[Cryptography Principles and Practice] Verification of Primitive Meta Elements

Prove that 7 is a primitive element of the prime number 7919.

Prime number decomposition is needed here. So first give the decomposed code

# -*- coding: utf-8 -*-
"""
Created on Tue Jan 12 15:05:08 2021

@author: sangliping
"""

#素数只能被1和它本身整除，不能再被其它数整除，能被2整除的都不是素数
try:
    n = 0
    while True:
        n = int(input("n="))
        if n >=1:
            break
except (ValueError):
    print("请输入整数")
i = 2
frist = True
#定义为True
while n>=i:
    while n%i==0:
        if frist==True:
            #当第一次检测，为True时,
            print("=",i,end="")
            #打印=号
            frist = False
            #这时将frist置为False，否则一直是True，因为上面初始值是True
        else:
            print("*",i,end="")
            #打印*号
        n=n//i
    i += 1

Test output:

n=7918
= 2* 37* 107

So the above question becomes relatively simple.
7918 = 2 37 107
and 7 ^7918/2 mod 7919=7918 ≠ 1 The
same is ^{true for} 7 ^7918/37 mod 7919=755≠1
7 ^7918/107 mod 7919=5549≠1
so Ord ₇₉₁₉ (7)=7918 is the primitive element of 7-bit modulo 7919