Probabilistic primality test

cardano.py

# Author: Pedja 

import random

print("                        ***** CARDANO *****\n\n\n")
while True:
	
    n=int(input("Enter a number : "))
    k=int(input("Enter an accuracy parameter : "))
	
    def isprime(n,b,a,m):
        F=[[2*a % m,b % m],[1 % m,0 % m]]
        expBySquaring(F,n-1,b,a,m)
        multiply2(F,a,m)
        return F[0][0]==a
	
    def multiply(F,M,m):
        x=F[0][0]*M[0][0]+F[0][1]*M[1][0]
        y=F[0][0]*M[0][1]+F[0][1]*M[1][1]
        z=F[1][0]*M[0][0]+F[1][1]*M[1][0]
        w=F[1][0]*M[0][1]+F[1][1]*M[1][1]
		
        F[0][0]=x % m
        F[0][1]=y % m
        F[1][0]=z % m
        F[1][1]=w % m
		
    def multiply2(F,a,m):
        x=(F[0][0]*a)+(F[0][1]*1)
        y=(F[1][0]*a)+(F[1][1]*1)
		
        F[0][0]=x % m
        F[0][1]=y % m
		
    def expBySquaring(F,n,b,a,m):
		
        if n==0 or n==1:
            return
        M=[[2*a % m,b % m],[1 % m,0 % m]]
        expBySquaring(F,n>>1,b,a,m)
        multiply(F,F,m)
		
        if (n % 2==1):
            multiply(F,M,m)


    m=n
	



    if k < 1:
        print("Accuracy parameter must be greater than zero")
    elif n < 2:
        print("Number must be greater than one")
    elif n==2 or n==3:
        print("probably prime")
    elif n==4:
        print("composite")
    else:
        j=0
        for i in range(1,k+1):
            b=random.randint(-100,100)
            a=random.randint(2,n-2)
            if(not(isprime(n,b,a,m))):
                print("composite")
                j+=1
                break
        if j==0:
            print("probably prime")
		
    try_again = ""
    # Loop until users opts to go again or quit
    while not(try_again == "1") and not(try_again == "0"):
        try_again = input("Press 1 to try again, 0 to exit. ")
        if try_again in ["1", "0"]:
            continue  # a valid entry found
        else:
            print("Invalid input- Press 1 to try again, 0 to exit.") 
    # at this point, try_again must be "0" or "1"
    if try_again == "0":
        break