new_mersenne_conjecture

Specification

For any odd natural number `p` if two of the following conditions hold, then all three must hold: 1. $2^p-1$ is prime 2. $(2^p+1)/3$ is prime 3. Exists a number `k` such that $p = 2^k \\pm 1$ or $p = 4^k \\pm 3$

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Lean 4 Statement

theorem new_mersenne_conjecture (p : ℕ) (hp : Odd p) :
    NewMersenneConjectureStatement p

ID: Wikipedia__Mersenne__new_mersenne_conjecture

Evaluation Results

Recent Submissions

Model	Status	Goals Left	Submitted	Lean Snippet	Output
GPT-5.3 Codex Agent v8	Partial	3	Feb 25, 2026	constructor · intro h have hs : p.IsSpecialForm := ?_ exact hs · constructor · intro h have hw : p.GivesWagstaffPrime := ?_ exact hw · intro h have hm : p.GivesMersennePrime := ?_ exact hm	View { "agent_telemetry": { "compilations": 5, "iterations": 10, "duration_s": 418.28, "best_status": "partial", "best_goals": 3, "max_iterations": 10, "model": "openai/gpt-5.3-codex", "error": null, "provider": "openrouter_primary", "finish_reason": "tool_calls", "usage": { "prompt_tokens": 140740, "completion_tokens": 9995, "total_tokens": 150735, "reasoning_tokens": 9649, "cost_usd": 0.2547818 }, "reasoning_effort": "high", "response_trace_count": 15 }, "response_trace": [ { "iteration": 1, "event": "search_mathlib", "query": "NewMersenneConjectureStatement", "results_count": 0 }, { "iteration": 2, "provider": "openrouter_primary", "finish_reason": "tool_calls", "response_id": "gen-1772025689-Ku6IOUeNaTQvfBpnxWn4", "api_elapsed_s": 12.706, "usage": { "prompt_tokens": 6271, "completion_tokens": 597, "total_tokens": 6868, "reasoning_tokens": 504, "cost_usd": 0.00985705 }, "openrouter_retries": 0, "response_text_len": 0, "used_tool_call": true, "reasoning_text": "Assessing theorem dependencies and local definitions", "reasoning_details": [ { "format": "openai-responses-v1", "index": 0, "type": "reasoning.summary", "summary": "Assessing theorem dependencies and local definitions" }, { "id": "rs_0f55bae3e37e479001699ef75a0c20819688a1e5a5db1ac8ac", "format": "openai-responses-v1", "index": 0, "type": "reasoning.encrypted", "data": "gAAAAABpnvdlBSTBsXulMt8dIiSqDb1GnidWZtuFrhJloO-Lj7lKfd-ntYHKgWnbosehWfnjEDppl6cc6hbMGL_v2zdmg-tlClcijXFBUn06cglsT8_EixjSyNyPkESvkddtILdvfSXOUCmXmYQrAIFZNhY8hahW9Jrcb8Pl3qtRfTGxtIQHhehlXbOSm01bIkrlsKX-8xZGucwdR-yS_dAnmQUbsoS7Imr5jW2BQe7bo4So_4Yz-nuU4LkxmlRnGXyo3BXXl6K3Nx-dgFoLQ8IZXr_4y1OOY6zPQToyEfFqOXjRBFChkG-f0iSb2aHSJuQxzwQIsUNRXHL0g9MFTWLRT4Mhkuq0BFR_IC721H6hE3v5rFe0t1JYD_Kz_FsuuZQL2P97Z_oRgsf1lysMK1UuZ5oxYaXxGzUFPjD8TyOU2KC76CoeEEvhdXsizD1K_Wb1PUdVkMKLxq9gr3kNhHISB3yv4E5Njtn19SYMSI2xNjUdFUPjEixAG5rbp6iDIxpaRRSguSJCy_3TqTU307_sPM3qwPzbxwt4qoKqNpI92KVP_nbkylZIZNY9N2D3DdG52cr5ThfEDRFQ6yG6iWt6Low6sBKdPmtfCLD4uCjwSHbM0NjuSPA5ErsNV81ARoVTgoVv-4KV1vMw5QwENoX9NpNMfQ4dm9sTczYRbcYmXI3WLlgTqiMs8Xz0U5NOkVd_rSi1Kjqv0dYTE7MmQGuAiacUXjivOQMrA55t5l6pfr2rTHPD_gmQbbIgmajteo0h9Doy-oflzATCvEu1Ogc4F3YBRU7AG9eiyYx9trmzAbSwCKQOjIQrDQNW_EAjtdeiqf5SELTsRhFfyKGvS-XvT7jjzM5zIkVVmeBeTlEjDeyl_-OfIjg4PfyAvxSaB6te_l-Dm_FKAduMb_nbG0ZK9DiReEjzG6NvpYP5qMB8adn1yS_6yeYfWDX0ZT571zodrPXDfaWyMCNzPwdPUEIXckVeTvg2sb4rHfhE9ZCkvV9MQcCsHXvxl6Uzvn9xZbOO4Tx3CXpTVN_PZLgRI6o3yk-VTy5j19GmHnZJEPfHtx9vpNF4YSDYM6ggWpEGIIqa9sI8YnuOr06AclBhQom_7w9kBboSv20v-dFjYuoRmyNfG8er2Pqz-w2eKPntllDvdxM0znWvHEHO_ifagL5AQSXoV4b7xf490rh4uVua7Vg7QrdT5i_KHK-KtXauFFrm2TjqUzppa3JnZF0pCRc0-HJBfVGMqMsAqGoEHozbbPXsdtEOv3sBuHs8LrUp_6VTDQW9v8cQBIOFuystnWeNOlup-3KEx8bgps_Lkh-t4Zk5KgVijra6AfibV3oUBMNK-_cdYE0Tc-pc-4tM5vwTA7Ay6Ll0EibE5_I-GNGbId8Tex8pt20_kZ1NyRxf_enNMv57JkYVEHwebdweNKlm8HJ7KwSkmbqpVHiD3hp-M1yWn25xXGX-C-BJkOpUVhomm_ml9eg5egMKUXiJL-58qAxN_pzLt1uk7LRQU0rFF9wsFQBnHGzSwZ5rc2V0wWO3WV3MsPUWI1QHFVr2Q6q5ndh2gHxGL3QbGOTgB6b4mC7nAaUKLhpZ4hTh7p9qaWaqGM9zuoPuZ-Y1l_loJhHT2qfNlkSIvJofEgdmvrGSSPs6fIKNndkuu17-QcK6gEq23pQYS4zPx6ClGSX_Zar6n7NmkPk3AShZvE7uGSe-XKnWMa0a86Z4AYmQ0lXdjmTCs0e7tfCTwYxyQ1TuMjF2qe5DrM3YZuoUSAU7bs-YyB1fTcio2mO4zCAu-Ag5szyd80uyY0SMs6tAX28M51kIqc_cfpuZLH3rYlv4AVPQ9EdqV_pjEiXBLtufrshccUjlLqv0R51rh7QWcrNJvsQZpseiWkm_6NwRlkH2uBZgje2RRMWlaBcPP-P3AR6QeSzrri9CiC5_ViiECDXkzx3vW_A3vmdaIL27xso2JAx3RYgquuT-OwBRE2nPB5kv8f-CSBU7bBmNDmJgwHhVyoNRtcPq0Gdb5VGVO_KLkBYOUzr_kEC2H8UI37FICebi_YXr5kBzs0VivgFWWLPWHNzzW32iQX4CQf9RikVI2QM3i0sNAu_Gff8Pfg5r-cpJJYlImq6kMTgUwBjzGEMj-AW_CyyVIENUNhU_sEHX4F95zzq9VXz9B3AMsT5Gw0t4e16wIkl1O3HiLCKnoyxTL64uHxqgzW-EfVyQ4X9y92EH9RrdLORt3EKC-8BqkFg6iwBBK2s2P1KGcpqPSDWMwgiwSiDApbxqkGvSadBw2sv973EFWvwf0rZvkBwOia1s0QHrc4wrdOPO_tgLEPnLK4l2cEWWHSzat0NsZ7QgryYBlMkQQI-M7reTlnXZzm5v6mYlnx5O2yVIM7huMkQ47b83S6R9Y8fXj8uE40Ce_F9bm571gfF05JEhyTr9oIYguGUnf7xl0On-CA2FAwstGqWNTG46ZqG9hC-aHwS6NmA-cMtsMzwo98HWinaWoMN9yr0PPT-Olncm0C60LScHGucnKfZubVaRBfBX6uzcgCMS6D7vCDG8x_aAYY3bWBERq0DByc8b4WGsS8UcK0OlJQd28Px__DQr6QvpbZ7O39Cw8sMyrg0-2GwG-dQO2XZ7arPVyOVbkCj8WaKV7wB_6eTyZZmceFvbQQKlqjPLdEiVQkXh-725bnZwtUYU-vRlbqBfcycEkAweS4-rk0T5WFhS-98XWTZVEfwSlUvgFpIK_HqjnZBu_7wZmrDXhhpUf-2snyE9Zizk2nBq59tEx1zADwAvHhk0Ar4R8S-vlwCh3zAW6t7L392lZXP0u3Y--faRlh90Hy2Bs9YUqVbM_Iktjig-ngmpiBfFDlabFc2XVYmjKIXJ8owS9IctNDTq6t9hxffmZqK1eKLYp2U7xP3drEbVu0JiKr3QQUbgy22jDubhEYeDbNTaifGXkbU7xMTOAt25alQILz8abQcHocO9zUxGl-CP99djfs909vzjkfs9rVis95WcY9sum0RGPUxDmmlPH453PGf5OeGF3fnDjlwGLoKOywn8g2qfRNUU0q_nwW4aWqichcnU7Nz5YuPT_oNONFkP8HD6cvwrmFU4BQrwoh7aYVuq48wMxiPHzKRgUCvhvAVK9OGwdygRWyWhn2bUPWKbpbeWPoSbKCMc_A0m2XJRFZLb24mwZpDVly-oRaMBjxFNWDmQqs3fPR1FiLtTL7HF_Dfzq3UT7NgnGD5wqq-faTey1uzCJY-dwLudFC4su8SYIDb5jiKWFYd1cgO4oWBNauMcfEwb16NeUdl_Z_qgO4C40XjTi03esmUK6AXYSwzVJUKnpm-D9bucmi8XnNKLyC5xJPoUj4YIrYsPcflY3gT2udtx8CsLqUyvQrOt_10mKh1sYxlXvzQYtLKcguuEnEXWgdgQLuRb9cQLIxzR4XEBIZzxJe1gGF3b26L-naqoq9z-HhGD1RD1BWZCHkj5OoT0zctgtRtCB1_IvWy4nxWBdMJrAsqNqufL8VQEMNMbwDnVtvyz05wPP9yx4yu7WCeLD9jv_cfaP5WqyR8RhFo4rvJfuYdKOD2u3B4GM-KZJ5wvnmIaSkTqOASLFXHPLVxqSasZyd_YwmyUG_b8xZqhs1B_IjL-AXi4SjZAwRD0FSTRAjDA3oDTj5aBpH7t9C67o_srnj9kUWpf_EUcez8_T_Yl9X7aQeNzHRjCBdaqh04icwSd1uvIwuWhy-XlocAbKoyzqWNKVnJf1R5DUQ==" } ] }, { "iteration": 2, "event": "compile_proof", "provider": "openrouter_primary", "status": "partial", "goals_remaining": 3, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro h\n have hs : p.IsSpecialForm := ?_\n exact hs\n\u00b7 constructor\n \u00b7 intro h\n have hw : p.GivesWagstaffPrime := ?_\n exact hw\n \u00b7 intro h\n have hm : p.GivesMersennePrime := ?_\n exact hm", "compiler_output_preview": "/app/asi_portal/verifier/quick_1772025702_6556.lean:52:2: error: unsolved goals\ncase left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p\n/app/asi_portal/verifier/quick_1772025702_6556.lean:56:4: error: unsolved goals\ncase right.left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesWagstaffPrime p\n/app/asi_portal/verifier/quick_1772025702_6556.lean:59:4: error: unsolved goals\ncase right.right.refine_1\n\n...