2407.lean`

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

8 declarations, 1 contain sorry, 0 declared as axioms

Cuban Primes

OEIS A002407 lists the primes that are differences of two consecutive positive cubes. The sequence is conjectured to be infinite.

References:

OEIS A002407

Imports (1)

FormalConjecturesUtil

def OeisA2407.A A natural number is in A002407 when it is prime and is the difference of two consecutive positive cubes line 36 source
Source documentation
A natural number is in A002407 when it is prime and is the difference of two consecutive positive cubes. The addition equality avoids truncated subtraction in ℕ.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Exists, GT.gt, OfNat.ofNat, Eq, HAdd.hAdd, HPow.hPow
8 instances, coercions and auxiliary constants left out.
```
def A (p : ℕ) : Prop :=
…
```
theorem OeisA2407.a_7 line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA2407.A, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, And, GT.gt, Eq, HAdd.hAdd, 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_0, Bool.false, Exists.intro, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_eq_true and 5 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.a_19 line 44 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA2407.A, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, And, GT.gt, Eq, HAdd.hAdd, 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_lt_true and 5 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.a_37 line 48 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA2407.A, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, And, GT.gt, Eq, HAdd.hAdd, 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_lt_true and 5 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.a_61 line 52 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA2407.A, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, And, GT.gt, Eq, HAdd.hAdd, 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_lt_true and 5 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.a_127 line 56 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA2407.A, OfNat.ofNat, Nat
Proof uses: And.intro, Nat.Prime, Exists, And, GT.gt, Eq, HAdd.hAdd, 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_2, Mathlib.Meta.NormNum.not_prime_mul_of_ble, Mathlib.Meta.NormNum.minFacHelper_0 and 7 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.not_a_91 line 60 source
standard axioms: Quot.sound, propext what this means
Statement uses: Not, OeisA2407.A, OfNat.ofNat, Nat
Proof uses: of_eq_true, Eq.trans, True, False, congrArg, And, Nat.Prime, Exists, GT.gt, Eq, HAdd.hAdd, HPow.hPow, LT.lt, congr, eq_false, Mathlib.Meta.NormNum.isNat_not_prime, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Mathlib.Meta.NormNum.not_prime_mul_of_ble, Bool and 8 more
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA2407.conjecture This sequence is believed to be infinite sorry line 67 source
Source documentation
This sequence is believed to be infinite.

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, OeisA2407.A
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 conjecture : {p : ℕ | A p}.Infinite := by
…
```
Mentions: OeisA2407.A