ix-number-theory

name	ix-number-theory
description	Number theory — prime sieving, primality tests, modular arithmetic
disable-model-invocation	true

Number Theory

Prime number operations and modular arithmetic utilities.

When to Use

When the user needs prime numbers, primality testing, modular exponentiation, GCD/LCM, or modular inverses.

Capabilities

• Sieve of Eratosthenes — Generate all primes up to a limit
• Primality testing — Trial division, Miller-Rabin (deterministic), Fermat
• Modular exponentiation — Fast base^exp mod m via squaring
• GCD / LCM — Greatest common divisor and least common multiple
• Modular inverse — Compute a^{-1} mod m when it exists
• Prime gaps — Analyze gaps between consecutive primes

Programmatic Usage

use ix_number_theory::sieve::sieve_of_eratosthenes;
use ix_number_theory::primality::{is_prime_trial, is_prime_miller_rabin};
use ix_number_theory::modular::{mod_pow, gcd, lcm, mod_inverse};

MCP Tool

Tool name: ix_number_theory Operations: sieve, is_prime, mod_pow, gcd, lcm, mod_inverse, prime_gaps