383.lean`

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L4DEL: Lean4 Domain Explanation Language

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 383

Reference: erdosproblems.com/383

Imports (1)

FormalConjecturesUtil

theorem Erdos383.erdos_383 Is it true that for every $k$ there are infinitely many primes $p$ such that the largest prime divisor of $$ \prod_{i = 0}^k (p ^ 2 + i) $$ is $p$? sorry line 39 source
Source documentation
Is it true that for every $k$ there are infinitely many primes $p$ such that the largest prime divisor of $$ \prod_{i = 0}^k (p ^ 2 + i) $$ is $p$?

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

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_383 : answer(sorry) ↔
    ∀ k, {p : ℕ | p.Prime ∧ Nat.maxPrimeFac (∏ i ∈ Finset.Icc 0 k, (p ^ 2 + i)) = p}.Infinite := by
…
```
Mentions: Nat.maxPrimeFac