<truncated>", "compile_elapsed_s": 45.948, "tactic_replay": { "tactic_count": 11, "successful_tactics": 1, "first_failure_step": 2, "goal_trajectory": [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2 ], "max_goals": 2, "final_goal_count": 2, "goals_opened": 5, "goals_closed": 4 }, "lsp_feedback": { "diagnostics": [ { "fullRange": { "end": { "character": 12, "line": 53 }, "start": { "character": 2, "line": 51 } }, "leanTags": [ 1 ], "message": "unsolved goals\ncase left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p", "range": { "end": { "character": 0, "line": 52 }, "start": { "character": 2, "line": 51 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 14, "line": 57 }, "start": { "character": 4, "line": 55 } }, "leanTags": [ 1 ], "message": "unsolved goals\ncase right.left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesWagstaffPrime p", "range": { "end": { "character": 0, "line": 56 }, "start": { "character": 4, "line": 55 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 14, "line": 60 }, "start": { "character": 4, "line": 58 } }, "leanTags": [ 1 ], "message": "unsolved goals\ncase right.right.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesMersennePrime p", "range": { "end": { "character": 0, "line": 59 }, "start": { "character": 4, "line": 58 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 6, "line": 62 }, "start": { "character": 0, "line": 62 } }, "message": "'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]", "range": { "end": { "character": 6, "line": 62 }, "start": { "character": 0, "line": 62 } }, "severity": 3, "source": "Lean 4" } ], "error_line": 51, "error_char": 2, "error_msg": "unsolved goals\ncase left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p", "goal_before_error": "```lean\ncase left\np : \u2115\nhp : Odd p\n\u22a2 Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p \u2192 Nat.IsSpecialForm p\n```\n---\n```lean\ncase right\np : \u2115\nhp : Odd p\n\u22a2 (Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesWagstaffPrime p) \u2227\n (Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesMersennePrime p)\n```", "full_timeline": [ { "line": 50, "code": "constructor", "goal": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "goal_count": 1, "ast_complexity": 63 }, { "line": 51, "code": "\u00b7 intro h", "goal": "```lean\ncase left\np : \u2115\nhp : Odd p\n\u22a2 Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p \u2192 Nat.IsSpecialForm p\n```\n---\n```lean\ncase right\np : \u2115\nhp : Odd p\n\u22a2 (Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesWagstaffPrime p) \u2227\n (Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesMersennePrime p)\n```", "goal_count": 2, "ast_complexity": 318 }, { "line": 52, "code": "have hs : p.IsSpecialForm := ?_", "goal": "```lean\ncase left\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p\n```", "goal_count": 1, "ast_complexity": 116 }, { "line": 53, "code": "exact hs", "goal": "```lean\ncase left.refine_2\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\nhs : Nat.IsSpecialForm p\n\u22a2 Nat.IsSpecialForm p\n```\n---\n```lean\ncase left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p\n```", "goal_count": 2, "ast_complexity": 280 }, { "line": 54, "code": "\u00b7 constructor", "goal": "```lean\ncase right\np : \u2115\nhp : Odd p\n\u22a2 (Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesWagstaffPrime p) \u2227\n (Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesMersennePrime p)\n```", "goal_count": 1, "ast_complexity": 199 }, { "line": 55, "code": "\u00b7 intro h", "goal": "```lean\ncase right.left\np : \u2115\nhp : Odd p\n\u22a2 Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesWagstaffPrime p\n```\n---\n```lean\ncase right.right\np : \u2115\nhp : Odd p\n\u22a2 Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesMersennePrime p\n```", "goal_count": 2, "ast_complexity": 246 }, { "line": 56, "code": "have hw : p.GivesWagstaffPrime := ?_", "goal": "```lean\ncase right.left\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesWagstaffPrime p\n```", "goal_count": 1, "ast_complexity": 122 }, { "line": 57, "code": "exact hw", "goal": "```lean\ncase right.left.refine_2\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\nhw : Nat.GivesWagstaffPrime p\n\u22a2 Nat.GivesWagstaffPrime p\n```\n---\n```lean\ncase right.left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesWagstaffPrime p\n```", "goal_count": 2, "ast_complexity": 297 }, { "line": 58, "code": "\u00b7 intro h", "goal": "```lean\ncase right.right\np : \u2115\nhp : Odd p\n\u22a2 Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p \u2192 Nat.GivesMersennePrime p\n```", "goal_count": 1, "ast_complexity": 121 }, { "line": 59, "code": "have hm : p.GivesMersennePrime := ?_", "goal": "```lean\ncase right.right\np : \u2115\nhp : Odd p\nh : Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesMersennePrime p\n```", "goal_count": 1, "ast_complexity": 123 }, { "line": 60, "code": "exact hm", "goal": "```lean\ncase right.right.refine_2\np : \u2115\nhp : Odd p\nh : Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p\nhm : Nat.GivesMersennePrime p\n\u22a2 Nat.GivesMersennePrime p\n```\n---\n```lean\ncase right.right.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesMersennePrime p\n```", "goal_count": 2, "ast_complexity": 299 } ], "tactic_count": 11, "successful_tactics": 1, "first_failure_step": 2, "cps": 9.090909090909092, "cps_peak_step": 1, "error_code": "\u00b7 intro h" } }, { "iteration": 3, "provider": "openrouter_primary", "finish_reason": "tool_calls", "response_id": "gen-1772025748-oJqgt48oh2Mmc2j0jNPa", "api_elapsed_s": 9.456, "usage": { "prompt_tokens": 10274, "completion_tokens": 429, "total_tokens": 10703, "reasoning_tokens": 406, "cost_usd": 0.0135023 }, "openrouter_retries": 0, "response_text_len": 0, "used_tool_call": true, "reasoning_text": "Exploring recursive theorem limitations", "reasoning_details": [ { "format": "openai-responses-v1", "index": 0, "type": "reasoning.summary", "summary": "Exploring recursive theorem limitations" }, { "id": "rs_0f55bae3e37e479001699ef794b830819691b3a7cc95087843", "format": "openai-responses-v1", "index": 0, "type": "reasoning.encrypted", "data": 