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erdos-lean

A collection of Lean proofs for problems from erdosproblems.com.

Each proof is self-contained. Every ErdosN.lean file's only import is import Mathlib, with no cross-references to other files in the repository. Additionally, some proofs depend on extra axioms declared in the proof itself, or on mechanisms that expand Lean's trusted base. The table below shows the state of each problem and any axioms or trust extensions it relies on (state definitions live in schema/problems.schema.json). Original sources are recorded in the sources field of data/problems.yaml.

For problem N, problems/N/ contains:

  • ErdosN.lean: the proof
  • lakefile.toml: package erdosN, Mathlib revision, library ErdosN
  • lean-toolchain: the Lean version
  • lake-manifest.json: dependency lockfile

Verify with:

cd problems/N
lake exe cache get
lake build

Catalog

199 proofs in the catalog (out of 199 Erdős problems with formalized solutions):

  • 182 complete
  • 3 trust_extended
  • 14 axiomatic
# State Lean Notes
16 complete problems/16/
24 complete problems/24/
26 complete problems/26/
31 complete problems/31/
34 complete problems/34/
38 complete problems/38/
42 complete problems/42/
45 complete problems/45/
46 complete problems/46/
47 complete problems/47/
56 complete problems/56/
71 complete problems/71/
90 axiomatic problems/90/ assumes Theorem 3.9.7 of Neukirch–Schmidt–Wingberg (golod_shafarevich_inequality) and Theorem 5.1 of Mayer (shafarevich_relation_rank_bound)
93 complete problems/93/
94 complete problems/94/
105 complete problems/105/
115 complete problems/115/
125 complete problems/125/
134 complete problems/134/
150 complete problems/150/
154 complete problems/154/
164 complete problems/164/
178 complete problems/178/
189 complete problems/189/
192 trust_extended problems/192/ uses native_decide
194 complete problems/194/
198 complete problems/198/
199 complete problems/199/
202 complete problems/202/
204 complete problems/204/
205 complete problems/205/
206 complete problems/206/
209 complete problems/209/
214 complete problems/214/
221 complete problems/221/
224 complete problems/224/
226 complete problems/226/
229 complete problems/229/
231 trust_extended problems/231/ uses native_decide
237 axiomatic problems/237/ assumes an intermediate result on page 7 in the proof of Theorem 1.1 of Maynard (maynard_prime_tuples)
246 complete problems/246/
258 axiomatic problems/258/ assumes Theorem 1.1 of Tao–Teräväinen (tao_teravainen)
259 complete problems/259/
268 complete problems/268/
275 complete problems/275/
280 complete problems/280/
281 complete problems/281/
283 complete problems/283/
290 complete problems/290/
296 complete problems/296/
298 complete problems/298/
299 complete problems/299/
303 complete problems/303/
314 complete problems/314/
315 complete problems/315/
316 complete problems/316/
328 complete problems/328/
330 complete problems/330/
331 complete problems/331/
333 complete problems/333/
337 complete problems/337/
347 complete problems/347/
350 complete problems/350/
351 complete problems/351/
353 complete problems/353/
355 complete problems/355/
363 complete problems/363/
369 complete problems/369/
370 complete problems/370/
379 complete problems/379/
392 complete problems/392/
397 complete problems/397/
399 complete problems/399/
401 complete problems/401/
403 complete problems/403/
418 trust_extended problems/418/ uses native_decide
419 complete problems/419/
426 complete problems/426/
427 axiomatic problems/427/ assumes Theorem 1 of Shiu (shiu_consecutive_primes)
429 complete problems/429/
433 complete problems/433/
434 complete problems/434/
435 complete problems/435/
443 complete problems/443/
447 complete problems/447/
453 complete problems/453/
457 complete problems/457/
459 complete problems/459/
464 complete problems/464/
476 complete problems/476/
481 complete problems/481/
