{"uid":"cap_d2YJr2iTqnu6wFa7LiwIf","slug":"fastx402-prime-factorization-c5c6f507","name":"FastX402 Prime Factorization","description":"200 pay-per-call tools for AI agents, from $0.001 per request in USDC on Base or Solana with x402. No account, no API key.","url":"https://fastx402.tools/prime-factorize?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["n"],"properties":{"n":{"type":"string","description":"Positive integer to factorize (1 to 10^15)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"n":{"type":"integer"},"factors":{"type":"array","items":{"type":"integer"}},"prime_powers":{"type":"array","items":{"type":"object","properties":{"prime":{"type":"integer"},"exponent":{"type":"integer"}}}}}}}}}},"responseSchema":{"type":"json","example":{"n":360,"factors":[2,2,2,3,3,5],"prime_powers":[{"prime":2,"exponent":3},{"prime":3,"exponent":2},{"prime":5,"exponent":1}]}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.001","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.001/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_kHBcG0ajSF3DFKomCbTYs","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.001","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Returns the complete prime factorization of a positive integer up to 10^15, including all prime factors and their exponents.","exampleAgentPrompt":"What's the prime factorization of 831600? Give me the full list of prime factors and their exponents.","exampleUseCases":[{"title":"Factorize large cryptographic modulus","prompt":"Can you find the prime factorization of 999999937? I need to know all prime factors and their exponents."},{"title":"Classroom math problem helper","prompt":"My homework asks for the prime factorization of 720 — can you break it down into primes and show me the exponents?"},{"title":"Check divisibility structure of a number","prompt":"What are the prime factors of 1000000007 and how many times does each prime appear?"}],"resultDescription":"A JSON object containing the original integer n, a flat list of all prime factors (with repetition), and an array of prime-power objects each showing a distinct prime and its exponent in the factorization.","failureModes":["n is not a positive integer or is out of range (1 to 10^15) — likely returns a 400 or error message","n is 0 or negative — invalid input, likely rejected","n is too large (> 10^15) — exceeds supported range","Payment failure or insufficient USDC balance — 402 response before computation","Non-numeric string passed as n — schema validation error"],"whenToPreferThis":"Choose this endpoint when you need fast, accurate prime factorization of integers up to 10^15 without setting up an account or API key. It is ideal for agents that occasionally need number-theory computations on demand and want pay-per-call pricing in USDC rather than a subscription. Prefer over local computation when the agent environment lacks a math library or when factorization of large numbers (close to 10^15) is needed reliably.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T07:21:03.287Z","isFirstParty":false,"canonicalSlug":"fastx402-prime-factorization-c5c6f507"}