mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
65 lines
2.1 KiB
Python
65 lines
2.1 KiB
Python
from __future__ import print_function
|
|
# Primality Testing with the Rabin-Miller Algorithm
|
|
|
|
import random
|
|
|
|
def rabinMiller(num):
|
|
s = num - 1
|
|
t = 0
|
|
|
|
while s % 2 == 0:
|
|
s = s // 2
|
|
t += 1
|
|
|
|
for trials in range(5):
|
|
a = random.randrange(2, num - 1)
|
|
v = pow(a, s, num)
|
|
if v != 1:
|
|
i = 0
|
|
while v != (num - 1):
|
|
if i == t - 1:
|
|
return False
|
|
else:
|
|
i = i + 1
|
|
v = (v ** 2) % num
|
|
return True
|
|
|
|
def isPrime(num):
|
|
if (num < 2):
|
|
return False
|
|
|
|
lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
|
|
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
|
|
131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191,
|
|
193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
|
|
263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
|
|
337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401,
|
|
409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
|
|
479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
|
|
569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631,
|
|
641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709,
|
|
719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
|
|
809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
|
|
881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967,
|
|
971, 977, 983, 991, 997]
|
|
|
|
if num in lowPrimes:
|
|
return True
|
|
|
|
for prime in lowPrimes:
|
|
if (num % prime) == 0:
|
|
return False
|
|
|
|
return rabinMiller(num)
|
|
|
|
def generateLargePrime(keysize = 1024):
|
|
while True:
|
|
num = random.randrange(2 ** (keysize - 1), 2 ** (keysize))
|
|
if isPrime(num):
|
|
return num
|
|
|
|
if __name__ == '__main__':
|
|
num = generateLargePrime()
|
|
print(('Prime number:', num))
|
|
print(('isPrime:', isPrime(num)))
|