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
if num == 1:
print(num, "is not a prime number")
elif 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")
Output
29 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
num = 407
# To take input from the user
#num = int(input("Enter a number: "))
if num == 1:
print(num, "is not a prime number")
elif 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.