Number Theory

A high-performance Python package for number theory operations, optimized for Project Euler and computational mathematics problems.

Features

• Fast prime number generation and primality testing

• Efficient prime factorization

• Arithmetic progression calculations

• Optimized for computational challenges and competitive programming

• Simple, intuitive API design

Installation

pip install num_theory

Usage

Prime Numbers

from num_theory import get_prime_list_under_n, is_prime, prime_factorization

# Generate all primes under 100
primes = get_prime_list_under_n(100)

# Check if a number is prime
is_prime(997)  # Returns True

# Get prime factorization
factors = prime_factorization(84)  # Returns [(2, 2), (3, 1), (7, 1)]

Arithmetic Progressions

from num_theory import arithmetic_progression

# Generate first 5 terms of AP with a=2, d=3
terms = arithmetic_progression(a=2, d=3, n=5)  # [2, 5, 8, 11, 14]

# Calculate sum of first 10 terms
sum_ap = arithmetic_progression(a=2, d=3, n=10, compute_sum=True)

# Find the 100th term
nth_term = arithmetic_progression(a=2, d=3, n=100, nth_term=True)

Key Functions

Function	Description	Example
get_prime_list_under_n(n)	Generates all primes less than n	get_prime_list_under_n(10) returns [2, 3, 5, 7]
prime_factorization(n)	Returns prime factors with their powers	prime_factorization(12) returns [(2, 2), (3, 1)]
arithmetic_progression(a, d, n, ...)	Handles arithmetic progression operations	See examples above
is_prime(n)	Tests primality efficiently	is_prime(17) returns True

Relevance in the Python Ecosystem

This package complements existing Python libraries by offering a targeted collection of number theory utilities specifically for solving Project Euler problems.

Related Packages:

• SymPy: This does provide some symbolic mathematics, including some number theory, but isn’t optimized for the computational challenges of advanced number theory.

• NumPy: The general-purpose library for numerical computations, but not specialized in number theory.

• primesieve: A highly efficient library for prime generation. This package provides similar functionalities.

Comparison with Other Libraries

Feature	num_theory	SymPy	NumPy	primesieve
Focus	Number Theory	Symbolic Math	Numerical Computing	Prime Generation
Optimization	Project Euler	General Math	General Purpose	Prime Numbers
Learning Curve	Simple	Steep	Moderate	Simple
Speed	Fast	Moderate	Fast	Very Fast

Contributing

Interested in contributing? Check out the contributing guidelines . Please note that this project is released with a Code of Conduct. By contributing to this project, you agree to abide by its terms.

Authors

• Dhruv Garg

• Dominic Lam

• Thamer Aldawood

• Tingting Chen

License

num_theory was created by Dhruv Garg, Dominic Lam, Thamer Aldawood, Tingting Chen. It is licensed under the terms of the MIT license.

Credits

num_theory was created with cookiecutter and the py-pkgs-cookiecutter template.