Python Program - Find all Prime Numbers less than the given 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.

Objective: Write a python code to find all prime numbers less than a given number.

Method 1: Using function to find prime number

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, end=" ")

x = 50
print("Prime numbers less than", x, "are:")
for i in range(2, x+1):
  primenumber(i)

The above code will give the following output:

Prime numbers less than 50 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 

Method 2: 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, end=" ")
  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, end=" ")

x = 100
print("Prime numbers less than", x, "are:")
for i in range(2, x+1):
  primenumber(i)

The above code will give the following output:

Prime numbers less than 100 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97