62.lean`

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

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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

Ben Green's Open Problem 62

Let $p$ be a large prime, and let $A$ be the set of all primes less than $p$. Is every $x \in \{1, \ldots, p-1\}$ congruent to some product $a_1 a_2$ where $a_1, a_2 \in A$?

This is a problem of Erdős, Odlyzko, and Sárközy [105] from 1987.

Reference: Ben Green's Open Problem 62

Imports (1)

FormalConjecturesUtil

theorem Green62.green_62 Let $p$ be a large prime, and let $A$ be the set of all primes less than $p$ sorry line 41 source
Source documentation
Let $p$ be a large prime, and let $A$ be the set of all primes less than $p$. Is every $x \in \{1, \ldots, p-1\}$ congruent to some product $a_1 a_2$ where $a_1, a_2 \in A$?

depends on sorry what this means
Statement uses: Iff, True, Filter.Eventually, Nat, Nat.Prime, Finset, Finset.filter, Finset.range, And, LE.le, OfNat.ofNat, LT.lt, Exists, Membership.mem, Eq, ZMod, HMul.hMul, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
36 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem green_62 :
    answer(sorry) ↔
      ∀ᶠ p in atTop, p.Prime →
        let A := (Finset.range p).filter Nat.Prime
…
```