# primitive root

I am writing a program to find the primitive root. In the lecture we have given that

x is a primitive root in F_p, where p a prime number, if
x^((p-1)/pi) is not 1. (With pi the prime factors of p-1).


So here my programm:

p = 468889
R = IntegerModRing(p)
factor(p-1)
#gives: p-1 =  2^3 * 3 * 7 * 2791

list = [2,3,7,2791]
c=True

(I changed the for loop:)

for x in range(1,p):
for pi in list:
a = (p-1)/pi
if a == int(a):
k = R(x^a)
if k==1:
c=False
else:
print k
else:
pass
if c==True:
print x
else:
print c, x


But still there is no result. Can anyone help? I don't see the problem. Thanks a lot!

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Can you tell us which error you got (I did not get one for a long time, then i stopped the loop) ?

Moreover, in the first pass through the loop (x = 1, p = 2), c get the value False, and it will never become True again, because it is not reset in the loop. So, your code will not print anything !

if c==True:


you can simply write:

if c:


because c is a boolean, which has value True or False.

Also, you can remove:

else:
pass

more

I found my mistake. In the end there was no error, only, that the programm did not give any primitive root. That's because the

c=True


Must lie inside the first loop. Otherwise it was all the time False if it did not work out once. So the correct version is:

for x in range(1,p):
c=True
for pi in list:
a = (p-1)/pi
if a == int(a):
k = R(x^a)
if k==1:
c=False
else:
print k
else:
pass
if c==True:
print 'Lösung:', x
break
else:
print c, x

more