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Erdős problem 1095 - log is Theta · Conjectures.io
Number theory
Erdős problem 1095 - log is Theta
Sorenson, Sorenson, and Webster [SSWE20] give heuristic evidence that logg(k)≍logkk.
0 α bounty·1 piece from 1 person·last one 26 days ago
week of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing publishedweek of 8 Nov 2025 · nothing publishedweek of 15 Nov 2025 · nothing published
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A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
11 Oct 2025a year of work on this problem3 Oct 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.
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