]},{"n":16,"exists":true,"pi":[16,15,14,13,12,11,10,9,4,3,8,7,6,5,2,1]},{"n":18,"exists":true,"pi":[18,17,16,15,14,13,12,11,8,7,6,5,10,9,4,3,2,1]},{"n":20,"exists":true,"pi":[18,17,20,19,14,13,12,11,10,9,8,7,16,15,2,1,6,5,4,3]},{"n":22,"exists":true,"pi":[18,17,20,19,14,13,22,21,8,7,6,5,16,15,4,3,12,11,10,9,2,1]},{"n":24,"exists":true,"pi":[22,21,16,15,12,11,24,23,4,3,2,1,18,17,14,13,20,19,10,9,8,7,6,5]},{"n":26,"exists":true,"pi":[22,21,20,19,14,13,24,23,2,1,6,5,18,17,16,15,26,25,12,11,10,9,8,7,4,3]},{"n":28,"exists":true,"pi":[18,17,26,25,12,11,24,23,4,3,8,7,28,27,22,21,20,19,10,9,16,15,14,13,6,5,2,1]},{"n":30,"exists":true,"pi":[10,9,26,25,14,13,30,29,8,7,6,5,28,27,16,15,24,23,22,21,20,19,18,17,12,11,4,3,2,1]},{"n":32,"exists":true,"pi":[12,11,26,25,18,17,30,29,4,3,2,1,28,27,14,13,24,23,22,21,32,31,20,19,16,15,10,9,8,7,6,5]},{"n":34,"exists":true,"pi":[16,15,28,27,24,23,34,33,2,1,6,5,30,29,8,7,26,25,22,21,32,31,20,19,18,17,14,13,12,11,10,9,4,3]},{"n":36,"exists":true,"pi":[22,21,20,19,26,25,34,33,4,3,12,11,28,27,14,13,36,35,24,23,32,31,30,29,16,15,10,9,18,17,6,5,8,7,2,1]},{"n":38,"exists":true,"pi":[28,27,16,15,32,31,34,33,2,1,18,17,30,29,8,7,26,25,22,21,38,37,36,35,12,11,14,13,24,23,10,9,20,19,6,5,4,3]},{"n":40,"exists":true,"pi":[22,21,20,19,32,31,36,35,4,3,30,29,28,27,14,13,24,23,34,33,40,39,38,37,16,15,10,9,18,17,12,11,26,25,8,7,6,5,2,1]},{"n":42,"exists":true,"pi":[18,17,26,25,42,41,34,33,8,7,32,31,30,29,16,15,20,19,40,39,38,37,36,35,12,11,14,13,24,23,22,21,28,27,6,5,10,9,4,3,2,1]},{"n":44,"exists":true,"pi":[22,21,34,33,32,31,24,23,10,9,36,35,40,39,14,13,12,11,42,41,38,37,44,43,18,17,20,19,30,29,28,27,26,25,8,7,16,15,2,1,6,5,4,3]},{"n":46,"exists":true,"pi":[18,17,20,19,32,31,34,33,8,7,36,35,40,39,16,15,14,13,42,41,46,45,44,43,28,27,26,25,24,23,30,29,38,37,6,5,22,21,4,3,12,11,10,9,2,1]},{"n":48,"exists":true,"pi":[10,9,26,25,42,41,36,35,4,3,32,31,48,47,22,21,12,11,40,39,46,45,20,19,34,33,44,43,30,29,28,27,38,37,2,1,24,23,14,13,18,17,16,15,8,7,6,5]},{"n":50,"exists":true,"pi":[18,17,28,27,38,37,36,35,2,1,42,41,46,45,26,25,14,13,48,47,50,49,24,23,34,33,44,43,32,31,30,29,40,39,6,5,22,21,8,7,20,19,10,9,16,15,12,11,4,3]},{"n":52,"exists":true,"pi":[22,21,26,25,42,41,40,39,4,3,48,47,46,45,32,31,6,5,52,51,50,49,30,29,36,35,44,43,38,37,28,27,34,33,12,11,24,23,14,13,18,17,16,15,8,7,20,19,10,9,2,1]},{"n":54,"exists":true,"pi":[30,29,38,37,48,47,34,33,10,9,50,49,54,53,44,43,2,1,52,51,46,45,36,35,42,41,40,39,32,31,22,21,26,25,18,17,16,15,4,3,20,19,28,27,14,13,24,23,12,