Python - Find the number of prime numbers within a given range of numbers

When it is required to find the prime numbers within a given range of numbers, the range is entered and it is iterated over. The % modulus operator is used to check divisibility and identify prime numbers.

What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11 are prime numbers.

Basic Approach

Below is a demonstration of finding prime numbers in a range ?

lower_range = 670
upper_range = 699
print("The lower and upper range are :")
print(lower_range, upper_range)
print("The prime numbers between", lower_range, "and", upper_range, "are:")

for num in range(lower_range, upper_range + 1):
    if num > 1:
        for i in range(2, num):
            if (num % i) == 0:
                break
        else:
            print(num)

The lower and upper range are :
670 699
The prime numbers between 670 and 699 are:
673
677
683
691

Optimized Method

We can optimize the algorithm by checking divisors only up to the square root of the number ?

import math

def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

lower_range = 10
upper_range = 30
print(f"Prime numbers between {lower_range} and {upper_range}:")

prime_count = 0
for num in range(lower_range, upper_range + 1):
    if is_prime(num):
        print(num, end=" ")
        prime_count += 1

print(f"\nTotal prime numbers found: {prime_count}")

Prime numbers between 10 and 30:
11 13 17 19 23 29 
Total prime numbers found: 6

How It Works

The algorithm follows these steps:

• Numbers less than 2 are not prime by definition

• For each number, check divisibility from 2 to its square root

• If any divisor is found, the number is not prime

• If no divisors are found, the number is prime

• The else clause of the for loop executes only when the loop completes without breaking

Complete Example with User Input

Here's a complete program that accepts user input for the range ?

def find_primes_in_range(start, end):
    primes = []
    for num in range(start, end + 1):
        if num > 1:
            is_prime = True
            for i in range(2, int(num**0.5) + 1):
                if num % i == 0:
                    is_prime = False
                    break
            if is_prime:
                primes.append(num)
    return primes

# Example usage
start_range = 20
end_range = 50
prime_numbers = find_primes_in_range(start_range, end_range)

print(f"Prime numbers between {start_range} and {end_range}:")
print(prime_numbers)
print(f"Count: {len(prime_numbers)}")

Prime numbers between 20 and 50:
[23, 29, 31, 37, 41, 43, 47]
Count: 7

Conclusion

Finding prime numbers in a range involves checking each number for divisibility. The optimized approach checks only up to the square root, significantly improving performance for larger numbers. The for-else construct in Python provides an elegant way to handle the prime detection logic.