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Number Theory Factorization
x402
Number Theory Factorization is a paid API for AI agents from numtheory.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-15).
Factorizes a positive integer (up to 10^15) into its prime factors
Price / call$0.004
Success—
StatusUnknown
How this service works
Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime.
Output
Returns the prime factorization of the submitted integer, identifying all prime factors (and their multiplicities) that multiply together to produce the input number.
Example use cases
Prime factorization for cryptographic analysis
“I need to know the prime factors of 999999999999937 — can you factorize it for me?”
Checking if a number is prime
“Factorize 104729 and tell me if it has any prime factors other than itself — I want to know if it's prime.”
Math homework prime decomposition
“What is the prime factorization of 720720? Break it down into all its prime components.”
Technical details
Endpoint
POSThttps://numtheory.openverbs.com/v1/factorizeWhen to prefer
Choose this endpoint when you need reliable, paid-API-quality prime factorization for integers up to 10^15. It's suitable for programmatic use cases in mathematics, cryptography education, number theory research, and automated pipelines that require factorization as a computation step. Prefer it over rolling your own factorization when accuracy and speed for numbers up to a quadrillion are needed without maintaining local number-theory code.
Side effects
- Input number exceeds 10^15 — rejected with validation error
- Non-numeric or non-integer string passed in the 'n' field — schema validation failure
- Empty or missing 'n' field — required field error
- Payment not provided or insufficient — x402 payment required response
- Network timeout for very large semiprime inputs near the upper bound
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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