Andrica.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Andrica's conjecture

References:

Imports (1)

FormalConjecturesUtil

theorem Andrica.andrica_conjecture Andrica's conjecture The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$, where $p_n$ is the $n$-th prime number sorry line 38 source
Source documentation
Andrica's conjecture The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$, where $p_n$ is the $n$-th prime number.

depends on sorry what this means
Statement uses: Nat, LT.lt, Real, HSub.hSub, Real.sqrt, Nat.nth, Nat.Prime, HAdd.hAdd, OfNat.ofNat
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 andrica_conjecture (n : ℕ) :
    Real.sqrt ((n+1).nth Nat.Prime) - Real.sqrt (n.nth Nat.Prime) < 1 := by
…
```
theorem Andrica.andrica_conjecture.ferreira_large_n Ferreira proved that Andrica's conjecture is true for sufficiently large n sorry line 46 source
Source documentation
Ferreira proved that Andrica's conjecture is true for sufficiently large n.

depends on sorry what this means
Statement uses: Filter.Eventually, Nat, LT.lt, Real, HSub.hSub, Real.sqrt, Nat.nth, Nat.Prime, HAdd.hAdd, OfNat.ofNat, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem andrica_conjecture.ferreira_large_n :
    ∀ᶠ n in atTop, Real.sqrt ((n+1).nth Nat.Prime) - Real.sqrt (n.nth Nat.Prime) < 1 := by
…
```