11,8,7,6,5]},{"n":56,"exists":true,"pi":[36,35,34,33,56,55,40,39,14,13,48,47,54,53,44,43,6,5,52,51,50,49,38,37,46,45,32,31,42,41,12,11,28,27,24,23,22,21,2,1,26,25,30,29,16,15,20,19,18,17,10,9,8,7,4,3]},{"n":58,"exists":true,"pi":[40,39,38,37,56,55,46,45,20,19,50,49,54,53,52,51,12,11,48,47,58,57,36,35,42,41,44,43,32,31,10,9,34,33,18,17,16,15,4,3,30,29,28,27,26,25,24,23,22,21,8,7,14,13,6,5,2,1]},{"n":60,"exists":true,"pi":[42,41,40,39,48,47,52,51,22,21,60,59,58,57,32,31,14,13,54,53,50,49,38,37,46,45,56,55,44,43,6,5,28,27,24,23,34,33,8,7,26,25,36,35,16,15,20,19,30,29,10,9,18,17,12,11,4,3,2,1]},{"n":62,"exists":true,"pi":[40,39,50,49,56,55,54,53,20,19,60,59,58,57,46,45,12,11,48,47,52,51,44,43,42,41,62,61,32,31,10,9,38,37,18,17,36,35,4,3,30,29,28,27,22,21,24,23,34,33,2,1,26,25,16,15,14,13,8,7,6,5]},{"n":64,"exists":true,"pi":[36,35,56,55,54,53,64,63,28,27,60,59,58,57,44,43,6,5,52,51,50,49,48,47,46,45,62,61,38,37,16,15,34,33,24,23,42,41,2,1,32,31,30,29,26,25,14,13,40,39,8,7,20,19,18,17,22,21,12,11,10,9,4,3]}],"repro":"import json\n\ndef is_prime(x):\n    if x < 2: return False\n    if x < 4: return True\n    if x % 2 == 0: return False\n    d = 3\n    while d * d <= x:\n        if x % d == 0: return False\n        d += 2\n    return True\n\ndef kuhn_match(cands):\n    owner = {}\n    assign = {}\n    def aug(i, seen):\n        for v in cands[i]:\n            if v in seen: continue\n            seen.add(v)\n            if v not in owner or aug(owner[v], seen):\n                owner[v] = i\n                assign[i] = v\n                return True\n        return False\n    for i in sorted(cands):\n        if not aug(i, set()):\n            return None\n    return assign\n\ndef solve(n):\n    cands = {}\n    for i in range(1, n + 1):\n        if i % 2 == 0:\n            vals = range(1, n + 1, 2)\n        else:\n            vals = range(2, n + 1, 2)\n        c = [v for v in vals if is_prime(i + v)]\n        if not c:\n            return None\n        cands[i] = c\n    return kuhn_match(cands)\n\ntable = []\nfor n in range(4, 65, 2):\n    a = solve(n)\n    if a is None:\n        table.append({\"n\": n, \"exists\": False, \"pi\": []})\n    else:\n        table.append({\"n\": n, \"exists\": True, \"pi\": [a[i] for i in range(1, n + 1)]})\nprint(json.dumps(table, ensure_ascii=False, separators=(\",\", \":\")))\n"},"hash":"96776de3aea7ee2fd529d266d3c84abaa1940714d1a913af06de03aef34791f7"},"hash":"3d4a8b8c6a91982ed1e5e31b7ca07b0f9ea74b58dccb0c49f29e8304664d63f7","childids":null}