FormalConjectures.ErdosProblems.«855»

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import FormalConjectures.Wikipedia.HardyLittlewood

Erdős Problem 855

Reference: erdosproblems.com/855

This is an "eventually" formulation of the Second Hardy–Littlewood conjecture.


open Filter

open scoped Nat.Prime


namespace Erdos855

Erdős Problem 855 (Segal's conjecture): $\pi(x + y) \le \pi(x) + \pi(y)$ for sufficiently large $x, y$.

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_855 : answer(sorry) ↔
    ∀ᶠ x in atTop, ∀ᶠ y in atTop, π (x + y) ≤ π x + π y := by⊢ True ↔ ∀ᶠ (x : ℕ) (y : ℕ) in atTop, π (x + y) ≤ π x + π y
  sorryAll goals completed! 🐙


end Erdos855