Primality test for specific class of Proth numbers

proth.py

# Author: Pedja 




print("                        ***** PROTH *****\n\n\n")
while True:
	
    
   
    k=int(input("Enter the coefficient : "))
    n=int(input("Enter the exponent : "))
  
	
	
    def polynomial(m,x):
        if m==0:
            return 2
        elif m==1:
            return x
        else:
            p0=2
            p1=x
            l=2
            while l<=m:
                p=x*p1-p0
                p0=p1
                p1=p
                l=l+1
            return p
			
    def test(k,n):
        N=k*2**n+1
        s=polynomial(k,8)
        ctr=1
        while ctr<=n-2:
            s=(s*s-2)%N
            ctr=ctr+1
        return int(s)==0
       
	
    if k%2==0:
        print("Coefficient must be an odd number")
    elif k<=0:
        print("Coefficient must be greater than zero")
    elif n<3:
        print("Exponent must be greater than two")
    elif k>=2**n:
        print("Coefficient must be less than 2^exponent")
    elif not(((k%30==1 or k%30==7) and n%4==0) or ((k%30==11 or k%30==23) and n%4==1) or ((k%30==13 or k%30==19) and n%4==2) or ((k%30==17 or k%30==29) and n%4==3)):
        print("That combination of the coefficient and exponent is not supported by this test")
    else:
        if test(k,n):
            print(str(k)+"*2^"+str(n)+"+1 is prime")
        else:
            print(str(k)+"*2^"+str(n)+"+1 is composite")
			
    
		
    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