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} ] }, { "iteration": 3, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "aesop", "compiler_output_preview": "/app/asi_portal/verifier/quick_1772025757_5726.lean:51:2: error: tactic 'aesop' failed, made no progress\nInitial goal:\n p : \u2115\n hp : Odd p\n \u22a2 NewMersenneConjectureStatement p\n'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]\n\n\n", "compile_elapsed_s": 27.893, "tactic_replay": { "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "goal_trajectory": [ 1 ], "max_goals": 1, "final_goal_count": 1, "goals_opened": 0, "goals_closed": 0 }, "lsp_feedback": { "diagnostics": [ { "fullRange": { "end": { "character": 7, "line": 50 }, "start": { "character": 2, "line": 50 } }, "message": "tactic 'aesop' failed, made no progress\nInitial goal:\n p : \u2115\n hp : Odd p\n \u22a2 NewMersenneConjectureStatement p", "range": { "end": { "character": 7, "line": 50 }, "start": { "character": 2, "line": 50 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "message": "'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]", "range": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "severity": 3, "source": "Lean 4" } ], "error_line": 50, "error_char": 2, "error_msg": "tactic 'aesop' failed, made no progress\nInitial goal:\n p : \u2115\n hp : Odd p\n \u22a2 NewMersenneConjectureStatement p", "goal_before_error": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "full_timeline": [ { "line": 50, "code": "aesop", "goal": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "goal_count": 1, "ast_complexity": 63 } ], "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "cps": 0.0, "cps_peak_step": 0, "error_code": "aesop" } }, { "iteration": 4, "provider": "openrouter_primary", "finish_reason": "tool_calls", "response_id": "gen-1772025785-yW0Q35vPnDb0oyOfKeNs", "api_elapsed_s": 5.725, "usage": { "prompt_tokens": 12267, "completion_tokens": 247, "total_tokens": 12514, "reasoning_tokens": 224, "cost_usd": 0.00839405 }, "openrouter_retries": 0, "response_text_len": 0, "used_tool_call": true, "reasoning_text": "Testing local theorem search", "reasoning_details": [ { "format": "openai-responses-v1", "index": 0, "type": "reasoning.summary", "summary": "Testing local theorem search" }, { "id": "rs_0f55bae3e37e479001699ef7ba16648196b1e334a8c682d8cd", "format": "openai-responses-v1", "index": 0, "type": "reasoning.encrypted", "data": 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} ] }, { "iteration": 4, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "library_search", "compiler_output_preview": "/app/asi_portal/verifier/quick_1772025791_6261.lean:51:3: error: unknown tactic\n/app/asi_portal/verifier/quick_1772025791_6261.lean:50:40: error: unsolved goals\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]\n\n\n", "compile_elapsed_s": 45.928, "tactic_replay": { "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "goal_trajectory": [ 1 ], "max_goals": 1, "final_goal_count": 1, "goals_opened": 0, "goals_closed": 0 }, "lsp_feedback": { "diagnostics": [ { "fullRange": { "end": { "character": 3, "line": 50 }, "start": { "character": 3, "line": 50 } }, "message": "unknown tactic", "range": { "end": { "character": 3, "line": 50 }, "start": { "character": 3, "line": 50 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 16, "line": 50 }, "start": { "character": 40, "line": 49 } }, "leanTags": [ 1 ], "message": "unsolved goals\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p", "range": { "end": { "character": 0, "line": 50 }, "start": { "character": 40, "line": 49 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "message": "'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]", "range": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "severity": 3, "source": "Lean 4" } ], "error_line": 49, "error_char": 40, "error_msg": "unsolved goals\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p", "goal_before_error": null, "full_timeline": [ { "line": 50, "code": "library_search", "goal": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "goal_count": 1, "ast_complexity": 63 } ], "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "cps": 0.0, "cps_peak_step": 0, "error_code": "NewMersenneConjectureStatement p := by" } }, { "iteration": 5, "event": "search_mathlib", "query": "Mersenne", "results_count": 8 }, { "iteration": 6, "event": "search_mathlib", "query": "Wagstaff", "results_count": 0 }, { "iteration": 7, "provider": "openrouter_primary", "finish_reason": "tool_calls", "response_id": "gen-1772025849-tRQWOwlfrKyVJfSqVZgk", "api_elapsed_s": 42.48, "usage": { "prompt_tokens": 14939, "completion_tokens": 1961, "total_tokens": 16900, "reasoning_tokens": 1905, "cost_usd": 0.03041325 }, "openrouter_retries": 0, "response_text_len": 0, "used_tool_call": true, "reasoning_text": "Exploring prime implications and simplifications", "reasoning_details": [ { "format": "openai-responses-v1", "index": 0, "type": "reasoning.summary", "summary": "Exploring prime implications 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sIYn3OCuL21goUr_Is-63gzDoDbutlAhZeIpDaqblqD1Fbm3cOVaMDPiktmWlnw03daUAoNgGZ6IBpC3B2v-bDIXfXetXMlH3qqT23BS3qRnbh_b4WsMSKtxoVGLmG1ako9OIk0FmxUz0uD6rtP0pCHVsaaE1V9kMWG9HMgHofFfheV1hmk4ynWiaHcmy70_YpKUa20Y7-0JYj5XRd7C3mgdErSjxLJ_XLMxM8VOI5cqlbljr9UWUTZkPdrukkaqjLrXlDEQ7jKgfNAMR8OR-VfieRXhZaqeLCBafMg5pYxWpmzwSIE35-oluJS3HbtD5sM7xjSS-b8JOZOQ53bVND2eKRQuEqt8YCTIQkQ3qwiVMLg1e5J_WOFiD6dtkZzWAIEeEWu8yscio5WxvZHSM5FjCuwMNoZw8qqUt0Zp1wAoDrTuJV6LgU5bJsXzKADCElWXfQ1V_e2sa4n_f8kjK1owtuTO7BIslVEgQE4nlW2S8lAtcrIgCkfArEkR5CBAtFKYezVWrS96eRXYT2BnRuY5dKzxTQ-3bra-AycvdZ5rzKRLvp9VSFwulm70-I-4zTnAUW43Azjy2TDKnVhCdz7CQLv1CB2QBwhko4l7301swanOJRPkK3uiuEnQtLYkAce3QXMeKOBrDyJvcphwFxihNL3rKJeTnCcOGvIWYUQuV2EJd4N8uUWg29kLB0u3w--_QEqoMWB_T7XWXR8D3eFxxlxrjUg9aRuNMtCGidHCqWlfEdZZPbsBUDNhPcG3uDn8BERvjL8EyPr0H0L0Z8FuNvrnX05zrFVWA_ejqQMEqi4qyhHhPDCffrFzlZe2KgW_ic58iG1-3kXEcip5cMdtkl3DsVCWKyowZNXXOTId-jrxpAEI6kGkzHYY7WaTf1OyEy-DQeWlL7XVFB_HhP-Rs4b_HHmdx4efssWvmyUF76A3-iutpVtMPgZVKLkBB8GN7LutX1_dV_n6g6F0NfSw3VkZh5WdIZofg85uquWU8eyae_Pvqgh2IfOBxnHn1jp5DNZrNt19jwu9XRDhBELFF6W68GY--ASu0zgok2G1gnXKLEZEF33sNocfQp59aCJZAswNO27i6vDk4vqUXDc78-OUkliNiFaE8pIvgV90CUM85WOwcFd7b8W5uraaRiag9J0OVyb4Ci3B8qkecvjSTpEm1_8KOYTLVmQ908cR4qNrCXknOnkRCPpk-0ltrAD0ebsAZ---uq4HkCU9as-Bi-QqgnhlrqMyDvMF_7amovW8HIJGSlcv3GFPJGaM3Taajv_zYydXaqut0KSk20EQi4rpnzui6nRBEKYSMVWtb5QFe-NGx_WKPJ4IhX3SJah8teTBm60LQiX3C53h-93H1dEY0EOlJI66jpdqIjWFid1TBxN-taKyAXy0YZVdfO3LhLFLZtebKDHtD4I0fTFK-EcaTcAls-y_wmNwfVJYGRgPs8WYlEF_MJK8NbZdby8jckHHyKZa7I9Gzv2SGIni8PCqI9l2JYh73wTTv8bA6ug8JmUFZ5rqwCqIXrUoRCACtiSTkCw4_ZL_MNg2irm9iQ2aweYcMvccuWzskxSeykSxc1AajJx5qfWhlND8mYe9Kz_hjUJVdTHZA44UMGlAhkSR6IV1YQtWNGi200sigq3nTDSdE57HqjeCLpNn5Oe35lS0OsKasSOFrVn6O3O_i3_pvIOQK-MrFUQeY_H6q3moOqMveP46BahoAOK7LCOXdzIIW15CUbb9UYf1RgssKD06yRtD9469EQ9rAoMmuSb-TpPCvY11t3aQB4vhAP9SjEDtzh-AJR3tXQJ6pza4DabS43EhIhWqUn9sfwAFh4lRYJtUv_YRA9H30yqPM6LMoZv8otDlVLHuO_zucmtEdfixZhQF7u7ELZEngYK_myCZFX5W8IjHmjcDxrJJ6JmwjCiexm6o-w5gN-gwK1VpgbPe2y84W8EMPd6NC2R6wu08kOhmg4v_av1gX_7CmJYfbW-NGE6nryGJZUMKGbgWaLkC8QTmaY_hr-6jPZj_jOJKbKmJd5WxooJS9c002i98MZrC7sM-ZwY5kVHlSsXcNjYklxy7_CD0RMQe0Xzu3fPd864b1PUECaVg0g0i7J_oZj0Yd3NbejaDYObYXDlyH9m9TvJ-gK07bTeTcfI4TB1dUwSP0qQIa7ss6zXQ8Ip8oTVBUOgzGl_q8e6RLlsE2yq_MitQc3UyPMdjiflARVlP4JFLpOMDE-AHMAVC4IfHQhMJOIBn9zNJmkRruDi9PvfvDfO-OXZWCWJ6SheLW89cbQRDpdXzf5Ydd-PNm4yoagGHnR5opDQnaU8hnjAPx25Jehrzu5y_kIsKMMQxe5woNX5WKwBuf8WArlD6Zqe_chyLP-hxrnlByXfAqWjXOcYzraBj6ZlbHGtEgoPK3Ib3vuzJSheSL7mOhKrSSAylnGUT3zOUD0ZzEg7BOqHKqUWyK-liyPlFfsrx9QwOxRo6U1eo1LHoMNDuTdeQG-zHZK9c0wRWwhhzBNGarOhcbYS82zTslYW8NfDEPw-qiGhLfhq6k8bb0EhM3Apbwj6UaH2cZbmFwo341cp9XvDhrKZgJcKc0pg4vlSIRAIVxFlW1nqjRzaMkpJwfa5pLXS6LX5MB0TffVTAJm2XeYtZONuzoaj-CXUla8yeEUm0em7C2sADBYSKfFwokSpnMBXkwJYCmLR3_oZct2LAmX-qbyJVvmFFC-YmuTgf7UR79maHdG0nqd2GO7AARt6boF-XKWSfPTFhIZ5Ei7sxyMaz4HTs8ZCpDdyCHPwvlCXyMMXt9Jv9MeQQ7dVPxTIKLXgeKfJYWz_x-0AFK4AQMNstDckBYP2KR_le7Bh9Q6C-ArXTaU7-9PCndGgE9DzhrIZt8PaC0__75ZnzZk1Nk0ci1qtXvoTKmkBUs9_x30jnmf9Q0HNoxqoWGfr4XBjw9KOuESrRTHQJPur6g3dFP6ynTsNSw0der80rtJgBcmAP9_l6U0hlgX33dhrOUZaWP3PkZDcPAfSw_xI2pnLyUiKmKnr8LQgcKzMTuTZ3YCRhs_A1cRf7bPHfzUcRJi-VoMqQeU5wwJ2K2kZQSKzQXAROUX1LAfeYhkWiqdkz20WoS3nblBEz3d7rcoGFWZDfP0406U_VyC_gFdT2qYQD54vD_9KBF9eJig8yZGGYyoSF5SGgS4iSPC4B0ro8DOM0pJuDlLvtFC6MXu61xCVGdWW-M1bXhfaO2b_cxpKxEzDYHC37qXpSG_0KD33jRe3On8wyiGQ8x1gv00rggjiR3kQb24hFQlFXDS991Lpk7qebf0SzMyy6SJoy5ySo8Z4_L0LoZdbUGEQp4T3KxYefWMZzWmIcfsE4HE-E7UJfyQdJgAPOvsPHD58ADNhdmoYEOZWN5KwDkPLhKR9X1naikUZICdq083EsH84jTjQAClyGOd_kkK4E9f4wJ-V3No0VIFgzPdijCPzrawPTkrvaeNtYb1bhdQRtFsAQnlK0Vm0uit6AZPe1tnVQdEWB4WhweSU3MvWfU7hiB_Dx0KeAIm7STaiCK9DHEzWucxOu5_2xL5iblbRfzjrlsdm6ZvkhnOpXVeGfygKUKAtw0qhY9C-Ltl7MhCAhLLuf3_U2TbAqfDMwL_QzgM8qUSmVWtpLFACkG0fOhTeQ46yeQASy28KZR4MSdh9kG6ozbLeNgyK1N6tMPZzYlXoQfTSwAWZYaId-KkP3hh6b69sIJlUvIvK-_afUOv2EmL9q98GsziqIoedDy-X0MhikV2LLVP9mePqgOSQtUR2WsquhekSqT7gUPTip4H06LtGcPQR5R6xoi5odavN24bBFkhJ5Bs8HQ_I0Tdi8dbyJZ6S7XRvvHJ4VUdIcv1AIEek-b8phGpBzk1ot-e7a2ujjO3QUWlrNYM2hRdtJu9UzDCBiHvkZEk_GLc_8wIcQ0a77KcX-u7jmJBrNfWpQpLzdp3mTWMEZrJPf2AJyDz6_zRgoBNSwB4EKZdTH3A3dfPTsfRG5NQBuVtO8JLPF8_u3N89BGOaQ20_vNa-R-VZVxePrM5ohLp9h5gK66NOQcHxAL_tTb8Dye6464bRSlh3m4rSFBMPothb4wrSJQMdKmGSzJba1v2lCw2XylXHDu32pGPN0HDYwixBOuuhhR0PDCcUew-9qjxm7JeEIEGux992LALjq-DgPXC3d2jR0zGBRifL0a-cu-BCZbTbONRHcbeDH1TNN8104WK1-47sXP3GWYjboixdr4roQyB_DK5HFzX72m-sbZgPGxN3ETa3tKXC_44JgUtalUD0OAzi_-XaYZ8B4T29Gj3x1pU-NIrAnBWv_IRJjkgMdXK5gMoY4DPdE_MWzG82g4Kt8q1vUdO37NsVdpzPjKdZ5A5prKXhw4MEbdwNr1Cw6q11NuedxkMlWsLkeIYsvVKNScgv_XgpptDdJbuf-CGi4pR6jHy-fHvZborA_xzPyn-oQFN0PAabwUfUxwoIxjIfmqdDjq8KYA4ig7-WGk9lr0uMQPz4_mlYDXW1_lU-xoQvDMbObvYKDRtMz3Z1RxcnVdZauHFhQVPZb4X1j1XLdbE5P_nzDmcLtuTWzF-viPXgnkpFoM0L93Xm_dB7Eoz-qpp2cp75vbmelTxU6OmQWuP4KLQvBCzb0XlFW8drVzskszR5q_JPMSFIPsS5q-JRfBSypkcNh7JhCEvN0F3jaHP_RjEvroSz1_wKHTsOAnFZbXAh3v12K6LN5BORb_WNEkJjosatUcv4DHkhjuXTqjwE-FOmsObTjXruUL7Xr0FHLU-neeaRWID3FJOqZKFRR3NwauuN1I2AreFObK3fZvMe9nMHRcXPwvNYPip4CmAVVK-1kjXJMsQvG4YTm4Fum00bXhBPrCTgkILqp0FFQCGsBQH-ErqsieEjFfnxcjO9i-85vZy2yXFbudLrKHi5Rc7wAoFkq3MZCLIK_qdmrAx_B6fkuHQOURZCfdzMAU7iHOV_qDOJ8htE_zgxoB7Md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} ] }, { "iteration": 7, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "simpa [NewMersenneConjectureStatement, Nat.GivesMersennePrime, Nat.GivesWagstaffPrime, Nat.IsSpecialForm, hp]", "compiler_output_preview": "/app/asi_portal/verifier/quick_1772025891_3764.lean:51:2: error: Tactic `assumption` failed\n\np : \u2115\nhp : Odd p\n\u22a2 (Nat.Prime (2 ^ p - 1) \u2192\n Nat.Prime ((2 ^ p + 1) / 3) \u2192 \u2203 k, p = 2 ^ k + 1 \u2228 p = 2 ^ k - 1 \u2228 p = 4 ^ k + 3 \u2228 p = 4 ^ k - 3) \u2227\n (Nat.Prime (2 ^ p - 1) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x - 3 \u2192 Nat.Prime ((2 ^ p + 1) / 3)) \u2227\n (Nat.Prime ((2 ^ p + 1) / 3) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x \n...<truncated>", "compile_elapsed_s": 46.945, "tactic_replay": { "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "goal_trajectory": [ 1 ], "max_goals": 1, "final_goal_count": 1, "goals_opened": 0, "goals_closed": 0 }, "lsp_feedback": { "diagnostics": [ { "fullRange": { "end": { "character": 111, "line": 50 }, "start": { "character": 2, "line": 50 } }, "message": "Tactic `assumption` failed\n\np : \u2115\nhp : Odd p\n\u22a2 (Nat.Prime (2 ^ p - 1) \u2192\n Nat.Prime ((2 ^ p + 1) / 3) \u2192 \u2203 k, p = 2 ^ k + 1 \u2228 p = 2 ^ k - 1 \u2228 p = 4 ^ k + 3 \u2228 p = 4 ^ k - 3) \u2227\n (Nat.Prime (2 ^ p - 1) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x - 3 \u2192 Nat.Prime ((2 ^ p + 1) / 3)) \u2227\n (Nat.Prime ((2 ^ p + 1) / 3) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x - 3 \u2192 Nat.Prime (2 ^ p - 1))", "range": { "end": { "character": 111, "line": 50 }, "start": { "character": 2, "line": 50 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "message": "'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]", "range": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "severity": 3, "source": "Lean 4" } ], "error_line": 50, "error_char": 2, "error_msg": "Tactic `assumption` failed\n\np : \u2115\nhp : Odd p\n\u22a2 (Nat.Prime (2 ^ p - 1) \u2192\n Nat.Prime ((2 ^ p + 1) / 3) \u2192 \u2203 k, p = 2 ^ k + 1 \u2228 p = 2 ^ k - 1 \u2228 p = 4 ^ k + 3 \u2228 p = 4 ^ k - 3) \u2227\n (Nat.Prime (2 ^ p - 1) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x - 3 \u2192 Nat.Prime ((2 ^ p + 1) / 3)) \u2227\n (Nat.Prime ((2 ^ p + 1) / 3) \u2192\n \u2200 (x : \u2115), p = 2 ^ x + 1 \u2228 p = 2 ^ x - 1 \u2228 p = 4 ^ x + 3 \u2228 p = 4 ^ x - 3 \u2192 Nat.Prime (2 ^ p - 1))", "goal_before_error": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "full_timeline": [ { "line": 50, "code": "simpa [NewMersenneConjectureStatement, Nat.GivesMersennePrime, Nat.GivesWagstaffPrime, Nat.IsSpecialForm, hp]", "goal": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "goal_count": 1, "ast_complexity": 63 } ], "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "cps": 0.0, "cps_peak_step": 0, "error_code": "simpa [NewMersenneConjectureStatement, Nat.GivesMersennePrime, Nat.GivesWagstaffPrime, Nat.IsSpecialForm, hp]" } }, { "iteration": 8, "provider": "openrouter_primary", "finish_reason": "tool_calls", "response_id": "gen-1772025938-zPisVkAl0UCa6WgMAwIh", "api_elapsed_s": 16.941, "usage": { "prompt_tokens": 20012, "completion_tokens": 662, "total_tokens": 20674, "reasoning_tokens": 632, "cost_usd": 0.0217098 }, "openrouter_retries": 0, "response_text_len": 0, "used_tool_call": true, "reasoning_text": "Testing unknown name suggestions", "reasoning_details": [ { "format": "openai-responses-v1", "index": 0, "type": "reasoning.summary", "summary": "Testing unknown name suggestions" }, { "id": "rs_0f55bae3e37e479001699ef85377b881969419291391a3a6de", "format": "openai-responses-v1", "index": 0, "type": "reasoning.encrypted", "data": 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} ] }, { "iteration": 8, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "exact new_mersenne_conjecture_statement", "compiler_output_preview": "/app/asi_portal/verifier/quick_1772025955_1010.lean:51:8: error(lean.unknownIdentifier): Unknown identifier `new_mersenne_conjecture_statement`\n'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]\n\n\n", "compile_elapsed_s": 30.298, "tactic_replay": { "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "goal_trajectory": [ 1 ], "max_goals": 1, "final_goal_count": 1, "goals_opened": 0, "goals_closed": 0 }, "lsp_feedback": { "diagnostics": [ { "code": "lean.unknownIdentifier", "fullRange": { "end": { "character": 41, "line": 50 }, "start": { "character": 8, "line": 50 } }, "message": "Unknown identifier `new_mersenne_conjecture_statement`", "range": { "end": { "character": 41, "line": 50 }, "start": { "character": 8, "line": 50 } }, "severity": 1, "source": "Lean 4" }, { "fullRange": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "message": "'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]", "range": { "end": { "character": 6, "line": 52 }, "start": { "character": 0, "line": 52 } }, "severity": 3, "source": "Lean 4" } ], "error_line": 50, "error_char": 8, "error_msg": "Unknown identifier `new_mersenne_conjecture_statement`", "goal_before_error": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "full_timeline": [ { "line": 50, "code": "exact new_mersenne_conjecture_statement", "goal": "```lean\np : \u2115\nhp : Odd p\n\u22a2 NewMersenneConjectureStatement p\n```", "goal_count": 1, "ast_complexity": 63 } ], "tactic_count": 1, "successful_tactics": 0, "first_failure_step": 1, "cps": 0.0, "cps_peak_step": 0, "error_code": "exact new_mersenne_conjecture_statement" } }, { "iteration": 9, "event": "search_mathlib", "query": "new_mersenne", "results_count": 0 }, { "iteration": 10, "event": "search_mathlib", "query": "conjecture", "results_count": 0 } ], "verification": { "banned_tokens": [], "command": [ "[path] "lean", "/app/asi_portal/verifier/quick_1772026013_6408.lean" ], "comparator_passed": null, "duration_s": 12.815887928009033, "goals_remaining": 3, "is_verified": false, "lean_file_path": "", "problem": { "axioms_check_name": "new_mersenne_conjecture", "axioms_check_skipped": false, "benchmark_id": "Wikipedia__Mersenne__new_mersenne_conjecture", "category": "research_open", "endings": [ "end Mersenne" ], "imports": [ "FormalConjectures.Util.ProblemImports" ], "preamble_chars": 1173, "source_file": "FormalConjectures/Wikipedia/Mersenne.lean", "title": "new_mersenne_conjecture" }, "returncode": 1, "status": "partial", "stderr": "", "stdout": "/app/asi_portal/verifier/quick_1772026013_6408.lean:52:2: error: unsolved goals\ncase left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.GivesWagstaffPrime p\n\u22a2 Nat.IsSpecialForm p\n/app/asi_portal/verifier/quick_1772026013_6408.lean:56:4: error: unsolved goals\ncase right.left.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesMersennePrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesWagstaffPrime p\n/app/asi_portal/verifier/quick_1772026013_6408.lean:59:4: error: unsolved goals\ncase right.right.refine_1\np : \u2115\nhp : Odd p\nh : Nat.GivesWagstaffPrime p \u2227 Nat.IsSpecialForm p\n\u22a2 Nat.GivesMersennePrime p\n'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]\n\n", "timed_out": false }, "phase2_error": "ProgressAnalysisResult.__init__() missing 1 required positional argument: 'progress_score'" }
Gemini 3.1 Pro Agent v8	Failed	--	Feb 24, 2026		View { "agent_telemetry": { "compilations": 0, "iterations": 0, "duration_s": 0.04, "best_status": "pending", "best_goals": null, "max_iterations": 10, "model": "google/gemini-3.1-pro-preview", "error": "OpenRouter API error 402: {\"error\":{\"message\":\"This request requires more credits, or fewer max_tokens. You requested up to 65536 tokens, but can only afford 58661. To increase, visit https://openrouter.ai/settings/keys and create a key with a higher total limit\",\"code\":402,\"metadata\":{\"provider_name\":null}},\"user_id\":\"user_2zsm3L1zzBL2yxyrvmrXwgeTimc\"}", "provider": "openrouter_primary", "finish_reason": "", "usage": { "prompt_tokens": 0, "completion_tokens": 0, "total_tokens": 0, "reasoning_tokens": null, "cost_usd": 0.0 }, "reasoning_effort": "high", "response_trace_count": 0 }, "response_trace": [] }
Gemini 3 Flash Agent v8	Partial	10	Feb 17, 2026	constructor · intro h rcases h with ⟨hM, hW⟩ unfold Nat.IsSpecialForm unfold Nat.GivesMersennePrime at hM unfold Nat.GivesWagstaffPrime at hW let n := 2^p - 1 let m := (2^p + 1) / 3 match p with \| 3 => use 1; simp \| 5 => use 2; simp \| 7 => use 3; simp \| 13 => use 2; simp [Or.comm] \| 17 => use 4; simp \| 19 => use 2; simp \| 31 => use 5; simp \| 61 => use 6; simp \| _ => refine ?_ · constructor · intro h rcases h with ⟨hM, ⟨k, hS⟩⟩ unfold Nat.GivesWagstaffPrime use hp unfold Nat.GivesMersennePrime at hM rcases hS with h1 \| h2 \| h3 \| h4 · rw [h1] at * refine ?_ · rw [h2] at * refine ?_ · rw [h3] at * refine ?_ · rw [h4] at * refine ?_ · intro h rcases h with ⟨hW, ⟨k, hS⟩⟩ unfold Nat.GivesMersennePrime unfold Nat.GivesWagstaffPrime at hW rcases hS with h1 \| h2 \| h3 \| h4 · rw [h1] at * refine ?_ · rw [h2] at * refine ?_ · rw [h3] at * refine ?_ · rw [h4] at * refine ?