A positive integer n greater than 1 is prime if and only if (n minus 1) factorial is congruent to negative one modulo n. It gives a computationally impractical but conceptually clean primality criterion.
Facts
StatementWilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n. 2 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Proved By
Sources
1. Wikipedia: Wilson's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n.
2. Wilson's Theorem (Wikipedia)
Wikimedia Foundationlead section, first paragraph
Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n.
History section
Lagrange gave the first proof in 1771.
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