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# Primality Testing with the Rabin-Miller Algorithm

import random

def rabinMiller(num: int) -> bool:

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: int) -> bool:

if num < 2:

return False

lowPrimes = [

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457,

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479,

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491,

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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: int = 1024) -> int:

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)))

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