prime-sieve-generator

# 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 ```json { "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 ```json { "type": "object", "properties": { "success": { "type": "boolean" }, "code": { "type": "string" }, "complexity": { "type": "object" }, "memoryUsage": { "type": "string" } }...