FormalConjectures/ErdosProblems/279.lean

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Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL
Lean4 Domain Explanation Language

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 279

Reference: erdosproblems.com/279

Imports (1)
  1. theorem Erdos279.erdos_279 Let $k\geq 3$ sorry line 35 source

    Source documentation

    Let $k\geq 3$. Is there a choice of congruence classes $a_p\pmod{p}$ for every prime $p$ such that all sufficiently large integers can be written as $a_p+tp$ for some prime $p$ and integer $t\geq k$?

    depends on sorry what this means

    Statement uses: Iff, True, Nat, GE.ge, OfNat.ofNat, Exists, And, Nat.Prime, LT.lt, Eq, HAdd.hAdd, HMul.hMul

    Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous

    14 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

    theorem erdos_279 :  answer(sorry) ↔ ∀ k : Nat, k ≥ 3 →
    ∃ a : Nat → Nat, ∃ N : Nat, (∀ p : Nat, p.Prime → a p < p) ∧
    ∀ n ≥ N, ∃ p : Nat, ∃ t ≥ k, p.Prime ∧ n = a p + t * p := by
…