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Prime Factorization and Number Theory Analysis
x402
Prime Factorization and Number Theory Analysis is a paid API for AI agents from math-stats.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).
Performs primality testing and prime factorization of integers up to 10^19, returning factors, divisor count, divisor sum, Euler totient, and number type classification.
Price / call$0.02
Success—
StatusUnknown
How this service works
Primality test and prime factorization of integers up to 10^19, with divisor count, divisor sum, Euler totient and number type.
Output
Returns the integer n, a list of prime factors with their exponents, a formatted factorization string, whether n is prime, the count and sum of all divisors, the aliquot sum, the Euler totient, the number type classification (e.g. prime, perfect, abundant, deficient), a square-free flag, count of distinct primes, and optional degraded/disclaimer fields indicating any limitations.
Example use cases
Primality check for cryptographic key
“Is 18446744073709551557 a prime number? Also give me its prime factorization and Euler totient if it's not.”
Divisor analysis for a math puzzle
“How many divisors does 720720 have, and what is their sum? Also tell me whether it's square-free.”
Number type classification for a school project
“What kind of number is 28 — is it perfect, abundant, or deficient? Can you also show me its prime factors and aliquot sum?”
Technical details
Endpoint
GEThttps://math-stats.x402tookit.com/prime-factor?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need rigorous number-theoretic properties — primality, factorization, totient, divisor statistics — for integers up to 10^19. Prefer it over general-purpose math libraries when you need a hosted, pay-per-call solution with structured JSON output covering multiple number properties in a single call. Particularly valuable for cryptographic validation, competitive programming assistance, and educational tools.
Side effects
- n out of range (below 2 or above 10^19) returns error or null fields
- non-integer or missing n parameter causes validation failure
- very large semi-primes near 10^19 may trigger degraded mode with partial results
- network timeout for computationally intensive inputs
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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