#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jun 14 13:42:48 2023

@author: richardson
"""

from math import *

from time import time

# code to input a number:
n = int(input("Give me an integer here: "))
#nn = 186711 # this assigns nn to be an integer.
print("Do you think "+str(n)+" is prime?") # these are strings; print displays it as output.


def isitprime1(nn):
    lastj = int(sqrt(nn)); # only need to 
    # check divisibility of numbers up to the 
    # square root of nn
    for j in range(2,lastj+1): 
        # range(2,nn) means the integers 2,3,4,...,lastj-1 
        # each time through the loop, j becomes 2, 
        # then 3, then 4, ... 
        # and the loop is run lastj-2 times.
        if nn%j==0: # need two = signs if you are 
        #checking if an equation is true are not.
            # a==b means True if a=b, False 
            # if a!=b. '!=' means not equal.
            # nn%j means nn mod j = remainder 
            # when nn is divided by j.
            return False
    return True

t1 = time() # number of seconds since a specific date.
bubba = isitprime1(n)
t2 = time()

print("Time elapsed for 1st method = "+str(t2-t1)+" seconds.")

if bubba:
    print("Yes, "+str(n)+" is prime.")
else:
    print("No, "+str(n)+" is composite.")
    
def isitprime2(nn):
    for j in range(2,nn): 
        # range(2,nn) means the integers 2,3,4,...,lastj-1 
        # each time through the loop, j becomes 2, 
        # then 3, then 4, ... 
        # and the loop is run lastj-2 times.
        if nn%j==0: # need two = signs if you are 
        #checking if an equation is true are not.
            # a==b means True if a=b, False 
            # if a!=b. '!=' means not equal.
            # nn%j means nn mod j = remainder 
            # when nn is divided by j.
            return False
    return True

t1 = time() # number of seconds since a specific date.
bubba = isitprime2(n)
t2 = time()

print("Time elapsed for second method = "+str(t2-t1)+" seconds.")

if bubba:
    print("Yes, "+str(n)+" is prime.")
else:
    print("No, "+str(n)+" is composite.")
    

def isitprime3(nn):
    lastj = int(sqrt(nn)); # only need to 
    # check divisibility of numbers up to the 
    # square root of nn
    for j in range(2,lastj+1): 
        # range(2,nn) means the integers 2,3,4,...,lastj-1 
        # each time through the loop, j becomes 2, 
        # then 3, then 4, ... 
        # and the loop is run lastj-2 times.
        if isitprime3(j) and nn%j==0: # recursive programming
            # i.e. calling the function from within itself
            # need two = signs if you are 
        #checking if an equation is true are not.
            # a==b means True if a=b, False 
            # if a!=b. '!=' means not equal.
            # nn%j means nn mod j = remainder 
            # when nn is divided by j.
            return False
    return True

t1 = time() # number of seconds since a specific date.
bubba = isitprime3(n)
t2 = time()

print("Time elapsed for 3rd method = "+str(t2-t1)+" seconds.")

if bubba:
    print("Yes, "+str(n)+" is prime.")
else:
    print("No, "+str(n)+" is composite.")