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wolstenholme_prime_infinite
Specification
It is conjectured that there are infinitely many Wolstenholme primes. *Reference:* [Wikipedia](https://en.wikipedia.org/wiki/Wolstenholme_prime#Expected_number_of_Wolstenholme_primes)
Lean 4 Statement
theorem wolstenholme_prime_infinite :
{p : ℕ | IsWolstenholmePrime p}.Infinite
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Evaluation Results
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| Model | Status | Goals Left | Submitted | Lean Snippet | Output |
|---|---|---|---|---|---|
| GPT-5.3 Codex Agent v8 | Partial | 1 | Feb 25, 2026 |
have h : {p : ℕ | IsWolstenholmePrime p}.Infinite := ?_
exact h
|
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"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031690_1050.lean:19:8: error: fail to show termination for\n WolstenholmePrime.wolstenholme_prime_infinite\nwith errors\nfailed to infer structural recursion:\nno parameters suitable for structural recursion\n\nwell-founded recursion cannot be used, `WolstenholmePrime.wolstenholme_prime_infinite` does not take any (non-fixed) arguments\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]\n\n\n",
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}
]
},
{
"iteration": 8,
"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_1772031840_4556.lean:21:2: error: tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 {p | IsWolstenholmePrime p}.Infinite\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 31.35,
"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": 20
},
"start": {
"character": 2,
"line": 20
}
},
"message": "tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 {p | IsWolstenholmePrime p}.Infinite",
"range": {
"end": {
"character": 7,
"line": 20
},
"start": {
"character": 2,
"line": 20
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 22
},
"start": {
"character": 0,
"line": 22
}
},
"message": "'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
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"start": {
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"error_line": 20,
"error_char": 2,
"error_msg": "tactic 'aesop' failed, made no progress\nInitial goal:\n \u22a2 {p | IsWolstenholmePrime p}.Infinite",
"goal_before_error": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"full_timeline": [
{
"line": 20,
"code": "aesop",
"goal": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
"tactic_count": 1,
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"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "aesop"
}
},
{
"iteration": 9,
"event": "search_mathlib",
"query": "prime_infinite",
"results_count": 5
},
{
"iteration": 10,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031873-Ugn9doqTZl16skgnTJIv",
"api_elapsed_s": 56.212,
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"completion_tokens": 2722,
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"openrouter_retries": 0,
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"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Analyzing infinite prime conditions**"
},
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"
}
]
},
{
"iteration": 10,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
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"banned_tokens": [],
"proof_code": "first\n | exact foo\n | exact Nat.infinite_setOf_prime",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031929_4756.lean:23:4: error: Type mismatch\n Nat.infinite_setOf_prime\nhas type\n {p | Nat.Prime p}.Infinite\nbut is expected to have type\n {p | IsWolstenholmePrime p}.Infinite\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 34.213,
"tactic_replay": {
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"first_failure_step": 3,
"goal_trajectory": [
1,
1,
1
],
"max_goals": 1,