_	View { "agent_telemetry": { "compilations": 8, "iterations": 8, "duration_s": 107.73, "best_status": "partial", "best_goals": 10, "max_iterations": 8, "model": "gemini-3-flash-preview", "error": null, "provider": "openrouter_primary", "finish_reason": "stop", "usage": { "prompt_tokens": 69637, "completion_tokens": 3281, "total_tokens": 72918, "reasoning_tokens": null, "cost_usd": 0.0410048 }, "reasoning_effort": "", "response_trace_count": 16 }, "response_trace": [ { "iteration": 1, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349386-UCqZUhBZdtxo8P5i0dNz", "api_elapsed_s": 5.861, "usage": { "prompt_tokens": 2097, "completion_tokens": 473, "total_tokens": 2570, "reasoning_tokens": null, "cost_usd": 0.0024675 }, "openrouter_retries": 0, "response_text_len": 1029 }, { "iteration": 1, "event": "compile_proof", "provider": "openrouter_primary", "status": "partial", "goals_remaining": 10, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro h\n rcases h with \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n unfold Nat.GivesMersennePrime at hM\n unfold Nat.GivesWagstaffPrime at hW\n let n := 2^p - 1\n let m := (2^p + 1) / 3\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; simp [Or.comm]\n \| 17 => use 4; simp\n \| 19 => use 2; simp\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| _ =>\n refine ?_\n\u00b7 constructor\n \u00b7 intro h\n rcases h with \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n use hp\n unfold Nat.GivesMersennePrime at hM\n rcases hS with h1 \| h2 \| h3 \| h4\n \u00b7 rw [h1] at \n refine ?_\n \u00b7 rw [h2] at \n refine ?_\n \u00b7 rw [h3] at \n refine ?_\n \u00b7 rw [h4] at \n refine ?_\n \u00b7 intro h\n rcases h with \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n unfold Nat.GivesWagstaffPrime at hW\n rcases hS with h1 \| h2 \| h3 \| h4\n \u00b7 rw [h1] at \n refine ?_\n \u00b7 rw [h2] at \n refine ?_\n \u00b7 rw [h3] at \n refine ?_\n \u00b7 rw [h4] at \n refine ?_", "compiler_output_preview": "[path]:67:9: error: unsolved goals\ncase h\np : \u2115\nn : \u2115 := 2 ^ p - 1\nm : \u2115 := (2 ^ p + 1) / 3\nhp : Odd 61\nhM : Nat.Prime (2 ^ 61 - 1)\nhW : Odd 61 \u2227 Nat.Prime ((2 ^ 61 + 1) / 3)\n\u22a2 False\n[path]:68:8: error: unsolved goals\np : \u2115\nn : \u2115 := 2 ^ p - 1\nm : \u2115 := (2 ^ p + 1) / \n...<truncated>" }, { "iteration": 2, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349399-VhJRgmuq9In1yLNupwgX", "api_elapsed_s": 15.911, "usage": { "prompt_tokens": 4119, "completion_tokens": 353, "total_tokens": 4472, "reasoning_tokens": null, "cost_usd": 0.0031185 }, "openrouter_retries": 0, "response_text_len": 821 }, { "iteration": 2, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n let n := p\n cases n with\n \| zero => \n exfalso\n exact (Nat.not_odd_zero hp)\n \| succ n =>\n match p with\n \| 1 => use 0; simp\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; ring\n \| 17 => use 4; simp\n \| 19 => use 5; right; right; right; ring\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n use hp\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 intro \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_", "compiler_output_preview": "[path]:58:30: error: Application type mismatch: In the application\n Nat.not_odd_zero hp\nthe argument\n hp\nhas type\n Odd p : Prop\nbut is expected to have type\n Odd 0 : Prop\n[path]:61:10: error: unsolved goals\ncase h\np : \u2115\nn\u271d : \u2115 := p\nn : \u2115\nhp : Odd 1\nhM : Nat.Give\n...<truncated>" }, { "iteration": 3, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349422-zrrq8hBGkq0EAL5airpS", "api_elapsed_s": 9.201, "usage": { "prompt_tokens": 5920, "completion_tokens": 370, "total_tokens": 6290, "reasoning_tokens": null, "cost_usd": 0.00224255 }, "openrouter_retries": 0, "response_text_len": 827 }, { "iteration": 3, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro h\n rcases h with \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n replace hM : Nat.Prime (2 ^ p - 1) := hM\n replace hW : Nat.Prime ((2 ^ p + 1) / 3) := hW.2\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; rfl\n \| 17 => use 4; simp\n \| 19 => use 2; right; right; right; rfl\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro h\n rcases h with \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n use hp\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 intro h\n rcases h with \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_", "compiler_output_preview": "[path]:61:39: error: tactic 'rfl' failed, the left-hand side\n 13\nis not definitionally equal to the right-hand side\n 4 ^ 2 + 3\ncase h.h.h.h\np : \u2115\nhp : Odd 13\nhM : Nat.Prime (2 ^ 13 - 1)\nhW : Nat.Prime ((2 ^ 13 + 1) / 3)\n\u22a2 13 = 4 ^ 2 + 3\n[path]:63:40: error: tactic\n...<truncated>" }, { "iteration": 4, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349439-25SO7VBFvB5WoVmHzME3", "api_elapsed_s": 2.686, "usage": { "prompt_tokens": 7769, "completion_tokens": 370, "total_tokens": 8139, "reasoning_tokens": null, "cost_usd": 0.00316525 }, "openrouter_retries": 0, "response_text_len": 827 }, { "iteration": 4, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro h\n rcases h with \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n replace hM : Nat.Prime (2 ^ p - 1) := hM\n replace hW : Nat.Prime ((2 ^ p + 1) / 3) := hW.2\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; rfl\n \| 17 => use 4; simp\n \| 19 => use 2; right; right; right; rfl\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro h\n rcases h with \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n use hp\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 intro h\n rcases h with \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_", "compiler_output_preview": "[path]:61:39: error: tactic 'rfl' failed, the left-hand side\n 13\nis not definitionally equal to the right-hand side\n 4 ^ 2 + 3\ncase h.h.h.h\np : \u2115\nhp : Odd 13\nhM : Nat.Prime (2 ^ 13 - 1)\nhW : Nat.Prime ((2 ^ 13 + 1) / 3)\n\u22a2 13 = 4 ^ 2 + 3\n[path]:63:40: error: tactic\n...<truncated>" }, { "iteration": 5, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349449-f4baRhfvbMNAEWv7XXFy", "api_elapsed_s": 2.738, "usage": { "prompt_tokens": 9618, "completion_tokens": 312, "total_tokens": 9930, "reasoning_tokens": null, "cost_usd": 0.005745 }, "openrouter_retries": 0, "response_text_len": 694 }, { "iteration": 5, "event": "compile_proof", "provider": "openrouter_primary", "status": "partial", "goals_remaining": 12, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; norm_num\n \| 17 => use 4; simp\n \| 19 => use 2; right; right; right; norm_num\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n refine \u27e8hp, ?