Editing Lucas primality test (section)

{{Short description|Algorithm for checking if a number is prime}}
{{for multi|the test for Mersenne numbers|Lucas–Lehmer primality test|the Lucas–Lehmer–Riesel test|Lucas–Lehmer–Riesel test|the Lucas probable prime test|Lucas pseudoprime}}

In [[computational number theory]], the '''Lucas test''' is a [[primality test]] for a natural number ''n''; it requires that the [[prime factors]] of ''n'' &minus; 1 be already known.<ref>{{cite book |last1=Crandall |first1=Richard |last2=Pomerance |first2=Carl
 |title=Prime Numbers: a Computational Perspective
|year=2005|publisher=Springer|isbn=0-387-25282-7 |page=173 |edition=2nd }}</ref><ref>{{cite book |last1=Křížek |first1=Michal |last2=Luca |first2=Florian |last3=Somer |first3=Lawrence |title=17 Lectures on Fermat Numbers: From Number Theory to Geometry  |series=CMS Books in Mathematics |volume= 9|year=2001|publisher=Canadian Mathematical Society/Springer|isbn=0-387-95332-9 |page=41}}</ref> It is the basis of the [[Pratt certificate]] that gives a concise verification that ''n'' is prime.