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Prime Numbers · vibeeval | DecimalAI

scienceby vibeeval

Prime Numbers

vibeeval/prime-numbers

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for prime numbers in graph number theory

SkillScore86Maintained

Automatic

Research pack

Last verified 8/3/2026

What it changes

Passed 19 of 22 test cases with the skill, and 13 of 22 without it.

Without skill59%

With skill86%

Checks it passed that the model alone missed

Recommends Pollard's rho algorithm
Selects Miller-Rabin primality test
Includes the command python -m runtime.harness scripts/sympy_compute.py factor "360"

and 3 more in the full report

6 fixed13 passed either way3 still failing0 broke

Pass-rate lift: +27 pp
Tokens: -12%
Agent turns: 0%
Response time: -48%

Model gemini-3.6-flashMeasured 8/3/2026v119 of 22 cases passed with skill

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-prime-numbers/SKILL.md https://app.decimal.ai/s/vibeeval-prime-numbers/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-prime-numbers, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-prime-numbers/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-prime-numbers

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-prime-numbers/SKILL.md https://app.decimal.ai/s/vibeeval-prime-numbers/SKILL.md

Raw file: /s/vibeeval-prime-numbers/SKILL.md ↗ · machine-readable summary at /s/vibeeval-prime-numbers.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 6 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 6

Prompt

I need to programmatically decompose 360 into prime factors using runtime scripts. What exact bash command invocation is specified for tool execution?

What was checked, without and with the skill
Checked	Without skill	With skill
Includes the command python -m runtime.harness scripts/sympy_compute.py factor "360"	Missed	Passed

case-08 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md64 linessingle file

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"

Track record

Benchmark

19 / 22

test cases passed, vs 13 / 22 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/graph-number-theory/prime-numbers/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

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See it in action

What's inside

Prime Numbers

When to Use

Decision Tree

Tool Commands

Sympy_Factor

Track record

Benchmark

Adoption

SkillSafety

Source

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