_\u27e9\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 intro \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_", "compiler_output_preview": "[path]:58:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 13\nhM : Nat.GivesMersennePrime 13\nhW : Nat.GivesWagstaffPrime 13\n\u22a2 False\n[path]:60:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 19\nhM : Nat.GivesMersennePrime 19\nhW : Nat.GivesWagstaffPrime 19\n\u22a2 \n...<truncated>" }, { "iteration": 6, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349459-9Dl65sVV4U3tWyZJjteL", "api_elapsed_s": 2.917, "usage": { "prompt_tokens": 11383, "completion_tokens": 359, "total_tokens": 11742, "reasoning_tokens": null, "cost_usd": 0.0067685 }, "openrouter_retries": 0, "response_text_len": 821 }, { "iteration": 6, "event": "compile_proof", "provider": "openrouter_primary", "status": "partial", "goals_remaining": 20, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; norm_num\n \| 17 => use 4; simp\n \| 19 => use 2; right; right; right; norm_num\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro \u27e8hM, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesWagstaffPrime\n refine \u27e8hp, ?_\u27e9\n induction k with\n \| zero => \n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_\n \| succ k ih =>\n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_\n \u00b7 intro \u27e8hW, \u27e8k, hS\u27e9\u27e9\n unfold Nat.GivesMersennePrime\n induction k with\n \| zero =>\n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_\n \| succ k ih =>\n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_", "compiler_output_preview": "[path]:58:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 13\nhM : Nat.GivesMersennePrime 13\nhW : Nat.GivesWagstaffPrime 13\n\u22a2 False\n[path]:60:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 19\nhM : Nat.GivesMersennePrime 19\nhW : Nat.GivesWagstaffPrime 19\n\u22a2 \n...<truncated>" }, { "iteration": 7, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349470-DE7vy3Z3sSuLrTMULhiv", "api_elapsed_s": 3.627, "usage": { "prompt_tokens": 13393, "completion_tokens": 424, "total_tokens": 13817, "reasoning_tokens": null, "cost_usd": 0.0079685 }, "openrouter_retries": 0, "response_text_len": 878 }, { "iteration": 7, "event": "compile_proof", "provider": "openrouter_primary", "status": "partial", "goals_remaining": 15, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro h\n unfold Nat.IsSpecialForm\n let \u27e8hM, hW\u27e9 := h\n rcases hp with \u27e8k, rfl\u27e9\n match k with\n \| 0 => exact \u27e80, Or.inl (by norm_num)\u27e9\n \| 1 => exact \u27e81, Or.inr (Or.inl (by norm_num))\u27e9\n \| 2 => exact \u27e82, Or.inr (Or.inl (by norm_num))\u27e9\n \| 3 => exact \u27e83, Or.inr (Or.inl (by norm_num))\u27e9\n \| 6 => exact \u27e82, Or.inr (Or.inr (Or.inl (by norm_num)))\u27e9\n \| 8 => exact \u27e84, Or.inl (by norm_num)\u27e9\n \| 9 => exact \u27e82, Or.inr (Or.inr (Or.inr (by norm_num)))\u27e9\n \| 15 => exact \u27e85, Or.inr (Or.inl (by norm_num))\u27e9\n \| 30 => exact \u27e86, Or.inr (Or.inl (by norm_num))\u27e9\n \| 63 => exact \u27e87, Or.inr (Or.inl (by norm_num))\u27e9\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro \u27e8hM, k, hS\u27e9\n unfold Nat.GivesWagstaffPrime\n use hp\n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_\n \u00b7 intro \u27e8hW, k, hS\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl <;> refine ?_", "compiler_output_preview": "[path]:57:29: error: unsolved goals\nk : \u2115\nh : Nat.GivesMersennePrime (2 * 0 + 1) \u2227 Nat.GivesWagstaffPrime (2 * 0 + 1)\nhM : Nat.GivesMersennePrime (2 * 0 + 1)\nhW : Nat.GivesWagstaffPrime (2 * 0 + 1)\n\u22a2 False\n[path]:58:37: error: unsolved goals\nk : \u2115\nh : Nat.GivesMerse\n...<truncated>" }, { "iteration": 8, "provider": "openrouter_primary", "finish_reason": "stop", "response_id": "gen-1771349481-OGq4dvGxFg378UCIiyoT", "api_elapsed_s": 4.319, "usage": { "prompt_tokens": 15338, "completion_tokens": 620, "total_tokens": 15958, "reasoning_tokens": null, "cost_usd": 0.009529 }, "openrouter_retries": 0, "response_text_len": 1422 }, { "iteration": 8, "event": "compile_proof", "provider": "openrouter_primary", "status": "failed", "goals_remaining": null, "timed_out": false, "banned_tokens": [], "proof_code": "constructor\n\u00b7 intro \u27e8hM, hW\u27e9\n unfold Nat.IsSpecialForm\n match p with\n \| 3 => use 1; simp\n \| 5 => use 2; simp\n \| 7 => use 3; simp\n \| 13 => use 2; right; right; left; norm_num\n \| 17 => use 4; simp\n \| 19 => use 2; right; right; right; norm_num\n \| 31 => use 5; simp\n \| 61 => use 6; simp\n \| 127 => use 7; simp\n \| _ => refine ?_\n\u00b7 constructor\n \u00b7 intro \u27e8hM, k, hS\u27e9\n unfold Nat.GivesWagstaffPrime\n refine \u27e8hp, ?_\u27e9\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 match k with \| 0 => norm_num \| 1 => exact hW.2 \| 2 => norm_num \| 3 => norm_num \| 4 => norm_num \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => norm_num \| 2 => exact hW.2 \| 3 => exact hW.2 \| 4 => norm_num \| 5 => exact hW.2 \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => exact hW.2 \| 2 => exact hW.2 \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => norm_num \| 2 => exact hW.2 \| _ => refine ?_\n \u00b7 intro \u27e8hW, k, hS\u27e9\n unfold Nat.GivesMersennePrime\n rcases hS with rfl \| rfl \| rfl \| rfl\n \u00b7 match k with \| 0 => norm_num \| 1 => exact hW.2 \| 2 => norm_num \| 3 => norm_num \| 4 => norm_num \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => norm_num \| 2 => exact hW.2 \| 3 => exact hW.2 \| 4 => norm_num \| 5 => exact hW.2 \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => exact hW.2 \| 2 => exact hW.2 \| _ => refine ?_\n \u00b7 match k with \| 0 => norm_num \| 1 => norm_num \| 2 => exact hW.2 \| _ => refine ?_", "compiler_output_preview": "[path]:58:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 13\nhM : Nat.GivesMersennePrime 13\nhW : Nat.GivesWagstaffPrime 13\n\u22a2 False\n[path]:60:9: error: unsolved goals\ncase h.h.h.h\np : \u2115\nhp : Odd 19\nhM : Nat.GivesMersennePrime 19\nhW : Nat.GivesWagstaffPrime 19\n\u22a2 \n...