Diffie-Hellman Starter 2

The task is to find the generator of the finite field. There are multiple ways to do this:

Naive implementation (brute-force). Credits to Landryl @ Cryptohack.

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'''
Rather than using a set and checking if every element of Fp has been
generated, we can also rapidly disregard a number from being a generator
by checking if the cycle it generates is smaller in size than p.
If we detect a cycle before p elements, k can't be a generator of Fp.
'''

def is_generator(k, p):
  for n in range(2, p):
    if pow(k, n, p) == k:
      return False
  return True

p = 28151
for k in range(p):
  if is_generator(k, p):
    print(k)

My solution in Sage:

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from sage.all import *

p = 28151
F = FiniteField(p, modulus='primitive')
print(F.gen())

Shorter solution in Sage:

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GF(28151).primitive_element()