Prime Range Analyzer

This project is a computational tool written in C designed to analyze a specific range of integers and determine the density of prime numbers within that interval.

🧮 Theoretical Background

A Prime Number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In cryptography and number theory, understanding the distribution of primes within specific intervals is a fundamental concept.

This algorithm solves the counting problem: $$Count(A, B) = \sum_{n=A}^{B} [is_prime(n)]$$

⚙️ How It Works

The program executes the following logic:

1. Input Parsing: Accepts two integer bounds (Start/End) from the user.
2. Interval Normalization: Automatically detects which input is the lower bound and which is the upper bound.
3. Iterative Validation: Loops through every integer in the range.
4. Primality Test: Uses trial division (checking divisibility from 2 to $n/2$) to verify if a number is prime.
5. Accumulation: Increments a counter for each verified prime found.

🚀 Usage

1. Compile the code:

   gcc main.c -o prime_counter

2. Run the executable:

   ./prime_counter

3. Enter two numbers (e.g., 10 and 50) to see how many prime numbers exist between them.

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This repository demonstrates nested loop logic and conditional algorithmic optimization in C.