prime-numbers
Solves complex prime number problems within graph number theory contexts.
Install
mkdir -p .claude/skills/prime-numbers && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/4575" && unzip -o skill.zip -d .claude/skills/prime-numbers && rm skill.zipInstalls to .claude/skills/prime-numbers
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for prime numbers in graph number theoryKey capabilities
- →Primality testing
- →Prime factorization
- →Prime distribution analysis
- →Modular arithmetic verification
How it works
It utilizes computational tools like Sympy and Z3 to verify prime number properties and distribution theorems.
Inputs & outputs
When to use prime-numbers
- →Test primality of large numbers
- →Perform prime factorization
- →Verify prime distribution theorems
About this skill
Prime Numbers
When to Use
Use this skill when working on prime-numbers problems in graph number theory.
Decision Tree
-
Primality testing hierarchy
- Trial division: O(sqrt(n)), exact
- Miller-Rabin: O(k log^3 n), probabilistic
- AKS: O(log^6 n), deterministic polynomial
-
Factorization
- Trial division for small factors
- Pollard's rho: probabilistic, medium numbers
- Quadratic sieve: large numbers
sympy_compute.py factor "n"
-
Prime distribution
- Prime Number Theorem: pi(x) ~ x/ln(x)
- Prime gaps: p_{n+1} - p_n
sympy_compute.py limit "pi(x) * ln(x) / x"
-
Fermat's Little Theorem
- a^{p-1} = 1 (mod p) for a not divisible by p
- Use for modular exponentiation
z3_solve.py prove "fermat_little"
-
Wilson's Theorem
- (p-1)! = -1 (mod p) iff p is prime
Tool Commands
Sympy_Factor
uv run python -m runtime.harness scripts/sympy_compute.py factor "n"
Z3_Primality
uv run python -m runtime.harness scripts/z3_solve.py prove "no_divisor_between_1_and_sqrt_n"
Sympy_Prime_Count
uv run python -m runtime.harness scripts/sympy_compute.py simplify "pi(x) ~ x/ln(x)"
Z3_Fermat_Little
uv run python -m runtime.harness scripts/z3_solve.py prove "a**(p-1) == 1 mod p"
Key Techniques
From indexed textbooks:
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
When not to use it
- →General graph theory problems
Prerequisites
Limitations
- →Limited to prime number problems
How it compares
It provides a decision tree and automated tools for prime number problems in graph theory.
Compared to similar skills
prime-numbers side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| prime-numbers (this skill) | 1 | 7mo | Review | Advanced |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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