# Copyright (c) 2012 the authors listed at the following URL, and/or
# the authors of referenced articles or incorporated external code:
# http://en.literateprograms.org/Miller-Rabin_primality_test_(Python)?action=history&offset=20110413052045
# 
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# a copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
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# permit persons to whom the Software is furnished to do so, subject to
# the following conditions:
# 
# The above copyright notice and this permission notice shall be
# included in all copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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# Retrieved from: http://en.literateprograms.org/Miller-Rabin_primality_test_(Python)?oldid=17104
import random, sys
def miller_rabin_pass(a, s, d, n):
    a_to_power = pow(a, d, n)
    if a_to_power == 1:
        return True
    for i in xrange(s-1):
        if a_to_power == n - 1:
            return True
        a_to_power = (a_to_power * a_to_power) % n
    return a_to_power == n - 1
def miller_rabin(n):
    d = n - 1
    s = 0
    while d % 2 == 0:
        d >>= 1
        s += 1
    for repeat in xrange(20):
        a = 0
        while a == 0:
            a = random.randrange(n)
        if not miller_rabin_pass(a, s, d, n):
            return False
    return True
if __name__ == "__main__":
    if sys.argv[1] == "test":
        n = long(sys.argv[2])
        print (miller_rabin(n) and "PRIME" or "COMPOSITE")
    elif sys.argv[1] == "genprime":
        nbits = int(sys.argv[2])
        while True:
            p = random.getrandbits(nbits)
            p |= 2**nbits | 1
            if miller_rabin(p):
                print p
                break