3625.lean`

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L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

7 declarations, 1 contain sorry, 0 declared as axioms

Primes congruent to $\{3, 5, 6\} \pmod 7$

Primes congruent to $3, 5, \text{ or } 6 \pmod 7$.

References:

A003625

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/OEIS/79727.lean

def OeisA3625.A A prime $p$ is in A003625 if $p \equiv 3, 5, \text{ or } 6 \pmod 7$ line 34 source
Source documentation
A prime $p$ is in A003625 if $p \equiv 3, 5, \text{ or } 6 \pmod 7$.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: And, Nat.Prime, Or, Eq, HMod.hMod, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.
```
def A (p : ℕ) : Prop :=
…
```
theorem OeisA3625.a_3 $3$ is in the sequence A003625 line 41 source
Source documentation
$3$ is in the sequence A003625.

extra axioms: _private.0.OeisA3625.a_3._native.decide.ax_1 what this means
Statement uses: OeisA3625.A, OfNat.ofNat, Nat
Proof uses: id, of_decide_eq_true, And, Nat.Prime, Or, Eq, HMod.hMod
9 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : A 3 := by
…
```
Mentions: OeisA3625.A
theorem OeisA3625.a_5 $5$ is in the sequence A003625 line 47 source
Source documentation
$5$ is in the sequence A003625.

extra axioms: _private.0.OeisA3625.a_5._native.decide.ax_1 what this means
Statement uses: OeisA3625.A, OfNat.ofNat, Nat
Proof uses: id, of_decide_eq_true, And, Nat.Prime, Or, Eq, HMod.hMod
9 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem a_5 : A 5 := by
…
```
Mentions: OeisA3625.A
theorem OeisA3625.a_13 $13$ is in the sequence A003625 line 53 source
Source documentation
$13$ is in the sequence A003625.

extra axioms: _private.0.OeisA3625.a_13._native.decide.ax_1 what this means
Statement uses: OeisA3625.A, OfNat.ofNat, Nat
Proof uses: id, of_decide_eq_true, And, Nat.Prime, Or, Eq, HMod.hMod
9 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem a_13 : A 13 := by
…
```
Mentions: OeisA3625.A
theorem OeisA3625.a_17 $17$ is in the sequence A003625 line 59 source
Source documentation
$17$ is in the sequence A003625.

extra axioms: _private.0.OeisA3625.a_17._native.decide.ax_1 what this means
Statement uses: OeisA3625.A, OfNat.ofNat, Nat
Proof uses: id, of_decide_eq_true, And, Nat.Prime, Or, Eq, HMod.hMod
9 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem a_17 : A 17 := by
…
```
Mentions: OeisA3625.A
theorem OeisA3625.a_19 $19$ is in the sequence A003625 line 65 source
Source documentation
$19$ is in the sequence A003625.

extra axioms: _private.0.OeisA3625.a_19._native.decide.ax_1 what this means
Statement uses: OeisA3625.A, OfNat.ofNat, Nat
Proof uses: id, of_decide_eq_true, And, Nat.Prime, Or, Eq, HMod.hMod
9 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem a_19 : A 19 := by
…
```
Mentions: OeisA3625.A
theorem OeisA3625.conjecture sorry line 79 source
depends on sorry what this means
Statement uses: Nat, Nat.Prime, Iff, OeisA3625.A, Irreducible, Polynomial, ZMod, HAdd.hAdd, HPow.hPow, Polynomial.X, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.