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Tutorial by:Rizwan Abdullah Date: 2016-06-16 00:53:39

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`

.

```
# Python program to check if the input number is prime or not
# 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 1**

Enter a number: 407 407 is not a prime number 11 times 37 is 407

**Output 2**

Enter a number: 853 853 is a prime number

In this program, user is asked to enter a number and this program check whether that number 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. Else the number is prime.

We can decrease 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, [2, `num` / 2] or [2, `num` ** 0.5]. The later range is based on the fact that a composite number must have a factor less than square root of that number. Otherwise the number is prime.