abhiprime 7.0.0

A powerful Python package for prime number operations

🔢 abhiprime

A powerful, efficient, and comprehensive Python package for prime number operations.

✨ Features

• 🔍 Primality Testing: Trial division + Miller-Rabin for all number sizes
• ⚡ High Performance: Sieve of Eratosthenes (standard & segmented)
• 🎯 Advanced Algorithms: Lucas-Lehmer, Baillie-PSW, prime counting
• 📊 Mathematical Functions: Twin primes, Goldbach partitions, prime gaps
• 🚀 CLI Tool: Command-line interface for quick operations
• 💾 Smart Caching: LRU cache for repeated queries
• 📝 Type Hints: Full type annotation support
• 🧪 Well Tested: Comprehensive test suite with >95% coverage

📦 Installation

pip install abhiprime

Upgrade from v1:

pip install --upgrade abhiprime

🚀 Quick Start

Basic Usage

import abhiprime as ap

# Test primality
ap.test_prime(17)        # True
ap.test_prime(18)        # False

# Find nearby primes
ap.prev_prime(20)        # 19
ap.next_prime(20)        # 23

# Get primes in range
ap.prime_upto(50)        # [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
ap.range_prime(10, 30)   # [11, 13, 17, 19, 23, 29]

# Prime factorization
ap.prime_factors(60)     # [2, 2, 3, 5]

Advanced Features

from abhiprime import (
    prime_count, nth_prime, twin_primes, 
    goldbach_partitions, segmented_sieve, PrimeCache
)

# Prime counting function π(n)
prime_count(100)         # 25
prime_count(1000)        # 168

# Find the nth prime
nth_prime(100)           # 541
nth_prime(10000)         # 104729

# Special prime pairs
twin_primes(50)          # [(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43)]
cousin_primes(50)        # [(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47)]
sexy_primes(50)          # [(5, 11), (7, 13), (11, 17), (13, 19), (17, 23), ...]

# Goldbach partitions
goldbach_partitions(100) # [(3, 97), (11, 89), (17, 83), (29, 71), (41, 59), (47, 53)]

# Memory-efficient segmented sieve for large ranges
segmented_sieve(10**12, 10**12 + 1000)

# Caching for repeated operations
cache = PrimeCache(maxsize=10000)
cache.is_prime(104729)   # Cached result
cache.stats()            # {'prime_cache_size': 1, 'sieve_cache_size': 0}

Large Number Support

from abhiprime import miller_rabin, baillie_psw, lucas_lehmer

# Probabilistic test for large numbers (cryptography-grade)
miller_rabin(2**61 - 1, k=20)  # True (Mersenne prime)

# Baillie-PSW (no known counterexamples)
baillie_psw(3825123056546413051)

# Lucas-Lehmer for Mersenne primes
lucas_lehmer(127)  # True (2^127 - 1 is prime)

🖥️ Command Line Interface

# Test if a number is prime
abhiprime test 17
# Output: 17 is prime

# Get primes up to n
abhiprime upto 50
# Output: Found 15 primes
# [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

# Prime factorization
abhiprime factors 60
# Output: Prime factors of 60: [2, 2, 3, 5]

# Count primes
abhiprime count 1000
# Output: π(1000) = 168

# Find nth prime
abhiprime nth 100
# Output: Prime #100 = 541

# Twin primes
abhiprime twins 100
# Output: Found 8 pairs
#   (3, 5)
#   (5, 7)
#   ...

# Goldbach partitions
abhiprime goldbach 100
# Output: Goldbach partitions of 100:
#   3 + 97 = 100
#   11 + 89 = 100
#   ...

# JSON output
abhiprime --format json upto 20
# Output: {"upper_bound": 20, "count": 8, "primes": [2, 3, 5, 7, 11, 13, 17, 19]}

📊 Performance Comparison

Operation	abhiprime v2	abhiprime v1	sympy
prime_upto(10^6)	0.05s	2.3s	0.08s
prime_upto(10^8)	4.2s	N/A	5.1s
test_prime(10^18)	0.001s	0.8s	0.002s
nth_prime(10^6)	0.3s	N/A	0.4s

Benchmarks on Intel i7, Python 3.11

🔧 API Reference

Core Functions

Function	Description	Time Complexity
test_prime(n)	Primality test	O(√n) small, O(k·log³n) large
prev_prime(n)	Largest prime < n	O(√n · gap)
next_prime(n)	Smallest prime > n	O(√n · gap)
prime_upto(n)	All primes ≤ n	O(n log log n)
range_prime(a, b)	Primes in [a, b]	O(n log log n)
prime_factors(n)	Prime factorization	O(√n)

Advanced Functions

Function	Description
miller_rabin(n, k=10)	Probabilistic primality test
lucas_lehmer(p)	Mersenne prime test
baillie_psw(n)	Deterministic probable prime test
prime_count(n)	Count primes ≤ n
nth_prime(n)	Find the nth prime
twin_primes(n)	Find twin prime pairs
goldbach_partitions(n)	Even number as sum of two primes
segmented_sieve(low, high)	Memory-efficient large range sieve
prime_generator()	Infinite prime generator

🧪 Running Tests

# Clone the repository
git clone https://github.com/abhi1628/prime-number-python-package.git
cd prime-number-python-package

# Install dependencies
pip install -e ".[dev]"

# Run tests
pytest tests/ -v --cov=abhiprime

# Run benchmarks
python benchmarks/benchmark.py

🤝 Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🙏 Acknowledgments

• Sieve of Eratosthenes implementation optimized with bytearray
• Miller-Rabin implementation based on deterministic variants
• Inspired by sympy.ntheory and primesieve

---

⭐ Star this repo if you find it useful!