mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-24 12:10:16 +00:00
725834b9bc
* Added binary exponentiaion with respect to modulo * Added miller rabin: the probabilistic primality test for large numbers * Removed unused import * Added test for miller_rabin * Add test to binary_exp_mod * Removed test parameter to make Travis CI happy * unittest.main() # doctest: +ELLIPSIS ... * Update binary_exp_mod.py * Update binary_exp_mod.py * Update miller_rabin.py * from .prime_check import prime_check Co-authored-by: Christian Clauss <cclauss@me.com>
51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
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(n, prec=1000):
|
|
"""
|
|
>>> from .prime_check import prime_check
|
|
>>> all(is_prime(i) == prime_check(i) for i in range(1000))
|
|
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(i)))
|