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declared openerdos:684
For the least kk at which the small-prime part of (nk)\binom{n}{k} exceeds n2n^2, how large can f(n)f(n) be?
number theoryprimesbinomial coefficientsA392019 · possible3 sources
declared proved (Lean) · formalizederdos:997
True ↔ ∀ (α : ℝ), ¬Erdos997.IsWellDistributed fun n => Int.fract (α * ↑(Nat.nth Nat.Prime n))
analysisdiscrepancyprimesN/A6 sources
declared disproved (Lean) · formalizederdos:1138
False ↔ ∀ C > 1, Asymptotics.IsEquivalent Erdos1138.snd_gt_half_fst (Erdos1138.primeCount_Ioc_mul_const C) fun x => match x with | (x, y) => C * ↑(Erdos1138.sup_primeGap x) / Real.log y
number theoryprimespossible6 sources
declared disproved (Lean) · formalizederdos:1141
False ↔ Infinite ↑{n | Erdos1141.Erdos1141Prop n}
number theoryprimesA2145836 sources
declared open · formalizederdos:1201
Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta, where P(m)P(m) is the greatest prime divisor of mm? A short argument via the Matomäki-Radziwiłł theorem establishes the lower-density version.
number theoryprimespossible4 sources
declared solvederdos:1202
Erdős problem 1202
number theoryprimespossible3 sources

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