Editing Lucas primality test (section)

==Algorithm==
The algorithm can be written in [[pseudocode]] as follows:

 '''algorithm''' lucas_primality_test '''is'''
     '''input''': ''n'' > 2, an odd integer to be tested for primality.
            ''k'', a parameter that determines the accuracy of the test.
     '''output''': ''prime'' if ''n'' is prime, otherwise ''composite'' or ''possibly composite''.
 
     determine the prime factors of ''n''&minus;1.
 
     LOOP1: '''repeat''' ''k'' times:
         pick ''a'' randomly in the range [2, ''n'' − 1]
             {{nowrap|'''if''' <math>a^{n-1} \not\equiv 1 \pmod n</math> '''then'''}}
                 '''return''' ''composite''
             '''else''' {{nowrap|{{color|gray|#}} <math>\color{Gray}{a^{n-1} \equiv 1 \pmod n}</math>}}
                 LOOP2: '''for''' all prime factors ''q'' of ''n''&minus;1:
                     {{nowrap|'''if''' <math>a^\frac{n-1}q \not\equiv 1 \pmod n</math> '''then'''}}
                         '''if''' we checked this equality for all prime factors of ''n''&minus;1 '''then'''
                             '''return''' ''prime''
                         '''else'''
                             '''continue''' LOOP2
                     '''else''' {{nowrap|{{color|gray|#}} <math>\color{Gray}{a^\frac{n-1}q \equiv 1 \pmod n}</math>}}
                         '''continue''' LOOP1
 
     '''return''' ''possibly composite''.