📌 PrimeSieveAPI

An efficient Prime Number API using the Sieve of Eratosthenes and MongoDB caching 🚀

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🔹 Features

✅ Fast prime number generation using Sieve of Eratosthenes
✅ MongoDB caching for frequently requested values
✅ Simple REST API with GET /api/primes/:N
✅ Built with Node.js, Express, and MongoDB

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🔹 Sieve of Eratosthenes Algorithm

The Sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to a given limit. It works by iteratively marking the multiples of each prime number starting from 2. The numbers which remain unmarked are primes.

How It Works:

1. Start with a list of numbers from 2 to N (the limit).
2. Starting from 2, mark all of its multiples as non-prime.
3. Move to the next unmarked number (it will be a prime), and mark all of its multiples as non-prime.
4. Repeat this process until you've processed all numbers up to N.
5. The remaining unmarked numbers are primes.

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🧐 Sneak Peek 1: The First Few Steps

For N = 20:

1. List numbers from 2 to 20:
   [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]

2. Mark multiples of 2:
   [2, 3, X, 5, X, 7, X, 9, X, 11, X, 13, X, 15, X, 17, X, 19, X]

3. Mark multiples of 3:
   [2, 3, X, 5, X, 7, X, 9, X, 11, X, 13, X, 15, X, 17, X, 19, X]

4. Continue marking multiples of each unmarked number.

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🧐 Sneak Peek 2: Final Prime Numbers

After applying the algorithm, the unmarked numbers up to 20 are:

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🚀 Installation & Setup

1️⃣ Clone the Repository

git clone https://github.com/your-username/PrimeSieveAPI.git
cd PrimeSieveAPI

2️⃣ Install Dependencies

npm install

3️⃣ Set Up Environment Variables

MONGO_URI=mongodb://localhost:27017/primeDB
PORT=5000

4️⃣ Start the Server

npm run dev

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🔹 API Endpoints

📌 Get Prime Numbers

GET /api/primes/:N

📥 Request:

Replace :N with any number (e.g., /api/primes/20).

📤 Response:

{
  "primes": [2, 3, 5, 7, 11, 13, 17, 19]
}

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🔹 Project Structure

PrimeSieveAPI/
│── src/
│   │── models/          # MongoDB Model
│   │── routes/          # API Routes
│   │── controllers/     # API Logic
│   │── db/              # Database Connection
│   │── app.js           # Express App
│── server.js            # Server Entry Point
│── .env                 # Environment Variables
│── package.json         # Dependencies
│── README.md            # Project Documentation

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🔹 Technologies Used

🚀 Node.js – Backend framework
🚀 Express.js – API routing
🚀 MongoDB – Caching for performance
🚀 Mongoose – Database ORM
🚀 Nodemon – Development utility

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🔹 Contributing

🔹 Fork the repo
🔹 Create a new branch (git checkout -b feature-name)
🔹 Commit changes (git commit -m "Added new feature")
🔹 Push to branch (git push origin feature-name)
🔹 Open a Pull Request 🚀

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🔹 License

📜 MIT License – Free to use & modify.