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Natural-number primality and divisibility
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Is a natural number p prime exactly when p ≥ 2 and every natural-number divisor m of p is either 1 or p?
Passage ID: prime-divisor-characterization:entry:v1
Source item: Nat.prime_def
Source record: mathlib-prime-defs@32d24245c7a12ded17325299fd41d412022cd3fe
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Problem publication v8
Source assessment
Proved
Proved characterization Nat.prime_def
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?
mathlib contributors
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mathlib · natural-number prime definitions
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