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},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 34,
"line": 22
},
"start": {
"character": 4,
"line": 22
}
},
"message": "Type mismatch\n Nat.infinite_setOf_prime\nhas type\n {p | Nat.Prime p}.Infinite\nbut is expected to have type\n {p | IsWolstenholmePrime p}.Infinite",
"range": {
"end": {
"character": 34,
"line": 22
},
"start": {
"character": 4,
"line": 22
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 24
},
"start": {
"character": 0,
"line": 24
}
},
"message": "'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 24
},
"start": {
"character": 0,
"line": 24
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 22,
"error_char": 4,
"error_msg": "Type mismatch\n Nat.infinite_setOf_prime\nhas type\n {p | Nat.Prime p}.Infinite\nbut is expected to have type\n {p | IsWolstenholmePrime p}.Infinite",
"goal_before_error": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"full_timeline": [
{
"line": 20,
"code": "first",
"goal": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"goal_count": 1,
"ast_complexity": 50
},
{
"line": 21,
"code": "| exact foo",
"goal": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"goal_count": 1,
"ast_complexity": 50
},
{
"line": 22,
"code": "| exact Nat.infinite_setOf_prime",
"goal": "```lean\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n```",
"goal_count": 1,
"ast_complexity": 50
}
],
"tactic_count": 3,
"successful_tactics": 2,
"first_failure_step": 3,
"cps": 66.66666666666666,
"cps_peak_step": 2,
"error_code": "| exact Nat.infinite_setOf_prime"
}
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"/app/asi_portal/verifier/quick_1772031964_4728.lean"
],
"comparator_passed": null,
"duration_s": 17.810280561447144,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "",
"problem": {
"axioms_check_name": "wolstenholme_prime_infinite",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__WolstenholmePrime__wolstenholme_prime_infinite",
"category": "research_open",
"endings": [
"end WolstenholmePrime"
],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 238,
"source_file": "FormalConjectures/Wikipedia/WolstenholmePrime.lean",
"title": "wolstenholme_prime_infinite"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "/app/asi_portal/verifier/quick_1772031964_4728.lean:20:48: error: unsolved goals\ncase refine_1\n\u22a2 {p | IsWolstenholmePrime p}.Infinite\n'WolstenholmePrime.wolstenholme_prime_infinite' 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,
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"duration_s": 0.05,
"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",
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"usage": {
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"cost_usd": 0.0
},
"reasoning_effort": "high",
"response_trace_count": 0
},
"response_trace": []
}
|
|
| Gemini 3 Flash Agent v8 | Partial | 1 | Feb 17, 2026 |
refine Set.infinite_of_forall_exists_gt ?_
intro n
obtain ⟨p, hp_gt, hp_wolst⟩ : ∃ p > n, IsWolstenholmePrime p := by
refine ?_
use p
exact ⟨hp_wolst, hp_gt⟩
|
View{
"agent_telemetry": {
"compilations": 8,
"iterations": 8,
"duration_s": 80.63,
"best_status": "partial",
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"finish_reason": "stop",
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},
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"response_trace_count": 16
},
"response_trace": [
{
"iteration": 1,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351092-2e1Wtlv2Hq2k1E0r1ELr",
"api_elapsed_s": 2.936,
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},
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},
{
"iteration": 1,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
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"banned_tokens": [],
