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Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Number theory
Erdős problem 1095 - log is Theta
Sorenson, Sorenson, and Webster [SSWE20] give heuristic evidence that logg(k)≍logkk.
$2,379 bounty
·1 piece from 1 person
·last one 12 days ago
week of 28 Sept 2025 · nothing publishedweek of 5 Oct 2025 · nothing publishedweek of 12 Oct 2025 · nothing publishedweek of 19 Oct 2025 · nothing publishedweek of 26 Oct 2025 · nothing publishedweek of 2 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
28 Sept 2025a year of work on this problem20 Sept 2026
erdosproblems.com/1095
[EES74] Ecklund, Jr., E. F. and Erd\H{o}s, P. and Selfridge, J. L., A new function associated with the prime factors of {(\spn\sbk)}. Math. Comp. (1974), 647--649.
[ELS93] Erdős, P. and Lacampagne, C. B. and Selfridge, J. L., Estimates of the least prime factor of a binomial coefficient. Math. Comp. (1993), 215--224.
[GrRa96] Granville, Andrew and Ramaré, Olivier, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Mathematika (1996), 73--107.
[Ko99b] Konyagin, S. V., Estimates of the least prime factor of a binomial coefficient. Mathematika (1999), 41--55.
[SSW20] Sorenson, Brianna and Sorenson, Jonathan and Webster, Jonathan, An algorithm and estimates for the {E}rdős-{S}elfridge function. (2020), 371--385.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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