Dubner.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Dubner's conjecture

Reference: Every even number greater than 4208 is the sum of two t-primes by Harvey Dubner.

Imports (1)

FormalConjecturesUtil

def DubnerConjecture.IsTwinPrime A twin prime is a prime number that has a prime gap of 2, meaning either p - 2 or p + 2 is also prime line 35 source
Source documentation
A twin prime is a prime number that has a prime gap of 2, meaning either p - 2 or p + 2 is also prime.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Or, HSub.hSub, OfNat.ofNat, HAdd.hAdd
5 instances, coercions and auxiliary constants left out.
```
def IsTwinPrime (p : ℕ) : Prop :=
…
```
theorem DubnerConjecture.t1 line 39 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Not, DubnerConjecture.IsTwinPrime, OfNat.ofNat, Nat
Proof uses: of_eq_true, Eq.trans, True, False, congrArg, And, Nat.Prime, Or, HSub.hSub, HAdd.hAdd, congr, eq_true, 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, eq_false and 11 more
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem DubnerConjecture.t2 line 43 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: DubnerConjecture.IsTwinPrime, OfNat.ofNat, Nat
Proof uses: of_eq_true, And, Nat.Prime, Or, HSub.hSub, HAdd.hAdd, Eq.trans, True, congr, congrArg, eq_true, 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 and 8 more
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem DubnerConjecture.t3 line 47 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: DubnerConjecture.IsTwinPrime, OfNat.ofNat, Nat
Proof uses: of_eq_true, And, Nat.Prime, Or, HSub.hSub, HAdd.hAdd, Eq.trans, True, congr, congrArg, eq_true, 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 and 5 more
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem DubnerConjecture.t4 line 51 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: DubnerConjecture.IsTwinPrime, OfNat.ofNat, Nat
Proof uses: of_eq_true, And, Nat.Prime, Or, HSub.hSub, HAdd.hAdd, Eq.trans, True, congr, congrArg, eq_true, 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_2, Mathlib.Meta.NormNum.not_prime_mul_of_ble and 11 more
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem DubnerConjecture.t5 line 55 source
standard axioms: propext what this means
Statement uses: Not, DubnerConjecture.IsTwinPrime, OfNat.ofNat, Nat
Proof uses: of_eq_true, Eq.trans, True, False, congrArg, And, Nat.Prime, Or, HSub.hSub, HAdd.hAdd, 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, Bool.false, Mathlib.Meta.NormNum.isNat_natSub, Mathlib.Meta.NormNum.isNat_add and 6 more
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem DubnerConjecture.dubner_conjecture Every even number greater than 4208 is the sum of two twin primes sorry line 62 source
Source documentation
Every even number greater than 4208 is the sum of two twin primes.

depends on sorry what this means
Statement uses: Nat, LT.lt, OfNat.ofNat, Even, Exists, And, DubnerConjecture.IsTwinPrime, Eq, HAdd.hAdd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem dubner_conjecture (n : ℕ) (hn : 4208 < n) (h : Even n) :
    ∃ p q : ℕ,
      IsTwinPrime p ∧
      IsTwinPrime q ∧
      p + q = n := by
…
```
Mentions: DubnerConjecture.IsTwinPrime