Proves density-one asymptotic f_c(n)=(c/(1-γ)+o(1))log n with Gaussian fluctuations for the small-prime threshold in binomial coefficients.
Short proofs in combinatorics and number theory
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Soohak is a 439-problem mathematician-curated benchmark where frontier LLMs reach at most 30.4% on research math challenges and no model exceeds 50% on refusal for ill-posed problems.
f(n) exceeds (C-o(1)) log n for any fixed C>1 and infinitely many n, so limsup f(n)/log n is infinite.
Proves R(B_8, B_10) = 37 via an AI-assisted short proof with a Lean formalization of the upper bound.
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An automated proof that R(B_8,B_10)=37
Proves R(B_8, B_10) = 37 via an AI-assisted short proof with a Lean formalization of the upper bound.