[Tutor] returning None from function definition

[Manprit Singh]

Dear Sir ,

Consider a problem :
WAP a program that accepts two integers as user input from keyboard (a and
b), and then prints all prime numbers within the range(a, b+1).

def prime(x):
    if x < 2:
        return None
    else:
        for i in range(2, int(x**0.5) + 1):
            if x % i == 0:
                return None
    return True

a = int(input("Enter first number"))
b = int(input("Enter second number"))
for k in range(a, b+1):
    if prime(k):
        print(k)

In this program each value within the range(a, b+1) will be checked if it
is prime number or not . and if it is a prime number it will get printed.

A second version of the function written above :

def prime(x):
    if x > 1:
        for i in range(2, int(x**0.5) + 1):
            if x % i == 0:
                return None
        else:
            return True
In this definition there is no check for values below or equal 1 , although
this function will also work in the problem stated at the top, values
equals or below 1 will never be printed as prime using this function.

So according to you, which function is more readable? keeping readability
as the main factor which function definition is more acceptable in this
case ? What about returning  None instead of False inside Function
definition in this case ?
Kindly suggest if any improvement needed.

Regards
Manprit Singh