Python Program to Find nth Prime Number

In the previous article, we have discussed Python Program to Delete Random Item from a List
Prime Number :

A prime number is one that can only be divided by one and itself.

Given a number ‘n’, and the task to find the nth prime number.

Examples:

Example1:

Input:

Given number = 8

Output:

The above given nth Prime Number is =  19

Example2:

Input:

Given number = 3

Output:

The above given nth Prime Number is =  5

Program to Find nth Prime Number

Below are the ways to find the nth prime number.

Using While, For Loop (Static Input)
Using While, For Loop (User Input)

Method #1: Using While, For Loop (Static Input)

Approach:

Give the number say ‘n’ as static input and store it in a variable.
Take a list say ‘prime_numbers’ and initialize it with 2, 3 values.
Take a variable and initialize it with 3 say ‘x’.
Check if the given number is between greater than 0 and less than 3 using the if conditional statement.
If the statement is true, then print the value of the list “prime_numbers[n-1] “.
Check if the given number is greater than 2 using the elif conditional statement.
Iterate the loop infinite times using the while loop i.e while(True).
Inside the loop increment the value of the above given ‘x’ variable by ‘1’.
Take a variable to say ‘y’ and initialize with ‘True’.
Loop from 2 to int((x/2)+1) using the for loop and int function().
Check if the value of variable ‘x’ modulus iterator value is equal to zero or not using the if conditional statement.
If the statement is true, assign “False” to the variable y, break the statement and come out of the loop.
Check if variable y is equal to True using the if conditional statement.
If the statement is true, then append the value of variable ‘x’ to the above list ‘prime_numbers’.
Check if the length of the above list ‘prime_numbers’ is equal to the given number.
If the statement is true, then give a break statement and come out of the while loop.
Print the value of the list “prime_numbers[n-1]” to get the nth prime number.
Else print “Invalid number. Please enter another number “.
The Exit of the Program.

Below is the implementation:

# Give the number say 'n' as static input and store it in a variable.
num = 5
# Take a list say 'prime_numbers' and initialize it with 2, 3 values.
prim_numbrs = [2, 3]
# Take a variable and initialize it with 3 say 'x'.
x = 3
# Check if the given number is between greater than 0 and less than 3 using the if
# conditional statement.
if(0 < num < 3):
 # If the statement is true, then print the value of the list "prime_numbers[n-1] ".
    print('The above given nth Prime Number is =', prim_numbrs[num-1])
# Check if the given number is greater than 2 using the elif conditional statement.
elif(num > 2):
  # Iterate the loop infinite times using the while loop i.e while(True).
    while (True):
     # Inside the loop increment the value of the above given 'x' variable by '1'.
        x += 1
 # Take a variable say 'y' and initialize with 'True'.
        y = True
  # Loop from 2 to int((x/2)+1) using the for loop and int function().
        for itr in range(2, int(x/2)+1):
          # Check if the value of variable 'x' modulus iterator value is equal to zero or not
          # using the if conditional statement.
            if(x % itr == 0):
                # If the statement is true, assign "False" to the variable y, break the statement and
                # come out of the loop.
                y = False
                break
 # Check if variable y is equal to True using the if conditional statement.
        if(y == True):
            # If the statement is true, then append the value of variable 'x' to the
            # above list 'prime_numbers'.
            prim_numbrs.append(x)
  # Check if the length of the above list 'prime_numbers' is equal to the given number.
        if(len(prim_numbrs) == num):
         # If the statement is true, then give a break statement and come out of the while loop.
            break
 # Print the value of the list "prime_numbers[n-1]" to get the nth prime number.
    print('The above given nth Prime Number is = ', prim_numbrs[num-1])
 # Else print "Invalid number. Please enter another number ".
else:
    print("Invalid number. Please enter another number ")

Output:

The above given nth Prime Number is =  11

Method #2: Using While, For Loop (User Input)

Approach:

Give the number say ‘n’ as user input using int(input()) and store it in a variable.
Take a list say ‘prime_numbers’ and initialize it with 2, 3 values.
Take a variable and initialize it with 3 say ‘x’.
Check if the given number is between greater than 0 and less than 3 using the if conditional statement.
If the statement is true, then print the value of the list “prime_numbers[n-1] “.
Check if the given number is greater than 2 using the elif conditional statement.
Iterate the loop infinite times using the while loop i.e while(True).
Inside the loop increment the value of the above given ‘x’ variable by ‘1’.
Take a variable to say ‘y’ and initialize with ‘True’.
Loop from 2 to int((x/2)+1) using the for loop and int function().
Check if the value of variable ‘x’ modulus iterator value is equal to zero or not using the if conditional statement.
If the statement is true, assign “False” to the variable y, break the statement and come out of the loop.
Check if variable y is equal to True using the if conditional statement.
If the statement is true, then append the value of variable ‘x’ to the above list ‘prime_numbers’.
Check if the length of the above list ‘prime_numbers’ is equal to the given number.
If the statement is true, then give a break statement and come out of the while loop.
Print the value of the list “prime_numbers[n-1]” to get the nth prime number.
Else print “Invalid number. Please enter another number “.
The Exit of the Program.

Below is the implementation:

# Give the number say 'n' as user input using int(input()) and store it in a variable.
num = int(input("Enter some random number = "))
# Take a list say 'prime_numbers' and initialize it with 2, 3 values.
prim_numbrs = [2, 3]
# Take a variable and initialize it with 3 say 'x'.
x = 3
# Check if the given number is between greater than 0 and less than 3 using the if
# conditional statement.
if(0 < num < 3):
 # If the statement is true, then print the value of the list "prime_numbers[n-1] ".
    print('The above given nth Prime Number is =', prim_numbrs[num-1])
# Check if the given number is greater than 2 using the elif conditional statement.
elif(num > 2):
  # Iterate the loop infinite times using the while loop i.e while(True).
    while (True):
     # Inside the loop increment the value of the above given 'x' variable by '1'.
        x += 1
 # Take a variable say 'y' and initialize with 'True'.
        y = True
  # Loop from 2 to int((x/2)+1) using the for loop and int function().
        for itr in range(2, int(x/2)+1):
          # Check if the value of variable 'x' modulus iterator value is equal to zero or not
          # using the if conditional statement.
            if(x % itr == 0):
                # If the statement is true, assign "False" to the variable y, break the statement and
                # come out of the loop.
                y = False
                break
 # Check if variable y is equal to True using the if conditional statement.
        if(y == True):
            # If the statement is true, then append the value of variable 'x' to the
            # above list 'prime_numbers'.
            prim_numbrs.append(x)
  # Check if the length of the above list 'prime_numbers' is equal to the given number.
        if(len(prim_numbrs) == num):
         # If the statement is true, then give a break statement and come out of the while loop.
            break
 # Print the value of the list "prime_numbers[n-1]" to get the nth prime number.
    print('The above given nth Prime Number is = ', prim_numbrs[num-1])
 # Else print "Invalid number. Please enter another number ".
else:
    print("Invalid number. Please enter another number ")

Output:

Enter some random number = 1
The above given nth Prime Number is = 2

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