BalancedPrimes.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Balanced prime conjecture

References:

Imports (1)

FormalConjecturesUtil

theorem BalancedPrimes.balanced_primes Let $p_k$ be the $k$-th prime number sorry line 37 source
Source documentation
Let $p_k$ be the $k$-th prime number. Are there infinitely many $n$ such that $(p_n + p_{n+2}) / 2$ is prime?

depends on sorry what this means
Statement uses: Iff, True, Set.Infinite, Nat, Set.ofPred, Prime, HDiv.hDiv, HAdd.hAdd, Nat.nth, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem balanced_primes :
    answer(sorry) ↔ {n : ℕ | Prime ((Nat.nth Prime n + Nat.nth Prime (n + 2)) / 2)}.Infinite := by
…
```
theorem BalancedPrimes.balanced_primes_order Let $p_k$ be the $k$-th prime number sorry line 47 source
Source documentation
Let $p_k$ be the $k$-th prime number. Are there infinitely many $n$ such that $p_n = \dfrac{\sum_{i = 1} ^ k p_{n - i} + p_{n + i}}{2*k}$?

depends on sorry what this means
Statement uses: Iff, True, Nat, GT.gt, OfNat.ofNat, Set.Infinite, Set.ofPred, And, LE.le, Eq, HMul.hMul, Nat.nth, Prime, Finset.sum, Finset.Ioc, HAdd.hAdd, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem balanced_primes_order :
    answer(sorry) ↔ ∀ k > 0, {n : ℕ | k ≤ n ∧ 2 * k * Nat.nth Prime n = ∑ i ∈ .Ioc 0 k,
      ((n - i).nth Prime + (n + i).nth Prime)}.Infinite := by
…
```