import random, sys

def miller_rabin_pass(a, s, d, n):
	''' 
	n is an odd number with
		n-1 = (2^s)d, and d odd
		and a is the base: 1 < a < n-1
	
	returns True iff n passes the MillerRabinTest for a 
	'''
	a_to_power = pow(a, d, n)
	i=0
	#Invariant: a_to_power = a^(d*2^i) mod n
	
	# we test whether (a^d) = 1 mod n
	if a_to_power == 1:
		return True
	
	# we test whether a^(d*2^i) = n-1 mod n
	# 	for 0<=i<=s-1
	while(i < s-1):
		if a_to_power == n - 1:
			return True
		a_to_power = (a_to_power * a_to_power) % n
		i+=1
	
	# we reach here if the test failed until i=s-2	
	return a_to_power == n - 1

def miller_rabin(n):
	'''
	Applies the MillerRabin Test to n (odd)
	
	returns True iff n passes the MillerRabinTest for
	K random bases
	'''
	#Compute s and d such that n-1 = (2^s)d, with d odd
	d = n-1
	s = 0
	while d%2 == 0:
		d >>= 1
		s+=1
	
	#Applies the test K times
	#The probability of a false positive is less than (1/4)^K
	K = 20
	
	i=1
	while(i<=K):
	# 1 < a < n-1
		a = random.randrange(2,n-1)
		if not miller_rabin_pass(a, s, d, n):
			return False
		i += 1

	return True

def gen_prime(nbits):
	'''
	Generates a prime of b bits using the
	miller_rabin_test
	'''
	while True:
			p = random.getrandbits(nbits)
			#force p to have nbits and be odd
			p |= 2**nbits | 1
			if miller_rabin(p):
				return p
				break

def gen_prime_range(start, stop):
	'''
	Generates a prime within the given range
	using the miller_rabin_test
	'''
	while True:
		p = random.randrange(start,stop-1)
		p |= 1
		if miller_rabin(p):
				return p
				break

if __name__ == "__main__":
	if sys.argv[1] == "test":
		n = sys.argv[2]
		print (miller_rabin(n) and "PRIME" or "COMPOSITE")
	elif sys.argv[1] == "genprime":
		nbits = int(sys.argv[2])
		print(gen_prime(nbits))