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Saylor Innovations Number Theory Toolkit
x402
Saylor Innovations Number Theory Toolkit is a paid API for AI agents from saylorinnovations.com, paid per call via x402, $0.01/call, status unknown (last checked 2026-10-18).
Analyzes a whole number and returns primality, factorization, divisors, totient, number class, roman numeral, English words, base representations, and optionally GCD/LCM with a second number
Price / call$0.01
Success—
StatusUnknown
How this service works
Number toolkit - primality, prime factorization, divisors, totient, perfect or abundant class, roman numeral, English words, bases and gcd or lcm with a second number
Output
A JSON object containing: the integer n, its English word form, primality boolean, prime factors, list of divisors, Euler totient, aliquot and divisor sums, number class (perfect/abundant/deficient), roman numeral, binary/octal/hexadecimal representations, digit count and digit sum, next prime, and optionally a with_m block containing GCD, LCM, and coprimality with a second number m.
Example use cases
Verify primality for cryptographic key
“Check whether 15485863 is prime, and if not, give me its prime factorization and the next prime above it.”
Compute GCD and LCM for fraction simplification
“What is the greatest common divisor and least common multiple of 144 and 60? Also tell me if they're coprime.”
Convert number to roman numerals and words
“Give me the roman numeral and English word spelling for 2024, plus whether it's a perfect, abundant, or deficient number.”
Technical details
Endpoint
GEThttps://saylorinnovations.com/api/math/number-theory?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need comprehensive number-theoretic properties of a single integer — primality, factorization, divisors, totient, classification, and multiple base representations — all in one call rather than calling separate specialized APIs. Especially useful when you also need GCD/LCM against a second number simultaneously.
Side effects
- Missing required parameter n returns an error
- n outside range 0–9007199254740991 returns a validation error
- Non-integer or non-numeric n causes a parse error
- Very large n near the maximum may have limited factorization accuracy
- GCD/LCM fields are null when m is not provided
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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