Erdős problem 252 · problems.science

Erdős Problem 252: irrationality of the sum for a given $k$ .

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FormalConjectures/ErdosProblems/

252.lean

Retained formal statement8 of 9

If the prime k-tuples conjecture is true, then ∑ σ k n / n! is irrational. This is proved in [FLC07].

FormalConjectures/ErdosProblems/252.leanErdos252.erdos_252.variants.prime_tuples6 linesExact file

1∀ {k : ℕ},2  4 ≤ k →3    (∀ (a : Fin k → ℕ+) (b : Fin k → ℕ),4        (∀ (p : ℕ), Nat.Prime p → ∃ n, ¬p ∣ ∏ i, (↑(a i) * n + b i)) →5          {n | ∀ (i : Fin k), Nat.Prime (↑(a i) * n + b i)}.Infinite) →6      Irrational (Erdos252.erdos_252_sum k)

SolvedStatement only, no proof

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