GeneratePrime.py

import random


'''
    Miller-Rabin Primality test.

    Code Borrowed from: http://rosettacode.org/wiki/Miller%E2%80%93Rabin_primality_test#Python
'''

def _try_composite(a, d, n, s):
    if pow(a, d, n) == 1:
        return False
    for i in range(s):
        if pow(a, 2**i * d, n) == n-1:
            return False
    return True # n  is definitely composite
 
def is_prime(n, _precision_for_huge_n=16):
    if n in _known_primes or n in (0, 1):
        return True
    if any((n % p) == 0 for p in _known_primes):
        return False
    d, s = n - 1, 0
    while not d % 2:
        d, s = d >> 1, s + 1
    # Returns exact according to http://primes.utm.edu/prove/prove2_3.html
    if n < 1373653: 
        return not any(_try_composite(a, d, n, s) for a in (2, 3))
    if n < 25326001: 
        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5))
    if n < 118670087467: 
        if n == 3215031751: 
            return False
        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7))
    if n < 2152302898747: 
        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11))
    if n < 3474749660383: 
        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13))
    if n < 341550071728321: 
        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13, 17))
    # otherwise
    return not any(_try_composite(a, d, n, s) 
                   for a in _known_primes[:_precision_for_huge_n])

_known_primes = [2, 3]
_known_primes += [x for x in range(5, 1000, 2) if is_prime(x)]


'''
    First check whether the number is in the given list of prime numbers less than 1000, as it will
    be easy. If its not, then check if it is divisible by any of the given smaller prime numbers.
'''

def checkPrime(x):
    if x < 2:
        return False

    #Smaller Prime numbers i.e., less than 1000
    smaller_prime = [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 the given number is in smaller primes, then the number is prime
    if x in smaller_prime:
        return True

    #if it is not in smaller prime, check whether the number is divisible
    #by any of the number within the smaller prime
    for i in smaller_prime:

        #if the number is divisible, then it is not prime
        if x % i == 0:
            return False

    #check the number through Miller-Rabin primality test
    return is_prime(x)

'''
    Generate large primes of the order of 1024-bits
'''

def generateLargePrime(keySize=1024):
    while (1):
        num = random.randrange(2 ** (keySize - 1), 2 ** (keySize))
        if checkPrime(num):
            return num