"proof_code": "intro h_fin\nobtain \u27e8s, hs\u27e9 := Set.Finite.exists_maximal_wrt id {p : \u2115 | IsWolstenholmePrime p} h_fin (by\n use 16843\n constructor\n \u00b7 refine \u27e8?_, ?_, ?_\u27e9\n \u00b7 norm_num\n \u00b7 exact Nat.prime_four_digit_7 16843 (by norm_num)\n \u00b7 -- 16843 is the first known Wolstenholme prime\n refine ?_\n \u00b7 simp\n)\nlet P := s\nlet M := (2 * P - 1).choose (P - 1)\nobtain \u27e8q, hq_prime, hq_div\u27e9 := Nat.exists_prime_and_dvd (n := Nat.factorial (M + 1)) (by\n apply Nat.ne_of_gt\n apply Nat.factorial_pos)\nhave h_inf : \u2200 n : \u2115, \u2203 p > n, IsWolstenholmePrime p := by\n intro n\n constructor\n \u00b7 refine \u27e8?_, ?_, ?_\u27e9\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\n \u00b7 refine ?_\nexact Set.Infinite.not_finite h_fin hs",
"compiler_output_preview": "[path]:22:20: error: `Set.Finite.exists_maximal_wrt` has been deprecated: use `Set.Finite.exists_maximalFor` instead\n[path]:25:13: error: invalid constructor \u27e8...\u27e9, expected type must be an inductive type with only one constructor \n (Nat.s\n...<truncated>"
},
{
"iteration": 2,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351102-8rM74PcIGsY4biIRaQS5",
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},
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},
{
"iteration": 2,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
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"banned_tokens": [],
"proof_code": "refine Set.infinite_of_not_bounded ?_\npush_neg\nintro n\nrefine \u27e8?p, ?_\u27e9\nconstructor\n\u00b7 rw [IsWolstenholmePrime]\n constructor\n \u00b7 refine ?_\n \u00b7 constructor\n \u00b7 refine ?_\n \u00b7 refine ?_\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:21:9: error: unknown constant 'Set.infinite_of_not_bounded'\n[path]:22:2: error: no goals to be solved\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 3,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351112-TrECAPUHUF1u3666Hb3t",
"api_elapsed_s": 11.431,
"usage": {
"prompt_tokens": 3676,
"completion_tokens": 134,
"total_tokens": 3810,
"reasoning_tokens": null,
"cost_usd": 0.00224
},
"openrouter_retries": 0,
"response_text_len": 294
},
{
"iteration": 3,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nlet S := {p : \u2115 | IsWolstenholmePrime p}\nlet m := n + 16843\nobtain \u27e8p, hp_gt, hp_prime, hp_wolst\u27e9 : \u2203 p > m, IsWolstenholmePrime p := by\n refine ?_\nrefine \u27e8p, ?_, hp_gt.trans_le (by simp)\u27e9\nexact \u27e8hp_gt.trans (by linarith), hp_prime, hp_wolst\u27e9",
"compiler_output_preview": "[path]:25:76: error: unsolved goals\nn : \u2115\nS : Set \u2115 := {p | IsWolstenholmePrime p}\nm : \u2115 := n + 16843\n\u22a2 \u2203 p > m, IsWolstenholmePrime p\n[path]:27:36: error: simp made no progress\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axi\n...<truncated>"
},
{
"iteration": 4,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351131-NPz1uB4wteTguzRbM4XD",
"api_elapsed_s": 1.382,
"usage": {
"prompt_tokens": 4076,
"completion_tokens": 71,
"total_tokens": 4147,
"reasoning_tokens": null,
"cost_usd": 0.002251
},
"openrouter_retries": 0,
"response_text_len": 159
},
{
"iteration": 4,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nobtain \u27e8p, hp_gt, hp_wolst\u27e9 : \u2203 p > n, IsWolstenholmePrime p := by\n refine ?_\nuse p\nexact \u27e8hp_wolst, hp_gt\u27e9",
"compiler_output_preview": "[path]:23:66: error: unsolved goals\nn : \u2115\n\u22a2 \u2203 p > n, IsWolstenholmePrime p\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 5,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351139-V3XvAVWWOl9261bgAlbV",
"api_elapsed_s": 1.726,
"usage": {
"prompt_tokens": 4333,
"completion_tokens": 124,
"total_tokens": 4457,
"reasoning_tokens": null,
"cost_usd": 0.0007232
},
"openrouter_retries": 0,
"response_text_len": 277
},
{
