Primality test for generalized Fermat numbers

fermat.py

'''
    This script was written in python 3.x.
    In order to run this script, please make sure your python version is 3.x or above.
    How to run:
        python fermat.py
    or if it doesn't work use this one:
        python3 fermat.py
    Author: Pedja Terzic <[email protected]>
'''

from mpmath import *
print("                        ***** FERMAT *****\n\n\n")
while True:
	
	b=int(input("Enter the base : "))
    
	n=int(input("Enter the exponent : "))
    
	F=b**2**n+1
	
	def polynomial(m,x):
        
		if 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 jacobi(a,q):
        
		j=1
        
		while a != 0:
            
			while a%2==0:
                
				a=a/2
                
				if q%8==3 or q%8==5:
                    
					j=-j
            
			#interchange(a,q)
            
			c=a
            
			a=q
            
			q=c
            
			if a%4==3 and q%4==3:
                
				j=-j
            
			a=fmod(a,q)
        
		if q==1:
            
			return j
        
		else:
            
			return 0
    
    
	if n < 2:
        
		print("Exponent must be greater than one")
    
	elif b%2==1:
        
		print("Base must be an even number")
    
	else:
        
		d=3
        
		while not(jacobi(d-2,F)==-1 and jacobi(d+2,F)==-1):
            
			d=d+1
        
		s=polynomial(b/2,polynomial(b/2,d))%F
        
		ctr=1
        
		while ctr<=2**n-2:
            
			s=polynomial(b,s)%F
            
			ctr=ctr+1
            
        
		if s==0:
            
			print(str(b) + "^2^" + str(n) + "+1 is prime")
        
		else:
            
			print(str(b) + "^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