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prime-sieve-generator

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Generate optimized prime sieves and factorization routines

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Source SKILL.md: https://github.com/a5c-ai/babysitter/blob/HEAD/library/specializations/algorithms-optimization/skills/prime-sieve-generator/SKILL.md

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Prime Sieve Generator Skill

Purpose

Generate optimized prime sieves and factorization routines for various competitive programming scenarios.

Capabilities

  • Sieve of Eratosthenes (segmented, linear)
  • Smallest prime factor sieve
  • Miller-Rabin primality testing
  • Pollard's rho factorization
  • Precompute prime-related values
  • Generate primes in range

Target Processes

  • prime-algorithms
  • number-theory-algorithms
  • combinatorics-counting

Sieve Variants

Basic Sieves

  • Sieve of Eratosthenes O(n log log n)
  • Linear sieve O(n)
  • Segmented sieve (for large ranges)

Factorization Sieves

  • Smallest prime factor (SPF) sieve
  • Mobius function sieve
  • Euler's totient sieve

Primality Testing

  • Miller-Rabin (deterministic for small n)
  • Fermat test
  • Trial division

Factorization

  • Trial division O(sqrt(n))
  • Pollard's rho O(n^1/4)
  • Using SPF sieve O(log n)

Input Schema

{
  "type": "object",
  "properties": {
    "type": {
      "type": "string",
      "enum": ["sieve", "primalityTest", "factorization", "spfSieve"]
    },
    "limit": { "type": "integer" },
    "optimizations": { "type": "array" },
    "language": {
      "type": "string",
      "enum": ["cpp", "python", "java"]
    }
  },
  "required": ["type"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "code": { "type": "string" },
    "complexity": { "type": "object" },
    "memoryUsage": { "type": "string" }
  },
  "required": ["success", "code"]
}