prime-number-generator 0.1.0

A utility package for generating, checking, and working with prime numbers

Prime Number Generator

Overview

prime_generator is a Python package designed to provide comprehensive utilities for working with prime numbers. Whether you're doing mathematical research, solving coding challenges, or just exploring number theory, this package offers a range of functions to help you work with prime numbers efficiently.

Installation

Prerequisites

• Python 3.8+
• pip

Install from Source

# Clone the repository
git clone https://github.com/yourusername/prime_generator.git

# Navigate to the project directory
cd prime_generator

# Install the package
pip install .

Install for Development

# Install in editable mode with test dependencies
pip install -e .[test]

Features

Prime Number Checking

• Check if a number is prime
• Efficiently implemented with square root optimization

Prime Number Generation

• Generate prime numbers within a specified range
• Flexible start and end parameters

Advanced Prime Number Operations

• Find the nth prime number
• Compute prime factors of a number
• Count prime numbers in a given range

Usage Examples

Basic Prime Checking

from prime_generator import is_prime

print(is_prime(17))  # True
print(is_prime(4))   # False

Generating Prime Numbers

from prime_generator import generate_primes

# Generate primes between 10 and 20
primes = generate_primes(10, 20)
print(primes)  # [11, 13, 17, 19]

Finding Nth Prime

from prime_generator import nth_prime

# Find the 5th prime number
print(nth_prime(5))  # 11

Prime Factorization

from prime_generator import prime_factors

# Get prime factors of 12
print(prime_factors(12))  # [2, 2, 3]

Counting Primes in a Range

from prime_generator import count_primes_in_range

# Count primes between 10 and 20
print(count_primes_in_range(10, 20))  # 4

Error Handling

The package includes comprehensive error handling:

• Raises ValueError for invalid inputs
• Prevents operations on numbers less than 2
• Ensures range validity in generation methods

Performance

• Optimized prime checking algorithm
• Linear time complexity for most operations
• Square root optimization for primality testing

Running Tests

# Requires pytest
pytest tests/

Contributing

Reporting Issues

• Use GitHub Issues
• Provide clear, reproducible examples
• Specify your Python version

Development Guidelines

1. Fork the repository
2. Create a feature branch
3. Write tests for new functionality
4. Ensure all tests pass
5. Submit a pull request

Performance Considerations

• Best suited for small to medium-sized number ranges
• For extremely large prime number operations, consider specialized libraries

License

MIT License

Future Roadmap

• Support for large prime number generation
• More advanced prime number algorithms
• Additional statistical prime number functions

Disclaimer

This package is intended for educational and computational purposes. Always verify critical mathematical computations.

Acknowledgments

Inspired by the beauty of number theory and the joy of mathematical exploration.