Python Program to Print all the Prime Number in an Interval

Python Program to Print all the Prime Number in an Interval

What is Prime numbers?

A prime number is referred to those numbers that can be divisible by them only. In simple words, those numbers can't divisible by a number lower than them. For example, if we take 13 as input then we check that the 13 is divisible by 2 or not, if not then we check if the number is divisible by 3 or not, we check this till 12, if till 12 no one can't be able to divide 13 completely so 13 is a prime number. If the 13 is divided completely by the number lower then it is not a prime number.

In the language of programming language, we will use a loop till 13 and check that 13 is divisible by the lower value or not. If it is divided by the lower value then we stop the execution and print that it is not a prime number else it is a prime number.

Numerical Example

Take a number=5 

Now, we have to check the prime number then we simply start dividing 5 with 2 not with 1 because anything divided by 1 its remainder is 0.

Now, after dividing 5 by 2 we get 2 in dividend and 1 in the remainder,

Now, divide 5 by 3 we get 1 in dividend and 2 in the remainder,

Now, divide 5 by 4 we get 1 in dividend and 1 in the remainder.

Hence, 5 is not completely divisible till 5, so 5 is a prime number.

How to check the prime numbers in python?

Let’s Understand an Example with the help of the program.

 #taking an input from the user
 num = int(input("Enter the number to check: "))
 #Declaring a variable 
 #which is required for the program
 flag=0
 #executing the For loop
 for no in range(2,num):
     #Checking for prime number
     if (num%no)==0:
         #Required for further checking
         flag=1
         #stop the execution of loop
         break
 #Checking the flag value 
 # for final declaration of prime number
 if flag==1:
     print(num," is not a prime number")
 else:
     print(num," is a prime number") 

Output:

 Enter the number to check: 13
 13 is a prime number
 Enter the number to check: 10
 10 is not a prime number 

Explaination:

In the above example, Firstly we ask the user to input a number and convert it from string to number with the help of the int() function and store it in a variable named num. Then we declare a variable flag that will help in the further procedure. Now, we used a for loop to implement the "no" variable in the range of 2 to the user entered number.

then we check the remainder of the num divided by no is equal to 0 or not with the help of if control statement. if the remainder is 0 then initialize the flag by 1 and stop the execution else continue. At last, if the flag value is 1 then the entered value is not a prime number else it is a prime number.

How to print all the Prime Numbers in an interval?

To print all the prime numbers existing in the interval we will implement two loops one to check the prime number and the other to check the number is in the interval or not. In this we are going to see 2 different methods to perform this program.

• Without the Function

Program:

Let us understand this query with the help of the program

 #taking interval from the user
 lower = int(input("Enter the lower Interval value: "))
 upper = int(input("Enter the upper Interval value: "))
 prime=[]
 #loop through the Interval and check individually
 for num in range(lower, upper+1):
         #Number should not be divisible
         #by any number between 1-num
         for no in range(2,num):
             if (num%no)==0:
                 break
         else:
             prime.append(num)
 print(prime) 

Output:

 Enter the lower Interval value: 100
 Enter the upper Interval value: 150
 [101, 103, 107, 109, 113, 127, 131, 137, 139, 149]
 Enter the lower Interval value: 10
 Enter the upper Interval value: 50
 [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] 

Explaination:

In the above example, firstly we ask the user to input the lower limit and upper limit. then we created a blank list named prime. then we implemented a For loop to check that the num is in the range of lower and upper limit. Then we declare a nested for loop to check that the "no" is in the range of 2 to the num. After that, we check that the remainder of num divided by no is equal to 0 or not. if it is equal to 0 then it stops the execution of the loop. and if the no is not in the range of 2 to num then it appends that number in the prime list. After all, execution is completed then we printed the list.

• With the Function

Program:

Let us understand this Program with the simple example.

 #creating the function
 def prime(upper,lower):
     #creating a blank list
     prime=[]
     #loop through the Interval and check individually
     for num in range(lower, upper+1):
         #Number should not be divisible
         #by any number between 1-num
         for x in range(2,num):
             if num%x==0:
                 break
         else:
             #print(num)
             prime.append(num)
     return prime
 #taking limits from the user
 lower = int(input("Enter the lower Interval value: "))
 upper = int(input("Enter the upper Interval value: "))
 #calling prime function
 prime=prime(upper,lower)
 #printing the prime list
 print(prime) 

Output:

 Enter the lower Interval value: 100
 Enter the upper Interval value: 150
 [101, 103, 107, 109, 113, 127, 131, 137, 139, 149]