prime-numbers skill
Problem-solving strategies for prime numbers in graph number theory
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Install the prime-numbers skill
A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3 mkdir -p ~/.claude/skills cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/graph-number-theory/prime-numbers ~/.claude/skills/prime-numbers
available in every project
In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub
The instructions your agent would load
SKILL.md as published, without the frontmatter. Read it on GitHub
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} - pn
- sympycompute.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
- z3solve.py prove "fermatlittle"
- 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"SympyPrimeCount
uv run python -m runtime.harness scripts/sympy_compute.py simplify "pi(x) ~ x/ln(x)"Z3FermatLittle
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.
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