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61 problems · 2/2NumberSourcesGraph view
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 open · formalizederdos:1139
True ↔ Filter.limsup (fun k => (↑↑(Nat.nth (fun n => 0 < n ∧ ArithmeticFunction.cardFactors n ≤ 2) (k + 1)) - ↑↑(Nat.nth (fun n => 0 < n ∧ ArithmeticFunction.cardFactors n ≤ 2) k)) / ↑(Real.log (↑k + 1))) Filter.atTop = ⊤
number theoryprimesA037143 · A1010413 sources
declared disproved (Lean) · formalizederdos:1141
False ↔ Infinite ↑{n | Erdos1141.Erdos1141Prop n}
number theoryprimesA2145836 sources
declared open · formalizederdos:1142
sorry ↔ Infinite ↑{n | Erdos1142.Erdos1142Prop n}
number theoryprimesA0396692 sources
declared openerdos:1143
Erdős problem 1143
number theoryprimesN/A2 sources
declared openerdos:1184
Erdős problem 1184
number theoryprimespossible
declared solvederdos:1187
Erdős problem 1187
number theoryprimesadditive combinatoricsN/A3 sources
declared openerdos:1200
Erdős problem 1200
number theoryprimespossible
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
declared open · formalizederdos:1212
∀ {a s : ℕ}, a < s → (∀ (p : ℕ), Nat.Prime p → p ∣ a → s < a + p) → a.gcd s = 1
number theoryprimespossible2 sources

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