Compositeness test for numbers of the form N=k*b^n+c

lux.py

# Author: Pedja 

from mpmath import *
from sympy import *

print("                        ***** LUX *****\n\n\n")
while True:
	
    
   
    k=int(input("Enter the coefficient : "))
    b=int(input("Enter the base : "))
    n=int(input("Enter the exponent : "))
    c=int(input("Enter the constant : "))
	
    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,b,n,c):
        N=k*b**n+c
        d=3
        while not(jacobi_symbol(d-2,N)==c//abs(c) and jacobi_symbol(d+2,N)==1):
            d=d+1
        s=polynomial(k*b,d)%N
        ctr=1
        while ctr<=n-1:
            s=polynomial(b,s)%N
            ctr=ctr+1
        if int(s)==polynomial(abs(c)-1,d):
            return "probably prime"
        else:
            return "composite"
	
        
	



   
    if k<1:
        print("Coefficient must be natural number greater than zero")
    elif b<2:
        print("Base must be natural number greater than one")
    elif n<2:
        print("Exponent must be natural number greater than one")
    elif c==0:
        print("Constant must be nonzero integer")
    elif c>0:
        print(str(k)+"*"+str(b)+"^"+str(n)+"+"+str(c)+" is "+test(k,b,n,c))
    else:
        print(str(k)+"*"+str(b)+"^"+str(n)+str(c)+" is "+test(k,b,n,c))
    
		
    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