Grimm.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Grimm's conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

theorem Grimm.grimm_conjecture Grimm's Conjecture If $n, n+1, \dots, n+k-1$ are all composite numbers, then there are $k$ distinct primes $p_i$ such that $p_i$ divides $n + i$ for all $0 \le i \le k-1$ sorry line 38 source
Source documentation
Grimm's Conjecture If $n, n+1, \dots, n+k-1$ are all composite numbers, then there are $k$ distinct primes $p_i$ such that $p_i$ divides $n + i$ for all $0 \le i \le k-1$.

depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Fin, Nat.Composite, HAdd.hAdd, Exists, Function.Embedding, And, Nat.Prime, Dvd.dvd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem grimm_conjecture (n k : ℕ) (hn : 1 ≤ n) (hk : 1 ≤ k)
    (h : ∀ i : Fin k, (n + i).Composite) :
    ∃ ps : Fin k ↪ ℕ,  ∀ i : Fin k, (ps i).Prime ∧ ps i ∣ (n + i) := by
…
```
theorem Grimm.grimm_conjecture_weak Grimm's Conjecture, weaker version If $n, n+1, \dots, n+k-1$ are all composite numbers, then their product has at least $k$ distinct prime divisors sorry line 49 source
Source documentation
Grimm's Conjecture, weaker version If $n, n+1, \dots, n+k-1$ are all composite numbers, then their product has at least $k$ distinct prime divisors.

depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Fin, Nat.Composite, HAdd.hAdd, Exists, Function.Embedding, And, Nat.Prime, Dvd.dvd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem grimm_conjecture_weak (n k : ℕ) (hn : 1 ≤ n) (hk : 1 ≤ k)
    (h : ∀ i : Fin k, (n + i).Composite) :
    ∃ ps : Fin k ↪ ℕ,  ∀ i : Fin k, (ps i).Prime ∧ ∃ j : Fin k, ps i ∣ (n + j) := by
…
```