determine if number is prime python

# Time Efficient Primality Check in Python

def primeCheck(n):
    # 0, 1, even numbers greater than 2 are NOT PRIME
    if n==1 or n==0 or (n % 2 == 0 and n > 2):
        return "Not prime"
    else:
        # Not prime if divisable by another number less
        # or equal to the square root of itself.
        # n**(1/2) returns square root of n
        for i in range(3, int(n**(1/2))+1, 2):
            if n%i == 0:
                return "Not prime"
        return "Prime"

def prime(num):
        for x in range(2,num):
            if num % x == 0:
                return False
        return True

#make the function
#to do this all hte vairibles go in side the function

def CheckIfPrime ():
    a1 = input("which number do you want to check")
    a = int(a1)#you need the checking number as an int not an str
    b = 2 #the number to check againts
    c = ("yes")
    while b < a:#run the loop
        if a%b == 0:#check if the division has a remainder
            c = ("no")#set the answer
        b = b+1
    print(c)#print the output
CheckIfPrime ()#call the function  

n=input('Enter the number you want to check: ')
try:
    n=int(n)
except:
    print('Wrong input.')
    quit()
if n==1 or n==0:
    print('This is neither prime nor composite')
else:
    c=0
    for i in range(2,n):
        if n%i==0:
            c=c+1
    if c==0:
        print("This is a prime number")
    else:
        print('This  is a composite number.')

import math
def prime(x):
    if x == 2 or x == 3 or x==5:
        return True
    if x == 1 or x == 4:
        return False
    num = 2
    a= math.sqrt(x)+4 
    while a > num:
        if x % num == 0:
            return False
        else:
            num = num + 1
    return True