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.

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

The above code will give the following output:

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

The above code will give the following 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