FactorialPrime.lean`

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4 declarations, 1 contain sorry, 0 declared as axioms

Factorial primes

A factorial prime is a prime that is one more or one less than a factorial. It is conjectured that there are infinitely many factorial primes.

References:

Imports (1)

FormalConjecturesUtil

def FactorialPrime.IsFactorialPrime A factorial prime is a prime one above or one below a factorial line 36 source
Source documentation
A factorial prime is a prime one above or one below a factorial.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Exists, Or, Eq, HAdd.hAdd, Nat.factorial, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.
```
def IsFactorialPrime (p : ℕ) : Prop :=
…
```
theorem FactorialPrime.seven_isFactorialPrime line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: FactorialPrime.IsFactorialPrime, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, Or, Eq, HAdd.hAdd, Nat.factorial, Mathlib.Meta.NormNum.isNat_prime_2, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.true, Mathlib.Meta.NormNum.isNat_minFac_4, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.minFacHelper_0, Bool.false, Exists.intro, Or.inl, Mathlib.Meta.NormNum.isNat_eq_true, Mathlib.Meta.NormNum.isNat_add and 1 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
theorem FactorialPrime.twentyThree_isFactorialPrime line 45 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: FactorialPrime.IsFactorialPrime, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, Or, Eq, HAdd.hAdd, Nat.factorial, Mathlib.Meta.NormNum.isNat_prime_2, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.true, Mathlib.Meta.NormNum.isNat_minFac_4, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.minFacHelper_3, Bool.false, Mathlib.Meta.NormNum.minFacHelper_0, Exists.intro, Or.inr, Mathlib.Meta.NormNum.isNat_eq_true and 2 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
theorem FactorialPrime.infinitely_many_factorial_primes There are infinitely many factorial primes sorry line 51 source
Source documentation
There are infinitely many factorial primes.

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, FactorialPrime.IsFactorialPrime
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem infinitely_many_factorial_primes :
    Set.Infinite {p : ℕ | IsFactorialPrime p} := by
…
```
Mentions: FactorialPrime.IsFactorialPrime