1065.lean`

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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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 1065

Reference: erdosproblems.com/1065

Imports (1)

FormalConjecturesUtil

theorem Erdos1065.erdos_1065.parts.i Are there infinitely many primes $p$ such that $p = 2^k * q + 1$ for some prime $q$ and $k ≥ 0$? sorry line 39 source
Source documentation
Are there infinitely many primes $p$ such that $p = 2^k * q + 1$ for some prime $q$ and $k ≥ 0$?
This is mentioned as B46 in Unsolved Problems in Number Theory by Richard K. Guy

L4DEL explanation
Are there infinitely many primes $p$ such that $p = 2^k * q + 1$ for some prime $q$ and $k ≥ 0$? This is mentioned as B46 in Unsolved Problems in Number Theory by Richard K. Guy
Sources and attribution: Pinned Lean source (1646ca16afd6)

depends on sorry what this means
Statement uses: Iff, True, Set.Infinite, Nat, Set.ofPred, Exists, And, Nat.Prime, Eq, HAdd.hAdd, HMul.hMul, HPow.hPow, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1065.parts.i :
    answer(sorry) ↔ Set.Infinite {p | ∃ q k, p.Prime ∧ q.Prime ∧ p = 2^k * q + 1} := by
…
```
theorem Erdos1065.erdos_1065.parts.ii Are there infinitely many primes $p$ such that $p = 2^k 3^l q + 1$ for some prime $q$ and $k ≥ 0$, $l ≥ 0$? sorry line 48 source
Source documentation
Are there infinitely many primes $p$ such that $p = 2^k 3^l q + 1$ for some prime $q$ and $k ≥ 0$, $l ≥ 0$?

depends on sorry what this means
Statement uses: Iff, True, Set.Infinite, Nat, Set.ofPred, Exists, And, Nat.Prime, Eq, HAdd.hAdd, HMul.hMul, HPow.hPow, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1065.parts.ii : answer(sorry) ↔
    Set.Infinite {p | ∃ q k l, p.Prime ∧ q.Prime ∧ p = 2^k * 3^l * q + 1} := by
…
```