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.

Method 1: Using conditional statements

In the example below, 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.")

The above code will give the following output:

17 is a prime number.

Method 2: Using function

In the example below, 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 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.")

primenumber(21)

The above code will give the following output:

21 is not a prime number.

Method 3: Optimized Code

• Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
• Except from 2 and 3, every prime number can be represented into 6k ± 1.

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.")

primenumber(21)

The above code will give the following output:

21 is not a prime number.