To test if an odd N is prime:

	for loop  1 to k do
		randomly select b from the set {1..N-1}
		if  GCD(b,N)==1  and  J(b,N)  b(N-1)/2(mod N)
		then	continue looping
		else	return  not prime
	return  prime with probability > 1-2-k

To calculate the value of J(x,y):

	if  x==1		then	return  1
	else if  x is even	then	return  J( x/2,y ) * (-1)(y2-1)/8
	else				return  J( y(mod x),x ) * (-1)(x-1)(y-1)/4

To calculate the value of b^(N-1)/2(mod N):

	x  (N-1)/2
	y  b
	a  1
	while x > 0  do
		if x is odd then a  ay(mod N)
		y  y2(mod N)
		x  floor(x/2)
	return  a