681.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 681

Reference: erdosproblems.com/681

Imports (1)

FormalConjecturesUtil

def Erdos681.IsLPF IsLPF p m says that p is the least prime factor of m line 31 source
Source documentation
IsLPF p m says that p is the least prime factor of m.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Dvd.dvd, LE.le
2 instances, coercions and auxiliary constants left out.
```
def IsLPF (p m : ℕ) : Prop := p.Prime ∧ p ∣ m ∧ ∀ q, q.Prime ∧ q ∣ m → p ≤ q
…
```
theorem Erdos681.erdos_681 Erdős problem 681 sorry line 40 source
Source documentation
Erdős problem 681. Is it true that for all large $n$ there exists $k$ such that $n + k$ is composite and $p(n+k) > k^2$, where $p(m)$ is the least prime factor of $m$ ?

depends on sorry what this means
Statement uses: Iff, True, Filter.Eventually, Nat, Exists, And, GT.gt, OfNat.ofNat, Nat.Composite, HAdd.hAdd, Erdos681.IsLPF, HPow.hPow, Filter.atTop
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_681 : answer(sorry) ↔
    ∀ᶠ n in .atTop, ∃ k > 0, (n + k).Composite ∧ ∀ p, IsLPF p (n + k) → p > k ^ 2 := by
…
```
Mentions: Erdos681.IsLPF