RepunitPrime.lean`

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

9 declarations, 1 contain sorry, 0 declared as axioms

Decimal Repunit Primes

A decimal repunit is a natural number whose decimal representation consists entirely of ones. It is conjectured that infinitely many decimal repunits are prime.

References:

Imports (1)

FormalConjecturesUtil

def RepunitPrime.repunit10 The decimal repunit of length $n$, defined as $1 + 10 + \cdots + 10^{n-1}$ line 38 source
Source documentation
The decimal repunit of length $n$, defined as $1 + 10 + \cdots + 10^{n-1}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.sum, Finset.range, HPow.hPow, OfNat.ofNat
6 instances, coercions and auxiliary constants left out.
```
def repunit10 (n : ℕ) : ℕ :=
…
```
theorem RepunitPrime.repunit10_one line 42 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, RepunitPrime.repunit10, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.natPow_zero and 13 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_two line 46 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, RepunitPrime.repunit10, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.natPow_one and 14 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_three line 50 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, RepunitPrime.repunit10, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.IsNatPowT.run and 16 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_four line 54 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, RepunitPrime.repunit10, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.IsNatPowT.run and 17 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_five line 58 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, RepunitPrime.repunit10, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, True, congrFun', congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.IsNatPowT.run and 19 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_two_prime line 62 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat.Prime, RepunitPrime.repunit10, OfNat.ofNat, Nat
Proof uses: of_eq_true, Eq.trans, True, congrArg, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Eq, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.natPow_one and 19 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.repunit10_three_not_prime line 66 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Not, Nat.Prime, RepunitPrime.repunit10, OfNat.ofNat, Nat
Proof uses: Eq.mpr, Exists, And, LT.lt, Dvd.dvd, Eq, id, Eq.trans, congrArg, LE.le, Mathlib.Meta.NormNum.IsNat.to_eq, Finset.sum, Finset.range, HPow.hPow, Eq.rec, Finset.cons, Finset.notMem_range_self, Mathlib.Meta.NormNum.IsNat, HAdd.hAdd, Mathlib.Meta.NormNum.isNat_add and 32 more
30 instances, coercions and auxiliary constants left out.

Tactic trace: 5 steps
Open to load the checked before-and-after goal states.
theorem RepunitPrime.infinitely_many_repunit_primes Wikipedia's repunit article states: "It has been conjectured that there are infinitely many repunit primes." sorry line 73 source
Source documentation
Wikipedia's repunit article states: "It has been conjectured that there are infinitely many repunit primes."

L4DEL explanation
Wikipedia's repunit article states: "It has been conjectured that there are infinitely many repunit primes."
Sources and attribution: Pinned Lean source (1646ca16afd6)

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, Nat.Prime, RepunitPrime.repunit10
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_repunit_primes :
    {n : ℕ | (repunit10 n).Prime}.Infinite := by
…
```
Mentions: RepunitPrime.repunit10