972.lean`

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 972

Reference: erdosproblems.com/972

Imports (1)

FormalConjecturesUtil

def Erdos972.primeSet The set of primes p such that Nat.floor (α * p) is also prime line 33 source
Source documentation
The set of primes p such that Nat.floor (α * p) is also prime.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Real, Set, Nat
Proof uses: Set.ofPred, And, Nat.Prime, Nat.floor, HMul.hMul
10 instances, coercions and auxiliary constants left out.
```
def primeSet (α : ℝ) : Set ℕ :=
…
```
theorem Erdos972.erdos_972 Erdős problem 972 sorry line 42 source
Source documentation
Erdős problem 972. Let $\alpha > 1$ be irrational. Are there infinitely many primes $p$ such that $\lfloor p\alpha \rfloor$ is also prime?

depends on sorry what this means
Statement uses: Iff, True, Real, GT.gt, OfNat.ofNat, Irrational, Set.Infinite, Nat, Erdos972.primeSet
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_972 : answer(sorry) ↔ ∀ α > 1, Irrational α → (primeSet α).Infinite := by
…
```
Mentions: Erdos972.primeSet