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name: prime-sieve-generator description: Generate optimized prime sieves and factorization routines allowed-tools:

• Read
• Write
• Grep
• Glob
• Edit graph: domains: [domain:computer-science] specializations: [specialization:algorithms-optimization] skillAreas: [skill-area:mathematical-reasoning] roles: [role:backend-engineer, role:computational-scientist]

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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"]
}