PierpontPrime.lean`

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4 declarations, 1 contain sorry, 0 declared as axioms

Pierpont primes

A Pierpont prime is a prime of the form $2^a 3^b + 1$, where $a$ and $b$ are nonnegative integers. Marc Gleason conjectured that there are infinitely many.

References:

Imports (1)

FormalConjecturesUtil

def PierpontPrime.IsPierpontPrime A Pierpont prime is a prime of the form $2^a3^b + 1$ line 36 source
Source documentation
A Pierpont prime is a prime of the form $2^a3^b + 1$.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Exists, Eq, HAdd.hAdd, HMul.hMul, HPow.hPow, OfNat.ofNat
9 instances, coercions and auxiliary constants left out.
```
def IsPierpontPrime (p : ℕ) : Prop :=
…
```
theorem PierpontPrime.two_isPierpontPrime line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: PierpontPrime.IsPierpontPrime, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, Eq, HAdd.hAdd, HMul.hMul, HPow.hPow, Mathlib.Meta.NormNum.isNat_prime_2, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.true, Mathlib.Meta.NormNum.isNat_minFac_2, Mathlib.Meta.NormNum.IsNat.raw_refl, Exists.intro, Mathlib.Meta.NormNum.isNat_eq_true, Mathlib.Meta.NormNum.isNat_add, Mathlib.Meta.NormNum.isNat_mul, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.natPow_zero
17 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
theorem PierpontPrime.thirtySeven_isPierpontPrime line 45 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: PierpontPrime.IsPierpontPrime, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, Eq, HAdd.hAdd, HMul.hMul, HPow.hPow, 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, Mathlib.Meta.NormNum.isNat_eq_true, Mathlib.Meta.NormNum.isNat_add and 4 more
17 instances, coercions and auxiliary constants left out.

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

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, PierpontPrime.IsPierpontPrime
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_pierpont_primes :
    Set.Infinite {p : ℕ | IsPierpontPrime p} := by
…
```
Mentions: PierpontPrime.IsPierpontPrime