A positive integer greater than 1 which has no other factors except 1 and the number itself is called a prime number. 2, 3, 5, 7 etc. are prime numbers as they do not have any other factors. But 6 is not prime (it is composite) since, `2 x 3 = 6`

.

## Example 1: Using a flag variable

```
# Program to check if a number is prime or not
num = 29
# To take input from the user
#num = int(input("Enter a number: "))
# define a flag variable
flag = False
# prime numbers are greater than 1
if num > 1:
# check for factors
for i in range(2, num):
if (num % i) == 0:
# if factor is found, set flag to True
flag = True
# break out of loop
break
# check if flag is True
if flag:
print(num, "is not a prime number")
else:
print(num, "is a prime number")
```

In this program, we have checked if `num` is prime or not. Numbers less than or equal to 1 are not prime numbers. Hence, we only proceed if the `num` is greater than 1.

We check if `num` is exactly divisible by any number from `2`

to `num - 1`

. If we find a factor in that range, the number is not prime, so we set `flag` to `True`

and break out of the loop.

Outside the loop, we check if `flag`

is `True`

or `False`

.

- If it is
`True`

,`num`

is not a prime number. - If it is
`False`

,`num`

is a prime number.

**Note**: We can improve our program by decreasing the range of numbers where we look for factors.

In the above program, our search range is from 2 to `num - 1`

.

We could have used the range, `range(2,num//2)`

or `range(2,math.floor(math.sqrt(num)+1))`

. The latter range is based on the fact that a composite number must have a factor less than or equal to the square root of that number. Otherwise, the number is prime.

You can change the value of variable `num` in the above source code to check whether a number is prime or not for other integers.

In Python, we can also use the `for...else`

statement to do this task without using an additional `flag`

variable.

## Example 2: Using a for...else statement

```
# Program to check if a number is prime or not
num = 407
# To take input from the user
#num = int(input("Enter a number: "))
# prime numbers are greater than 1
if num > 1:
# check for factors
for i in range(2,num):
if (num % i) == 0:
print(num,"is not a prime number")
print(i,"times",num//i,"is",num)
break
else:
print(num,"is a prime number")
# if input number is less than
# or equal to 1, it is not prime
else:
print(num,"is not a prime number")
```

**Output**

407 is not a prime number 11 times 37 is 407

Here, we have used a `for..else`

statement to check if `num`

is prime.

It works on the logic that the `else`

clause of the `for`

loop runs if and only if we don't break out the `for`

loop. That condition is met only when no factors are found, which means that the given number is prime.

So, in the `else`

clause, we print that the number is prime.