Every problem here was open when it entered the pool.
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 - lower conjecture
Erdős, Lacampagne, and Selfridge [ELS93] write 'it is clear to every right-thinking person' that
g(k)≥exp(clogkk) for some constant c>0
.
$2,689 bounty·1 piece from 1 person·last one 12 days ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
27 Sept 2025a year of work on this problem19 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.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.