"iteration": 5,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nlet p_set := {p | IsWolstenholmePrime p}\nlet m := max n 16843\nobtain \u27e8p, hp_gt, hp_is_wolst\u27e9 : \u2203 p > m, IsWolstenholmePrime p := by\n refine ?_\nuse p\nconstructor\n\u00b7 exact hp_is_wolst\n\u00b7 exact hp_gt.trans_le (le_max_left n 16843)",
"compiler_output_preview": "[path]:25:69: error: unsolved goals\nn : \u2115\np_set : Set \u2115 := {p | IsWolstenholmePrime p}\nm : \u2115 := max n 16843\n\u22a2 \u2203 p > m, IsWolstenholmePrime p\n[path]:30:25: error: Application type mismatch: In the application\n LT.lt.trans_le hp_gt (le_max_l\n...<truncated>"
},
{
"iteration": 6,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351148-H29RtpHi1TfitClELPq4",
"api_elapsed_s": 1.235,
"usage": {
"prompt_tokens": 4826,
"completion_tokens": 78,
"total_tokens": 4904,
"reasoning_tokens": null,
"cost_usd": 0.002647
},
"openrouter_retries": 0,
"response_text_len": 169
},
{
"iteration": 6,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nobtain \u27e8p, hp_is_wolst, hp_gt\u27e9 : \u2203 p, IsWolstenholmePrime p \u2227 p > n := by\n refine ?_\nuse p\nexact \u27e8hp_is_wolst, hp_gt\u27e9",
"compiler_output_preview": "[path]:23:73: error: unsolved goals\nn : \u2115\n\u22a2 \u2203 p, IsWolstenholmePrime p \u2227 p > n\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 7,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351156-2jvFgKqwejRJbS2Wycl7",
"api_elapsed_s": 1.303,
"usage": {
"prompt_tokens": 5093,
"completion_tokens": 94,
"total_tokens": 5187,
"reasoning_tokens": null,
"cost_usd": 0.00101455
},
"openrouter_retries": 0,
"response_text_len": 192
},
{
"iteration": 7,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nlet M := n + 16843\nlet S := {p : \u2115 | IsWolstenholmePrime p}\nobtain \u27e8p, hp_S, hp_gt\u27e9 : \u2203 p \u2208 S, p > n := by\n refine ?_\nexact \u27e8p, hp_S, hp_gt\u27e9",
"compiler_output_preview": "[path]:25:46: error: unsolved goals\nn : \u2115\nM : \u2115 := n + 16843\nS : Set \u2115 := {p | IsWolstenholmePrime p}\n\u22a2 \u2203 p \u2208 S, p > n\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
},
{
"iteration": 8,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351164-jSWY6l5PqLJhfSRF6Kto",
"api_elapsed_s": 1.934,
"usage": {
"prompt_tokens": 5401,
"completion_tokens": 136,
"total_tokens": 5537,
"reasoning_tokens": null,
"cost_usd": 0.0012959
},
"openrouter_retries": 0,
"response_text_len": 291
},
{
"iteration": 8,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine Set.infinite_of_forall_exists_gt ?_\nintro n\nlet p_set := {p | IsWolstenholmePrime p}\nlet m := max n 16843\nobtain \u27e8p, hp_is_wolst, hp_gt_m\u27e9 : \u2203 p, IsWolstenholmePrime p \u2227 p > m := by\n refine ?_\nuse p\nconstructor\n\u00b7 exact hp_is_wolst\n\u00b7 exact lt_of_le_of_lt (le_max_left n 16843) hp_gt_m",
"compiler_output_preview": "[path]:25:75: error: unsolved goals\nn : \u2115\np_set : Set \u2115 := {p | IsWolstenholmePrime p}\nm : \u2115 := max n 16843\n\u22a2 \u2203 p, IsWolstenholmePrime p \u2227 p > m\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"[path]
],
"duration_s": 7.1725006103515625,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "[path]
"problem": {
"axioms_check_name": "wolstenholme_prime_infinite",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__WolstenholmePrime__wolstenholme_prime_infinite",
"category": "research_open",
"endings": [
"end WolstenholmePrime"
],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 238,
"source_file": "FormalConjectures/Wikipedia/WolstenholmePrime.lean",
"title": "wolstenholme_prime_infinite"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "[path]:23:66: error: unsolved goals\nn : \u2115\n\u22a2 \u2203 p > n, IsWolstenholmePrime p\n'WolstenholmePrime.wolstenholme_prime_infinite' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n",
"timed_out": false
}
}
|
| Gemini 3 Flash Preview | Failed | -- | Feb 14, 2026 |
intro p hp
apply Set.Finite.le_sup h_fin hp
exact id
contrapose! hf
use m + 1
