Conjectured primality test for numbers of the form 2kp^n +/- 1

LLRT.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 LLRT.py
    or if it doesn't work use this one:
        python3 LLRT.py
    Author: Pedja Terzic <[email protected]>
'''
from sympy import *
from mpmath import *
from tkinter import *
import tkinter.messagebox
from tkinter.ttk import Frame, Label, Entry, Radiobutton, Button, Style

mp.dps = 50000; mp.pretty = True

class LLRT(Frame):
    def __init__(self, parent):
        Frame.__init__(self, parent)
        self.parent = parent
        self.initUI()

    def initUI(self):
        self.parent.title("LLRT")
        self.pack(fill=BOTH, expand=True)
        global value
        value = 0
        global v
        v = IntVar()
        v.set(1)
        global coeff
        coeff = StringVar()
        global base
        base = StringVar()
        global exp
        exp = StringVar()
        global res
        res = StringVar()

        frame1 = Frame(self,style='My.TFrame')
        frame1.pack(fill=X)
		
        
        rb1 = Radiobutton(frame1, text = "2*k*p^n-1", variable = v, value = 1,style='My.TRadiobutton')
        rb1.pack( anchor = W )
		
        rb2 = Radiobutton(frame1, text = "2*k*p^n+1", variable = v, value = 2,style='My.TRadiobutton')
        rb2.pack( anchor = W )
		
        
        frame2 = Frame(self,style='My.TFrame')
        frame2.pack(fill=X)

        lbl2 = Label(frame2, text="k:", width=2,background='orange')
        lbl2.pack(side=LEFT, padx=5, pady=5)

        entry2 = Entry(frame2,textvariable=coeff,style='My.TEntry')
        entry2.pack(fill=X, padx=5, expand=True)
		
        frame3 = Frame(self,style='My.TFrame')
        frame3.pack(fill=X)

        lbl3 = Label(frame3, text="p:", width=2,background='orange')
        lbl3.pack(side=LEFT, padx=5, pady=5)

        entry3 = Entry(frame3,textvariable=base,style='My.TEntry')
        entry3.pack(fill=X, padx=5, expand=True)
		
        frame4 = Frame(self,style='My.TFrame')
        frame4.pack(fill=X)

        lbl4 = Label(frame4, text="n:", width=2,background='orange')
        lbl4.pack(side=LEFT, padx=5, pady=5)

        entry4 = Entry(frame4,textvariable=exp,style='My.TEntry')
        entry4.pack(fill=X, padx=5, expand=True)

        
        frame5 = Frame(self,style='My.TFrame')
        frame5.pack(fill=X)

        result = Label(frame5, textvariable=res, width=70,background='orange')
        result.pack(side=LEFT, padx=30, pady=5)

		
        frame6 = Frame(self,style='My.TFrame')
        frame6.pack(fill=X)

        btntest = Button(frame6, text="Check", width=8, command=self.test,style='My.TButton')
        btntest.pack(side=LEFT, anchor=N, padx=5, pady=5)
		
        btnclear = Button(frame6, text="Clear", width=8, command=self.clear,style='My.TButton')
        btnclear.pack(side=LEFT, anchor=N, padx=5, pady=5)
		
        btnclose = Button(frame6, text="Close", width=8, command=self.quit,style='My.TButton')
        btnclose.pack(side=LEFT, anchor=N, padx=5, pady=5)

    def errorMsg(self,msg):
        if msg == 'error':
            tkinter.messagebox.showerror('Error!', 'Something went wrong! Maybe invalid entries!')
        elif msg == 'errc':
            tkinter.messagebox.showerror('Error!', '2k must be less than 2^n!')
        elif msg == 'errb':
            tkinter.messagebox.showerror('Error!', 'p must be greater than one!')
        elif msg == 'erre':
            tkinter.messagebox.showerror('Error!', 'n must be greater than two!')
        elif msg == 'errd':
            tkinter.messagebox.showerror('Error!', 'p must be a prime number!')
			
    
        
    

    def test(self):
        try:
            k = int(coeff.get())
            p = int(base.get())
            n = int(exp.get())
			
            if 2**n<=k:
                self.errorMsg('errc')
            elif p<2:
                self.errorMsg('errb')
            elif n<3:
                self.errorMsg('erre')
            elif not(isprime(p)):
                self.errorMsg('errd')
            else:
				
                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 v.get()==1:
                    M=2*k*p**n-1
                    d=3
                    while not(jacobi(d-2,M)==1 and jacobi(d+2,M)==-1):
                        d=d+1
                    s=polynomial(k*p**2,d)%M
                    ctr=1
                    while ctr<=n-2:
                        s=polynomial(p,s)%M
                        ctr=ctr+1
                    if int(s)==M-2:
                        value=str(2*k) + "*" + str(p) + "^" + str(n) + "-1 is prime"
                        res.set(self.makeAsItIs(value))
                    else:
                        value=str(2*k) + "*" + str(p) + "^" + str(n) + "-1 is composite"
                        res.set(self.makeAsItIs(value))
					
                else:
                    N=2*k*p**n+1
                    d=3
                    while not(jacobi(d-2,N)==-1 and jacobi(d+2,N)==-1):
                        d=d+1
                    s=polynomial(k*p**2,d)%N
                    ctr=1
                    while ctr<=n-2:
                        s=polynomial(p,s)%N
                        ctr=ctr+1
                    if int(s)==N-2:
                        value=str(2*k) + "*" + str(p) + "^" + str(n) + "+1 is prime"
                        res.set(self.makeAsItIs(value))
                    else:
                        value=str(2*k) + "*" + str(p) + "^" + str(n) + "+1 is composite"
                        res.set(self.makeAsItIs(value))

          
        except:
            self.errorMsg('error')
			
    def clear(self):
        try:
            res.set('')
            coeff.set('')
            base.set('')
            exp.set('')
        except:
            self.errorMsg('error')
			
    
    def makeAsItIs(self, value):
        return value

def main():
    root = Tk()
    root.resizable(0,0)
    s = Style()
    s.configure('My.TFrame', background='orange')
    s.configure('My.TButton', background='light gray')
    s.configure('My.TEntry', fieldbackground='light gray')
    s.configure('My.TRadiobutton', background='orange')
    s.map('My.TRadiobutton', background=[('active', '#FFC133')])
    root.geometry("250x177")
    llrt = LLRT(root)
    root.mainloop()

if __name__ == '__main__':
    main()