# Services from numtheory.openverbs.com on Zero

> numtheory.openverbs.com serves 6 paid API services for AI agents, indexed by Zero. Each is callable per call with payment handled by Zero.

Canonical page: https://www.zero.xyz/host/numtheory.openverbs.com
Live health (JSON, refreshed every minute): https://www.zero.xyz/host/numtheory.openverbs.com/health.json

## Services

- [Euler Totient Function Calculator](https://www.zero.xyz/c/euler-totient-function-calculator-1f980f80/llms.txt): $0.004/call via x402. Computes Euler's totient function φ(n) — the count of integers from 1 to n that are coprime with n
- [Number Theory Modular Exponentiation (modpow)](https://www.zero.xyz/c/number-theory-modular-exponentiation-modpow-523722cb/llms.txt): $0.004/call via x402. Computes modular exponentiation: (base ^ exponent) mod modulus for arbitrarily large integers supplied as decimal strings.
- [Number Theory Factorization](https://www.zero.xyz/c/number-theory-factorization-072dbead/llms.txt): $0.004/call via x402. Factorizes a positive integer (up to 10^15) into its prime factors
- [Number Theory Is-Prime Checker](https://www.zero.xyz/c/number-theory-is-prime-checker-a3c4bb7a/llms.txt): $0.004/call via x402. Determines whether a given non-negative integer is a prime number
- [Number Theory LCM](https://www.zero.xyz/c/number-theory-lcm-502c3e47/llms.txt): $0.004/call via x402. Computes the Least Common Multiple (LCM) of two or more non-negative integers supplied as decimal strings
- [Number Theory GCD](https://www.zero.xyz/c/number-theory-gcd-7f4cf1be/llms.txt): $0.004/call via x402. Computes the Greatest Common Divisor (GCD) of two or more non-negative integers supplied as decimal strings.

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

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