<truncated>" } ], "verification": { "banned_tokens": [], "command": [ "[path] "lean", "[path] ], "duration_s": 8.0054030418396, "goals_remaining": 10, "is_verified": false, "lean_file_path": "[path] "problem": { "axioms_check_name": "new_mersenne_conjecture", "axioms_check_skipped": false, "benchmark_id": "Wikipedia__Mersenne__new_mersenne_conjecture", "category": "research_open", "endings": [ "end Mersenne" ], "imports": [ "FormalConjectures.Util.ProblemImports" ], "preamble_chars": 1173, "source_file": "FormalConjectures/Wikipedia/Mersenne.lean", "title": "new_mersenne_conjecture" }, "returncode": 1, "status": "partial", "stderr": "", "stdout": "[path]:67:9: error: unsolved goals\ncase h\np : \u2115\nn : \u2115 := 2 ^ p - 1\nm : \u2115 := (2 ^ p + 1) / 3\nhp : Odd 61\nhM : Nat.Prime (2 ^ 61 - 1)\nhW : Odd 61 \u2227 Nat.Prime ((2 ^ 61 + 1) / 3)\n\u22a2 False\n[path]:68:8: error: unsolved goals\np : \u2115\nn : \u2115 := 2 ^ p - 1\nm : \u2115 := (2 ^ p + 1) / 3\nx\u271d : \u2115\nhp : Odd x\u271d\nhM : Nat.Prime (2 ^ x\u271d - 1)\nhW : Odd x\u271d \u2227 Nat.Prime ((2 ^ x\u271d + 1) / 3)\n\u22a2 \u2203 k, x\u271d = 2 ^ k + 1 \u2228 x\u271d = 2 ^ k - 1 \u2228 x\u271d = 4 ^ k + 3 \u2228 x\u271d = 4 ^ k - 3\n[path]:77:6: error: unsolved goals\ncase right.inl\np : \u2115\nhp : Odd p\nhM : Nat.Prime (2 ^ p - 1)\nk : \u2115\nh1 : 2 ^ k + 1 = 2 ^ k + 1\n\u22a2 Nat.Prime ((2 ^ (2 ^ k + 1) + 1) / 3)\n[path]:79:6: error: unsolved goals\ncase right.inr.inl\np : \u2115\nhp : Odd p\nhM : Nat.Prime (2 ^ p - 1)\nk : \u2115\nh2 : 2 ^ k - 1 = 2 ^ k - 1\n\u22a2 Nat.Prime ((2 ^ (2 ^ k - 1) + 1) / 3)\n[path]:81:6: error: unsolved goals\ncase right.inr.inr.inl\np : \u2115\nhp : Odd p\nhM : Nat.Prime (2 ^ p - 1)\nk : \u2115\nh3 : 4 ^ k + 3 = 4 ^ k + 3\n\u22a2 Nat.Prime ((2 ^ (4 ^ k + 3) + 1) / 3)\n[path]:83:6: error: unsolved goals\ncase right.inr.inr.inr\np : \u2115\nhp : Odd p\nhM : Nat.Prime (2 ^ p - 1)\nk : \u2115\nh4 : 4 ^ k - 3 = 4 ^ k - 3\n\u22a2 Nat.Prime ((2 ^ (4 ^ k - 3) + 1) / 3)\n[path]:90:6: error: unsolved goals\ncase right.right.intro.intro.inl\np : \u2115\nhp : Odd p\nhW : Odd p \u2227 Nat.Prime ((2 ^ p + 1) / 3)\nk : \u2115\nh1 : 2 ^ k + 1 = 2 ^ k + 1\n\u22a2 Nat.Prime (2 ^ (2 ^ k + 1) - 1)\n[path]:92:6: error: unsolved goals\ncase right.right.intro.intro.inr.inl\np : \u2115\nhp : Odd p\nhW : Odd p \u2227 Nat.Prime ((2 ^ p + 1) / 3)\nk : \u2115\nh2 : 2 ^ k - 1 = 2 ^ k - 1\n\u22a2 Nat.Prime (2 ^ (2 ^ k - 1) - 1)\n[path]:94:6: error: unsolved goals\ncase right.right.intro.intro.inr.inr.inl\np : \u2115\nhp : Odd p\nhW : Odd p \u2227 Nat.Prime ((2 ^ p + 1) / 3)\nk : \u2115\nh3 : 4 ^ k + 3 = 4 ^ k + 3\n\u22a2 Nat.Prime (2 ^ (4 ^ k + 3) - 1)\n[path]:96:6: error: unsolved goals\ncase right.right.intro.intro.inr.inr.inr\np : \u2115\nhp : Odd p\nhW : Odd p \u2227 Nat.Prime ((2 ^ p + 1) / 3)\nk : \u2115\nh4 : 4 ^ k - 3 = 4 ^ k - 3\n\u22a2 Nat.Prime (2 ^ (4 ^ k - 3) - 1)\n[path]:63:25: warning: This simp argument is unused:\n Or.comm\n\nHint: Omit it from the simp argument list.\n simp \u0335[\u0335O\u0335r\u0335.\u0335c\u0335o\u0335m\u0335m\u0335]\u0335\n\nNote: This linter can be disabled with `set_option linter.unusedSimpArgs false`\n'Mersenne.new_mersenne_conjecture' depends on axioms: [propext, sorryAx]\n", "timed_out": false } }
Gemini 3 Flash Preview	Partial	9	Feb 14, 2026	unfold NewMersenneConjectureStatement constructor · intro h rcases h with ⟨h1, h2⟩ unfold Nat.GivesMersennePrime at h1 unfold Nat.GivesWagstaffPrime at h2 unfold Nat.IsSpecialForm aesop · constructor · intro h rcases h with ⟨h1, h2⟩ unfold Nat.GivesMersennePrime at h1 unfold Nat.IsSpecialForm at h2 unfold Nat.GivesWagstaffPrime refine ⟨hp, ?_⟩ aesop · intro h rcases h with ⟨h1, h2⟩ unfold Nat.GivesWagstaffPrime at h1 unfold Nat.IsSpecialForm at h2 unfold Nat.GivesMersennePrime aesop	View { "generation": { "attempts": 1, "banned_tokens_found": [], "elapsed_s": 3.64, "finish_reason": "stop", "max_tokens": 8192, "model_id": "google/gemini-3-flash-preview", "proof_code_length": 545, "raw_content_length": 1505, "reasoning_effort": "", "structured_output": true, "temperature": 0.0, "usage": { "completion_tokens": 468, "completion_tokens_details": { "image_tokens": 0, "reasoning_tokens": 0 }, "cost": 0.0023965, "cost_details": { "upstream_inference_completions_cost": 0.001404, "upstream_inference_cost": 0.0023965, "upstream_inference_prompt_cost": 0.0009925 }, "is_byok": false, "prompt_tokens": 1985, "prompt_tokens_details": { "audio_tokens": 0, "cache_write_tokens": 0, "cached_tokens": 0, "video_tokens": 0 }, "total_tokens": 2453 } }, "verification": { "banned_tokens": [], "command": [ "[path] "lean", "[path] ], "duration_s": 11.401841878890991, "goals_remaining": 9, "is_verified": false, "lean_file_path": "[path] "problem": { "benchmark_id": "Wikipedia__Mersenne__new_mersenne_conjecture", "category": "research_open", "endings": [ "end Mersenne" ], "imports": [ "FormalConjectures.Util.ProblemImports" ], "preamble_chars": 1173, "source_file": "FormalConjectures/Wikipedia/Mersenne.lean", "title": "new_mersenne_conjecture" }, "returncode": 1, "status": "partial", "stderr": "", "stdout": "[path]:58:4: error: aesop: failed to prove the goal after exhaustive search.\n[path]:53:2: error: unsolved goals\ncase left.intro\np : \u2115\nh1 : Nat.Prime (2 ^ p - 1)\nleft : Odd p\nright : Nat.Prime ((2 ^ p + 1) / 3)\n\u22a2 \u2203 k, p = 2 ^ k + 1 \u2228 p = 2 ^ k - 1 \u2228 p = 4 ^ k + 3 \u2228 p = 4 ^ k - 3\n[path]:66:6: error: aesop: failed to prove the goal after exhaustive search.\n[path]:60:4: error: unsolved goals\ncase right.left.intro.inl\nw : \u2115\nhp : Odd (2 ^ w + 1)\nh1 : Nat.Prime (2 ^ (2 ^ w + 1) - 1)\n\u22a2 Nat.Prime ((2 ^ (2 ^ w + 1) + 1) / 3)\n\ncase right.left.intro.inr.inl\nw : \u2115\nhp : Odd (2 ^ w - 1)\nh1 : Nat.Prime (2 ^ (2 ^ w - 1) - 1)\n\u22a2 Nat.Prime ((2 ^ (2 ^ w - 1) + 1) / 3)\n\ncase right.left.intro.inr.inr.inl\nw : \u2115\nhp : Odd (4 ^ w + 3)\nh1 : Nat.Prime (2 ^ (4 ^ w + 3) - 1)\n\u22a2 Nat.Prime ((2 ^ (4 ^ w + 3) + 1) / 3)\n\ncase right.left.intro.inr.inr.inr\nw : \u2115\nhp : Odd (4 ^ w - 3)\nh1 : Nat.Prime (2 ^ (4 ^ w - 3) - 1)\n\u22a2 Nat.Prime ((2 ^ (4 ^ w - 3) + 1) / 3)\n[path]:72:6: error: aesop: failed to prove the goal after exhaustive search.\n[path]:67:4: error: unsolved goals\ncase right.right.intro.inl\nw : \u2115\nleft : Odd (2 ^ w + 1)\nright : Nat.Prime ((2 ^ (2 ^ w + 1) + 1) / 3)\n\u22a2 Nat.Prime (2 ^ (2 ^ w + 1) - 1)\n\ncase right.right.intro.inr.inl\nw : \u2115\nleft : Odd (2 ^ w - 1)\nright : Nat.Prime ((2 ^ (2 ^ w - 1) + 1) / 3)\n\u22a2 Nat.Prime (2 ^ (2 ^ w - 1) - 1)\n\ncase right.right.intro.inr.inr.inl\nw : \u2115\nleft : Odd (4 ^ w + 3)\nright : Nat.Prime ((2 ^ (4 ^ w + 3) + 1) / 3)\n\u22a2 Nat.Prime (2 ^ (4 ^ w + 3) - 1)\n\ncase right.right.intro.inr.inr.inr\nw : \u2115\nleft : Odd (4 ^ w - 3)\nright : Nat.Prime ((2 ^ (4 ^ w - 3) + 1) / 3)\n\u22a2 Nat.Prime (2 ^ (4 ^ w - 3) - 1)\n", "timed_out": false } }

new_mersenne_conjecture

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