# 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.

### Example: Using function to find prime number

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, end=" ")

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


Output

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


### 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, 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):


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