Python Program to Find Prime Numbers in a Given Range

1. Introduction

Finding prime numbers within a specified range is a classic problem in computer science and mathematics. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. Python provides a straightforward way to implement this using loops and conditional logic.

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, it has exactly two distinct positive divisors: 1 and the number itself.

2. Program Steps

1. Define the range within which to find prime numbers.

2. Iterate over this range using a loop.

3. For each number, check if it is prime by trying to divide it by all smaller numbers except 1.

4. If a number is only divisible by itself and 1, consider it prime and store or print it.

5. Continue this process for the entire range.

3. Code Program

# Function to check if a number is prime
def is_prime(num):
    if num <= 1:
        return False
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            return False
    return True

# Function to print prime numbers in a range
def print_primes_in_range(start, end):
    for number in range(start, end + 1):
        if is_prime(number):
            print(number)

# Define the range
start_range = 10
end_range = 50
# Call the function to print prime numbers in the range
print_primes_in_range(start_range, end_range)

Output:

11
13
17
19
23
29
31
37
41
43
47

Explanation:

1. is_prime is a helper function that takes an integer num and returns True if the number is prime.

2. Inside is_prime, any number less than or equal to 1 is immediately not prime.

3. The function uses a for loop to iterate from 2 to the square root of num (an optimized check for divisors).

4. If num is divisible by any number in this range (checked using num % i == 0), it is not prime.

5. print_primes_in_range is the main function that prints all prime numbers in a specified range from start to end.

6. It loops through each number in the range and calls is_prime to check if the number is prime.

7. If is_prime returns True, the number is printed.

8. When print_primes_in_range is called with the range 10 to 50, it prints all the prime numbers within that range.