# Wilson theorem

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Wilson theorem](https://ocme.evemisslab.com/en/atlas/atlas-wilson-theorem/)

An integer n>1 is prime exactly when (n−1)! is congruent to−1 modulo n.

atlas-wilson-theorem · canonical_mko

[Wilson theorem](https://ocme.evemisslab.com/en/mko/mko-wilson-theorem/)

## Prerequisite nodes


- [Prime natural number](https://ocme.evemisslab.com/en/atlas/atlas-prime-number/)
- [Natural-number congruence modulo a positive modulus](https://ocme.evemisslab.com/en/atlas/atlas-modular-congruence/)
- [Factorial](https://ocme.evemisslab.com/en/atlas/atlas-factorial/)
- [Modular inverse](https://ocme.evemisslab.com/en/atlas/atlas-modular-inverse/)