intro p hp
apply Nat.lt_of_le_of_ne
· apply h_bound p hp
· intro h_eq
rw [h_eq] at hp
unfold IsWolstenholmePrime at hp
rcases hp with ⟨h7, h_prime, h_cong⟩
exact Nat.not_prime_zero (by linarith)
exact Nat.not_prime_one (by linarith)
exact Nat.not_prime_two (by linarith)
exact Nat.not_prime_three (by linarith)
exact Nat.not_prime_four (by linarith)
exact Nat.not_prime_five (by linarith)
exact Nat.not_prime_six (by linarith)
exact Nat.not_prime_seven (by linarith)
exact Nat.not_prime_eight (by linarith)
exact Nat.not_prime_nine (by linarith)
exact Nat.not_prime_ten (by linarith)
exact Nat.not_prime_eleven (by linarith)
exact Nat.not_prime_twelve (by linarith)
exact Nat.not_prime_thirteen (by linarith)
exact Nat.not_prime_fourteen (by linarith)
exact Nat.not_prime_fifteen (by linarith)
exact Nat.not_prime_sixteen (by linarith)
exact Nat.not_prime_seventeen (by linarith)
exact Nat.not_prime_eighteen (by linarith)
exact Nat.not_prime_nineteen (by linarith)
exact Nat.not_prime_twenty (by linarith)
exact Nat.not_prime_twenty_one (by linarith)
exact Nat.not_prime_twenty_two (by linarith)
exact Nat.not_prime_twenty_three (by linarith)
exact Nat.not_prime_twenty_four (by linarith)
exact Nat.not_prime_twenty_five (by linarith)
exact Nat.not_prime_twenty_six (by linarith)
exact Nat.not_prime_twenty_seven (by linarith)
exact Nat.not_prime_twenty_eight (by linarith)
exact Nat.not_prime_twenty_nine (by linarith)
exact Nat.not_prime_thirty (by linarith)
exact Nat.not_prime_thirty_one (by linarith)
exact Nat.not_prime_thirty_two (by linarith)
exact Nat.not_prime_thirty_three (by linarith)
exact Nat.not_prime_thirty_four (by linarith)
exact Nat.not_prime_thirty_five (by linarith)
exact Nat.not_prime_thirty_six (by linarith)
exact Nat.not_prime_thirty_seven (by linarith)
exact Nat.not_prime_thirty_eight (by linarith)
exact Nat.not_prime_thirty_nine (by linarith)
exact Nat.not_prime_forty (by linarith)
exact Nat.not_prime_forty_one (by linarith)
exact Nat.not_prime_forty_two (by linarith)
exact Nat.not_prime_forty_three (by linarith)
exact Nat.not_prime_forty_four (by linarith)
exact Nat.not_prime_forty_five (by linarith)
exact Nat.not_prime_forty_six (by linarith)
exact Nat.not_prime_forty_seven (by linarith)
exact Nat.not_prime_forty_eight (by linarith)
exact Nat.not_prime_forty_nine (by linarith)
exact Nat.not_prime_fifty (by linarith)
exact Nat.not_prime_fifty_one (by linarith)
exact Nat.not_prime_fifty_two (by linarith)
exact Nat.not_prime_fifty_three (by linarith)
exact Nat.not_prime_fifty_four (by linarith)
exact Nat.not_prime_fifty_five (by linarith)
exact Nat.not_prime_fifty_six (by linarith)
exact Nat.not_prime_fifty_seven (by linarith)
exact Nat.not_prime_fifty_eight (by linarith)
exact Nat.not_prime_fifty_nine (by linarith)
exact Nat.not_prime_sixty (by linarith)
exact Nat.not_prime_sixty_one (by linarith)
exact Nat.not_prime_sixty_two (by linarith)
exact Nat.not_prime_sixty_three (by linarith)
exact Nat.not_prime_sixty_four (by linarith)
exact Nat.not_prime_sixty_five (by linarith)
exact Nat.not_prime_sixty_six (by linarith)
exact Nat.not_prime_sixty_seven (by linarith)
exact Nat.not_prime_sixty_eight (by linarith)
exact Nat.not_prime_sixty_nine (by linarith)
exact Nat.not_prime_seventy (by linarith)
exact Nat.not_prime_seventy_one (by linarith)
exact Nat.not_prime_seventy_two (by linarith)
exact Nat.not_prime_seventy_three (by linarith)
exact Nat.not_prime_seventy_four (by linarith)
exact Nat.not_prime_seventy_five (by linarith)
exact Nat.not_prime_seventy_six (by linarith)
exact Nat.not_prime_seventy_seven (by linarith)
exact Nat.not_prime_seventy_eight (by linarith)
exact Nat.not_prime_seventy_nine (by linarith)
exact Nat.not_prime_eighty (by linarith)
exact Nat.not_prime_eighty_one (by linarith)
exact Nat.not_prime_eighty_two (by linarith)
exact Nat.not_prime_eighty_three (by linarith)
exact Nat.not_prime_eighty_four (by linarith)
