find_the_prime_numbers.py

from Crypto.Util import number
a = 2622440554406490912 
b = 147433867683690946 
c = 4258610457570922687


p = 42727
q = 58757
n = p * q

print(a * b - c)
print(n)

x = b * number.inverse(n + 1, n * n) % (n * n)
n1 = a * number.inverse(x, n * n) % (n * n)

assert x * n1 * (n + 1) * x % (n * n) == c

print("znlog(%d,Mod(%d, %d))" % (n1 ,n+1, n*n))

m = int(input())

assert x * pow(n + 1, m, n * n) % (n * n) == a
assert x * (n + 1) % (n * n) == b
assert x * x * pow(n + 1, m + 1, n * n) % (n * n) == c