{"x402Version":2,"name":"Number Theory","description":"Elementary number theory on arbitrary-precision integers — GCD and LCM, prime factorization, primality testing, Euler's totient, and modular exponentiation.","version":"0.1.0","openapi":"https://numtheory.openverbs.com/openapi.json","resources":[{"url":"https://numtheory.openverbs.com/v1/gcd","method":"POST","description":"Greatest common divisor of two or more non-negative integers (arbitrary precision).","tags":["greatest common divisor","compute gcd","gcd api","common divisor lookup","integer gcd","bigint gcd"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]},{"url":"https://numtheory.openverbs.com/v1/lcm","method":"POST","description":"Least common multiple of two or more positive integers (arbitrary precision).","tags":["least common multiple","compute lcm","lcm api","common multiple lookup","integer lcm","bigint lcm"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]},{"url":"https://numtheory.openverbs.com/v1/factorize","method":"POST","description":"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.","tags":["prime factorization","factor integer","integer factors api","prime factors lookup","divisor count","factorize number"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]},{"url":"https://numtheory.openverbs.com/v1/is-prime","method":"POST","description":"Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer. Returns { prime }.","tags":["primality test","check prime number","is prime api","miller rabin test","validate prime","prime lookup"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]},{"url":"https://numtheory.openverbs.com/v1/totient","method":"POST","description":"Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed from the prime factorization).","tags":["euler totient","compute phi","totient function","coprime count","number theory totient","totient api"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]},{"url":"https://numtheory.openverbs.com/v1/modpow","method":"POST","description":"Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.","tags":["modular exponentiation","mod pow","compute base exponent mod","fast modular power","modular arithmetic api","bigint modpow"],"accepts":[{"scheme":"exact","network":"eip155:8453","price":"$0.004","payTo":"0xb3f4de103F34b99f0Da19B4F16D6B53a14C2194A","asset":"USDC"}]}]}