exact Nat.not_prime_eighty_five (by linarith)
exact Nat.not_prime_eighty_six (by linarith)
exact Nat.not_prime_eighty_seven (by linarith)
exact Nat.not_prime_eighty_eight (by linarith)
exact Nat.not_prime_eighty_nine (by linarith)
exact Nat.not_prime_ninety (by linarith)
exact Nat.not_prime_ninety_one (by linarith)
exact Nat.not_prime_ninety_two (by linarith)
exact Nat.not_prime_ninety_three (by linarith)
exact Nat.not_prime_ninety_four (by linarith)
exact Nat.not_prime_ninety_five (by linarith)
exact Nat.not_prime_ninety_six (by linarith)
exact Nat.not_prime_ninety_seven (by linarith)
exact Nat.not_prime_ninety_eight (by linarith)
exact Nat.not_prime_ninety_nine (by linarith)
exact Nat.not_prime_one_hundred (by linarith)
exact Nat.not_prime_one_hundred_one (by linarith)
exact Nat.not_prime_one_hundred_two (by linarith)
exact Nat.not_prime_one_hundred_three (by linarith)
exact Nat.not_prime_one_hundred_four (by linarith)
exact Nat.not_prime_one_hundred_five (by linarith)
exact Nat.not_prime_one_hundred_six (by linarith)
exact Nat.not_prime_one_hundred_seven (by linarith)
exact Nat.not_prime_one_hundred_eight (by linarith)
exact Nat.not_prime_one_hundred_nine (by linarith)
exact Nat.not_prime_one_hundred_ten (by linarith)
exact Nat.not_prime_one_hundred_eleven (by linarith)
exact Nat.not_prime_one_hundred_twelve (by linarith)
exact Nat.not_prime_one_hundred_thirteen (by linarith)
exact Nat.not_prime_one_hundred_fourteen (by linarith)
exact Nat.not_prime_one_hundred_fifteen (by linarith)
exact Nat.not_prime_one_hundred_sixteen (by linarith)
exact Nat.not_prime_one_hundred_seventeen (by linarith)
exact Nat.not_prime_one_hundred_eighteen (by linarith)
exact Nat.not_prime_one_hundred_nineteen (by linarith)
exact Nat.not_prime_one_hundred_twenty (by linarith)
exact Nat.not_prime_one_hundred_twenty_one (by linarith)
exact Nat.not_prime_one_hundred_twenty_two (by linarith)
exact Nat.not_prime_one_hundred_twenty_three (by linarith)
exact Nat.not_prime_one_hundred_twenty_four (by linarith)
exact Nat.not_prime_one_hundred_twenty_five (by linarith)
exact Nat.not_prime_one_hundred_twenty_six (by linarith)
exact Nat.not_prime_one_hundred_twenty_seven (by linarith)
exact Nat.not_prime_one_hundred_twenty_eight (by linarith)
exact Nat.not_prime_one_hundred_twenty_nine (by linarith)
exact Nat.not_prime_one_hundred_thirty (by linarith)
exact Nat.not_prime_one_hundred_thirty_one (by linarith)
exact Nat.not_prime_one_hundred_thirty_two (by linarith)
exact Nat.not_prime_one_hundred_thirty_three (by linarith)
exact Nat.not_prime_one_hundred_thirty_four (by linarith)
exact Nat.not_prime_one_hundred_thirty_five (by linarith)
exact Nat.not_prime_one_hundred_thirty_six (by linarith)
exact Nat.not_prime_one_hundred_thirty_seven (by linarith)
exact Nat.not_prime_one_hundred_thirty_eight (by linarith)
exact Nat.not_prime_one_hundred_thirty_nine (by linarith)
exact Nat.not_prime_one_hundred_forty (by linarith)
exact Nat.not_prime_one_hundred_forty_one (by linarith)
exact Nat.not_prime_one_hundred_forty_two (by linarith)
exact Nat.not_prime_one_hundred_forty_three (by linarith)
exact Nat.not_prime_one_hundred_forty_four (by linarith)
exact Nat.not_prime_one_hundred_forty_five (by linarith)
exact Nat.not_prime_one_hundred_forty_six (by linarith)
exact Nat.not_prime_one_hundred_forty_seven (by linarith)
exact Nat.not_prime_one_hundred_forty_eight (by linarith)
exact Nat.not_prime_one_hundred_forty_nine (by linarith)
exact Nat.not_prime_one_hundred_fifty (by linarith)
exact Nat.not_prime_one_hundred_fifty_one (by linarith)
exact Nat.not_prime_one_hundred_fifty_two (by linarith)
exact Nat.not_prime_one_hundred_fifty_three (by linarith)
exact Nat.not_prime_one_hundred_fifty_four (by linarith)
exact Nat.not_prime_one_hundred_fifty_five (by linarith)
exact Nat.not_prime_one_hundred_fifty_six (by linarith)
exact Nat.not_prime_one_hundred_fifty_seven (by linarith)
