# Python Program - Find all Prime Numbers in a given Interval

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 in a given internal.

### 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 = 10
y = 50
print("Prime numbers between", x, "and", y, "are:")
for i in range(x, y+1):


Output

Prime numbers between 10 and 50 are:
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
y = 200
print("Prime numbers between", x, "and", y, "are:")
for i in range(x, y+1):


Output

Prime numbers between 100 and 200 are:
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199