Conjectured primality test for numbers of the form M=k*b^n-1

mersenne.py

# Author: Pedja 

from mpmath import *

print("                        ***** MERSENNE *****\n\n\n")
while True:
	
    
    k=int(input("Enter the coefficient : "))
    b=int(input("Enter the base : "))
    n=int(input("Enter the exponent : "))
	
    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
            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 2**n<=k:
        print("Coefficient must be less than 2^exponent")
    elif b<2:
        print("Base must be natural number greater than one")
    elif n<3:
        print("Exponent must be natural number greater than two")
    elif b%2==1 and k%2==1:
        print(str(k)+"*"+str(b)+"^"+str(n)+"-1 is composite")
    else:
        M=k*b**n-1
        d=3
        while not(jacobi(d-2,M)==1 and jacobi(d+2,M)==-1):
            d=d+1
        s=polynomial(k*b**2/2,d)%M
        ctr=1
        while ctr<=n-2:
            s=polynomial(b,s)%M
            ctr=ctr+1
        if int(s)==M-2:
            print(str(k)+"*"+str(b)+"^"+str(n)+"-1 is prime")
        else:
            print(str(k)+"*"+str(b)+"^"+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