Natural-number prime statements
2 cited passages ↓1 problem ↓Record 32d24245c7a12ded17325299fd41d412022cd3fe ↓
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
For each natural number n, there is a prime p satisfying n ≤ p.
Passage ID: prime-at-or-above-bound:entry:0:v1
Source item: Mathlib/Data/Nat/Prime/Infinite.lean lines 31–42
Source record: mathlib-prime-infinite@32d24245c7a12ded17325299fd41d412022cd3fe
For every natural number n, does there exist a prime p with n < p?
Passage ID: prime-infinitude:entry:1:v1
Source item: Mathlib/Data/Nat/Prime/Infinite.lean lines 31–42
Source record: mathlib-prime-infinite@32d24245c7a12ded17325299fd41d412022cd3fe
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v8
Source assessment
Proved
Proved declaration Nat.exists_infinite_primes
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Source assessment
Proved
Proved declaration Nat.exists_infinite_primes
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Source assessment
Proved
Proved declaration Nat.exists_infinite_primes
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Source assessment
Proved
Proved declaration Nat.exists_infinite_primes
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Question
Why are there infinitely many primes?
Further reading
Inspect the formal statement, assumptions and reported checks.
mathlib contributors
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mathlib · infinitude of primes
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