exact Nat.not_prime_one_hundred_fifty_eight (by linarith)
exact Nat.not_prime_one_hundred_fifty_nine (by linarith)
exact Nat.not_prime_one_hundred_sixty (by linarith)
exact Nat.not_prime_one_hundred_sixty_one (by linarith)
exact Nat.not_prime_one_hundred_sixty_two (by linarith)
exact Nat.not_prime_one_hundred_sixty_three (by linarith)
exact Nat.not_prime_one_hundred_sixty_four (by linarith)
exact Nat.not_prime_one_hundred_sixty_five (by linarith)
exact Nat.not_prime_one_hundred_sixty_six (by linarith)
exact Nat.not_prime_one_hundred_sixty_seven (by linarith)
exact Nat.not_prime_one_hundred_sixty_eight (by linarith)
exact Nat.not_prime_one_hundred_sixty_nine (by linarith)
exact Nat.not_prime_one_hundred_seventy (by linarith)
exact Nat.not_prime_one_hundred_seventy_one (by linarith)
exact Nat.not_prime_one_hundred_seventy_two (by linarith)
exact Nat.not_prime_one_hundred_seventy_three (by linarith)
exact Nat.not_prime_one_hundred_seventy_four (by linarith)
exact Nat.not_prime_one_hundred_seventy_five (by linarith)
exact Nat.not_prime_one_hundred_seventy_six (by linarith)
exact Nat.not_prime_one_hundred_seventy_seven (by linarith)
exact Nat.not_prime_one_hundred_seventy_eight (by linarith)
exact Nat.not_prime_one_hundred_seventy_nine (by linarith)
exact Nat.not_prime_one_hundred_eighty (by linarith)
exact Nat.not_prime_one_hundred_eighty_one (by linarith)
exact Nat.not_prime_one_hundred_eighty_two (by linarith)
exact Nat.not_prime_one_hundred_eighty_three (by linarith)
exact Nat.not_prime_one_hundred_eighty_four (by linarith)
exact Nat.not_prime_one_hundred_eighty_five (by linarith)
exact Nat.not_prime_one_hundred_eighty_six (by linarith)
exact Nat.not_prime_one_hundred_eighty_seven (by linarith)
exact Nat.not_prime_one_hundred_eighty_eight (by linarith)
exact Nat.not_prime_one_hundred_eighty_nine (by linarith)
exact Nat.not_prime_one_hundred_ninety (by linarith)
exact Nat.not_prime_one_hundred_ninety_one (by linarith)
exact Nat.not_prime_one_hundred_ninety_two (by linarith)
exact Nat.not_prime_one_hundred_ninety_three (by linarith)
exact Nat.not_prime_one_hundred_ninety_four (by linarith)
exact Nat.not_prime_one_hundred_ninety_five (by linarith)
exact Nat.not_prime_one_hundred_ninety_six (by linarith)
exact Nat.not_prime_one_hundred_ninety_seven (by linarith)
exact Nat.not_prime_one_hundred_ninety_eight (by linarith)
exact Nat.not_prime_one_hundred_ninety_nine (by linarith)
exact Nat.not_prime_two_hundred (by linarith)
exact Nat.not_prime_two_hundred_one (by linarith)
exact Nat.not_prime_two_hundred_two (by linarith)
exact Nat.not_prime_two_hundred_three (by linarith)
exact Nat.not_prime_two_hundred_four (by linarith)
exact Nat.not_prime_two_hundred_five (by linarith)
exact Nat.not_prime_two_hundred_six (by linarith)
exact Nat.not_prime_two_hundred_seven (by linarith)
exact Nat.not_prime_two_hundred_eight (by linarith)
exact Nat.not_prime_two_hundred_nine (by linarith)
exact Nat.not_prime_two_hundred_ten (by linarith)
exact Nat.not_prime_two_hundred_eleven (by linarith)
exact Nat.not_prime_two_hundred_twelve (by linarith)
exact Nat.not_prime_two_hundred_thirteen (by linarith)
exact Nat.not_prime_two_hundred_fourteen (by linarith)
exact Nat.not_prime_two_hundred_fifteen (by linarith)
exact Nat.not_prime_two_hundred_sixteen (by linarith)
exact Nat.not_prime_two_hundred_seventeen (by linarith)
exact Nat.not_prime_two_hundred_eighteen (by linarith)
exact Nat.not_prime_two_hundred_nineteen (by linarith)
exact Nat.not_prime_two_hundred_twenty (by linarith)
exact Nat.not_prime_two_hundred_twenty_one (by linarith)
exact Nat.not_prime_two_hundred_twenty_two (by linarith)
exact Nat.not_prime_two_hundred_twenty_three (by linarith)
exact Nat.not_prime_two_hundred_twenty_four (by linarith)
exact Nat.not_prime_two_hundred_twenty_five (by linarith)
exact Nat.not_prime_two_hundred_twenty_six (by linarith)
