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number-theory-explorer skill

/skills/mathematics/number-theory-explorer

This skill helps you explore number theory topics, identify gaps, and manage research sources for primes, modular arithmetic, and cryptographic applications.

npx playbooks add skill sandraschi/advanced-memory-mcp --skill number-theory-explorer

Review the files below or copy the command above to add this skill to your agents.

Files (6)
SKILL.md
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---
name: number-theory-explorer
description: Number theory expert covering primes, divisibility, modular arithmetic, Diophantine equations, and cryptographic applications
license: Proprietary
---

# Number Theory Explorer
> **Status**: ⚠️ Legacy template awaiting research upgrade
> **Last validated**: 2025-11-08
> **Confidence**: 🔴 Low — Legacy template awaiting research upgrade

## How to use this skill
1. Start with [modules/research-checklist.md](modules/research-checklist.md) and capture up-to-date sources.
2. Review [modules/known-gaps.md](modules/known-gaps.md) and resolve outstanding items.
3. Load topic-specific modules from [_toc.md](_toc.md) only after verification.
4. Update metadata when confidence improves.

## Module overview
- [Core guidance](modules/core-guidance.md) — legacy instructions preserved for review
- [Known gaps](modules/known-gaps.md) — validation tasks and open questions
- [Research checklist](modules/research-checklist.md) — mandatory workflow for freshness

## Research status
- Fresh web research pending (conversion captured on 2025-11-08).
- Document all new sources inside `the Source Log` and the research checklist.
- Do not rely on this skill until confidence is upgraded to `medium` or `high`.

Overview

This skill is a number-theory expert focused on primes, divisibility, modular arithmetic, Diophantine equations, and cryptographic applications. It synthesizes theory, worked examples, and practical heuristics for problem solving and algorithm design. Current content is based on a legacy template and requires explicit source verification before critical use.

How this skill works

The skill provides conceptual explanations, proof sketches, algorithm outlines, and step-by-step worked examples across core number-theory topics. It flags areas that need fresh literature checks and logs validation tasks for maintainers. Use it interactively to generate proofs, compute modular arithmetic results, or sketch cryptographic primitives and their number-theoretic foundations.

When to use it

  • Learning or reviewing fundamentals of primes and divisibility
  • Designing or analyzing modular arithmetic algorithms
  • Formulating and solving simple Diophantine equations
  • Exploring number theory concepts relevant to cryptography
  • Generating worked examples and explanation drafts for teaching

Best practices

  • Treat current content as a starting draft; validate results against up-to-date sources before relying on them
  • Record any new references and reconciliation steps to improve confidence levels
  • Cross-check algorithmic complexity claims with independent benchmarks
  • Prefer constructive examples and numeric verification for conjectural claims
  • Mark and resolve any flagged gaps before publishing derivative material

Example use cases

  • Compute modular inverses, residues, and congruence class reasoning for homework or implementation
  • Sketch solutions to linear and simple quadratic Diophantine equations with worked steps
  • Compare primality tests and outline practical choices for cryptographic settings
  • Produce explanatory notes for students about Euclid’s algorithm, Euler’s theorem, and Chinese remainder theorem
  • Prototype number-theory routines for cryptographic toy systems and simulate small examples

FAQ

Is the material production-ready for security-sensitive use?

No. The content is a legacy template requiring fresh literature checks and validation; do not use it for security-sensitive decisions until confidence is upgraded.

How do I improve the skill's reliability?

Add current, authoritative references, resolve listed validation tasks, run numeric and formal verifications, and update the confidence metadata when checks complete.