python prime check

1# Time Efficient Primality Check in Python
2
3def primeCheck(n):
4    # 0, 1, even numbers greater than 2 are NOT PRIME
5    if n==1 or n==0 or (n % 2 == 0 and n > 2):
6        return "Not prime"
7    else:
8        # Not prime if divisable by another number less
9        # or equal to the square root of itself.
10        # n**(1/2) returns square root of n
11        for i in range(3, int(n**(1/2))+1, 2):
12            if n%i == 0:
13                return "Not prime"
14        return "Prime"

1def isPrime(n):
2  if n<2:		#1, 0 and all negative numbers are not prime
3    return False
4  elif n==2:	#2 is prime but cannot be calculated with the formula below becuase of the range function
5    return True
6  else:
7    for i in range(2, n):
8      if (n % i) == 0:	#if you can precisely divide a number by another number, it is not prime
9        return False
10    return True			#if the progam dont return False and arrives here, it means it has checked all the numebrs smaller than n and nono of them divides n. So n is prime

1# There is no quick way to calculate the prime factors of a number.
2# In fact, prime factorization is so famously hard that it's what puts the "asymmetric" in asymmetric RSA encryption.
3# That being said, it can be sped up a little bit by using divisibility rules, like checking if the sum of the digits is divisible by 3.
4
5def factors(num):
6        ps = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149] # Primes from https://primes.utm.edu/lists/small/10000.txt. Primes can also be generated by iterating through numbers and checking for factors, or by using a probabilistic test like Rabin-Miller.
7        pdict = {}
8        for p in ps:
9                if p <= num:
10                        while (num / p).is_integer():
11                                if str(p) in pdict:
12                                        pdict[str(p)] += 1
13                                else:
14                                        pdict[str(p)] = 1
15                                num /= p
16                if num == 1: break
17        return pdict
18
19# Returns a dictionary in the form {"base": "exponent"}

1#make the function
2#to do this all hte vairibles go in side the function
3
4def CheckIfPrime ():
5    a1 = input("which number do you want to check")
6    a = int(a1)#you need the checking number as an int not an str
7    b = 2 #the number to check againts
8    c = ("yes")
9    while b < a:#run the loop
10        if a%b == 0:#check if the division has a remainder
11            c = ("no")#set the answer
12        b = b+1
13    print(c)#print the output
14CheckIfPrime ()#call the function  
15