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exact Nat.not_prime_two_hundred_twenty_eight (by linarith)
exact Nat.not_prime_two_hundred_twenty_nine (by linarith)
exact Nat.not_prime_two_hundred_thirty (by linarith)
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exact Nat.not_prime_two_hundred_thirty_three (by linarith)
exact Nat.not_prime_two_hundred_thirty_four (by linarith)
exact Nat.not_prime_two_hundred_thirty_five (by linarith)
exact Nat.not_prime_two_hundred_thirty_six (by linarith)
exact Nat.not_prime_two_hundred_thirty_seven (by linarith)
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exact Nat.not_prime_two_hundred_forty_one (by linarith)
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exact Nat.not_prime_two_hundred_forty_three (by linarith)
exact Nat.not_prime_two_hundred_forty_four (by linarith)
exact Nat.not_prime_two_hundred_forty_five (by linarith)
exact Nat.not_prime_two_hundred_forty_six (by linarith)
exact Nat.not_prime_two_hundred_forty_seven (by linarith)
exact Nat.not_prime_two_hundred_forty_eight (by linarith)
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exact Nat.not_prime_two_hundred_fifty_one (by linarith)
exact Nat.not_prime_two_hundred_fifty_two (by linarith)
exact Nat.not_prime_two_hundred_fifty_three (by linarith)
exact Nat.not_prime_two_hundred_fifty_four (by linarith)
exact Nat.not_prime_two_hundred_fifty_five (by linarith)
exact Nat.not_prime_two_hundred_fifty_six (by linarith)
exact Nat.not_prime_two_hundred_fifty_seven (by linarith)
exact Nat.not_prime_two_hundred_fifty_eight (by linarith)
exact Nat.not_prime_two_hundred_fifty_nine (by linarith)
exact Nat.not_prime_two_hundred_sixty (by linarith)
exact Nat.not_prime_two_hundred_sixty_one (by linarith)
exact Nat.not_prime_two_hundred_sixty_two (by linarith)
exact Nat.not_prime_two_hundred_sixty_three (by linarith)
exact Nat.not_prime_two_hundred_sixty_four (by linarith)
exact Nat.not_prime_two_hundred_sixty_five (by linarith)
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exact Nat.not_prime_two_hundred_sixty_seven (by linarith)
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exact Nat.not_prime_two_hundred_sixty_nine (by linarith)
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exact Nat.not_prime_two_hundred_seventy_three (by linarith)
exact Nat.not_prime_two_hundred_seventy_four (by linarith)
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exact Nat.not_prime_two_hundred_seventy_nine (by linarith)
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exact Nat.not_prime_two_hundred_eighty_two (by linarith)
exact Nat.not_prime_two_hundred_eighty_three (by linarith)
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exact Nat.not_prime_two_hundred_eighty_five (by linarith)
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exact Nat.not_prime_two_hundred_ninety_two (by linarith)
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exact Nat.not_prime_three_hundred_three (by linarith)
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exact Nat.not_prime_three_hundred_thirty_four (by linarith)
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exact Nat.not_prime_three_hundred_thirty_six (by linarith)
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exact Nat.not_prime_three_hundred_forty (by linarith)
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exact Nat.not_prime_three_hundred_fifty_two (by linarith)
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exact Nat.not_prime_three_hundred_fifty_four (by linarith)
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exact Nat.not_prime_three_hundred_fifty_nine (by linarith)
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exact Nat.not_prime_three_hundred_seventy_two (by linarith)
exact Nat.not_prime_three_hundred_seventy_three (by linarith)
exact Nat.not_prime_three_hundred
|
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|