Python Program to Check Prime Number


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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.")

primenumber(21)

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.")

primenumber(21)

Output

21 is not a prime number.




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