# Python Program to Check Prime Number

A Prime number is a natural number greater than $1$ and divisible by $1$ and itself only, for example $- 2, 3, 5, 7,$ etc.

### Example: Using conditional statements

In the below example, the number called MyNum is checked for prime number by dividing it with all natural numbers starting from $2$ to $N-1$.

MyNum = 17
n = 0
for i in range(2,MyNum):
if MyNum % i == 0:
n = n + 1
break
if n == 0:
print(MyNum,"is a prime number.")
else:
print(MyNum,"is not a prime number.")


Output

17 is a prime number.


### Example: Using function

In the below example, a function called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from $2$ to $\frac{N}{2}$.

def primenumber(MyNum):
n = 0
i = 2
for i in range(2,MyNum//2+1):
if MyNum % i == 0:
n = n + 1
break
if n == 0:
print(MyNum,"is a prime number.")
else:
print(MyNum,"is not a prime number.")



Output

21 is not a prime number.


### Example: Optimized Code

• Instead of checking the divisibility of given number from $2$ to $\frac{N}{2}$, it is checked till $\sqrt{N}$. For a factor larger than $\sqrt{N}$, there must the a smaller factor which is already checked in the range of $2$ to $\sqrt{N}$.
• Except from $2$ and $3$, every prime number can be represented into $6k\pm1$.

def primenumber(MyNum):
n = 0
i = 2
if MyNum == 2 or MyNum == 3:
print(MyNum,"is a prime number.")
elif MyNum % 6 == 1 or MyNum % 6 == 5:
while i*i <= MyNum:
if MyNum % i == 0:
n = n + 1
break
i = i + 1
if n == 0:
print(MyNum,"is a prime number.")
else:
print(MyNum,"is not a prime number.")
else:
print(MyNum,"is not a prime number.")


21 is not a prime number.