484 complete problems/484/
487 complete problems/487/
490 axiomatic problems/490/ assumes prime bounds of Dusart: Theorem 3.3 (dusart_chebyshev), equation 5.4 of Corollary 5.2 (dusart_pi_lower, dusart_pi_upper), and Theorem 5.9 (dusart_mertens_product)
493 complete problems/493/
497 complete problems/497/
498 complete problems/498/
499 complete problems/499/
502 complete problems/502/
505 complete problems/505/
512 complete problems/512/
519 complete problems/519/
532 complete problems/532/
537 complete problems/537/
540 complete problems/540/
541 complete problems/541/
582 complete problems/582/
610 axiomatic problems/610/ assumes Corollary 2 of Joret–Micek–Reed–Smid (jmrs_theorem) and Theorem 1.1 of Kim (kim_theorem)
613 complete problems/613/
618 complete problems/618/
619 complete problems/619/
621 complete problems/621/
639 complete problems/639/
645 complete problems/645/
646 complete problems/646/
648 complete problems/648/
649 complete problems/649/
650 complete problems/650/
658 axiomatic problems/658/ assumes Theorem 2.2 of Solymosi (frankl_roedl_theorem)
659 axiomatic problems/659/ assumes Theorems 1 and 2 on page 92 of Bernays (bernays)
666 complete problems/666/
674 complete problems/674/
678 complete problems/678/
692 complete problems/692/
694 axiomatic problems/694/ assumes equation 2 of Linnik (linnik_dvd)
696 axiomatic problems/696/ assumes equation 22 of Walfisz (siegel_walfisz)
698 complete problems/698/
707 complete problems/707/
716 complete problems/716/
728 complete problems/728/
729 complete problems/729/
741 complete problems/741/
751 complete problems/751/
753 complete problems/753/
756 complete problems/756/
760 complete problems/760/
762 complete problems/762/
765 complete problems/765/
775 complete problems/775/
785 complete problems/785/
794 complete problems/794/
798 complete problems/798/
818 complete problems/818/
844 complete problems/844/
845 complete problems/845/
846 complete problems/846/
862 complete problems/862/
867 complete problems/867/
871 complete problems/871/
897 complete problems/897/
898 complete problems/898/
904 complete problems/904/
905 complete problems/905/
907 complete problems/907/
914 complete problems/914/
923 complete problems/923/
927 complete problems/927/
947 complete problems/947/
958 complete problems/958/
964 axiomatic problems/964/ assumes Theorem 1 of Eberhard (goldston_graham_pintz_yildirim)
966 complete problems/966/
967 complete problems/967/
974 complete problems/974/
990 complete problems/990/
997 axiomatic problems/997/ assumes Corollary 3 of Banks–Freiberg–Turnage-Butterbaugh (maynardTaoBFT)
1000 complete problems/1000/
1007 complete problems/1007/
1008 complete problems/1008/
1014 complete problems/1014/
1022 complete problems/1022/
1023 complete problems/1023/
1026 complete problems/1026/
1028 complete problems/1028/
1034 complete problems/1034/
1036 complete problems/1036/
1037 complete problems/1037/
1043 complete problems/1043/
1044 complete problems/1044/
1047 complete problems/1047/
1048 complete problems/1048/
1051 complete problems/1051/
1067 complete problems/1067/
1071 complete problems/1071/
1080 complete problems/1080/
1090 complete problems/1090/
1098 complete problems/1098/
1102 complete problems/1102/
1121 complete problems/1121/
1125 complete problems/1125/
1126 complete problems/1126/
1134 complete problems/1134/
1136 complete problems/1136/
1138 complete problems/1138/
1141 axiomatic problems/1141/ assumes Theorem 1.3 of Pollack (pollack_theorem_1_3)
1148 axiomatic problems/1148/ assumes an immediate consequence of Theorem 2.3 of Einsiedler–Lindenstrauss–Michel–Venkatesh (theorem_2_3)
1190 complete problems/1190/
1193 complete problems/1193/
1196 complete problems/1196/
1197 complete problems/1197/

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A collection of Lean proofs for problems from erdosproblems.com.

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