## Python, math, miller_rabin.py

``````import random

from .binary_exp_mod import bin_exp_mod

# This is a probabilistic check to test primality, useful for big numbers!
# if it's a prime, it will return true
# if it's not a prime, the chance of it returning true is at most 1/4**prec
def is_prime_big(n, prec=1000):
"""
>>> from maths.prime_check import prime_check
>>> # all(is_prime_big(i) == prime_check(i) for i in range(1000))  # 3.45s
>>> all(is_prime_big(i) == prime_check(i) for i in range(256))
True
"""
if n < 2:
return False

if n % 2 == 0:
return n == 2

# this means n is odd
d = n - 1
exp = 0
while d % 2 == 0:
d /= 2
exp += 1

# n - 1=d*(2**exp)
count = 0
while count < prec:
a = random.randint(2, n - 1)
b = bin_exp_mod(a, d, n)
if b != 1:
flag = True
for i in range(exp):
if b == n - 1:
flag = False
break
b = b * b
b %= n
if flag:
return False
count += 1
return True

if __name__ == "__main__":
n = abs(int(input("Enter bound : ").strip()))
print("Here's the list of primes:")
print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))
``````