Discover / numtheory.openverbs.com

Prime factorization

■ Challenge detected

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.

x402
Base
USDC

Listed price: $0.004
Challenge detected: 10 of the last 10 checks
Median response: 220 ms
Last checked: 17 Oct, 09:26 UTC
In our index since: 26 Sept 2026

Endpoint

curl -i https://numtheory.openverbs.com/v1/factorize
# 402 Payment Required: pay with an x402 client (USDC on Base),
# then send the same request again with the payment attached.

6 listed endpoints · on x402 Bazaar

Checks and payment terms on this page refer to the endpoint above. Other listed endpoints have not been checked individually.

Base URLhttps://numtheory.openverbs.com/v1

POST/lcm$0.004Least common multiple of two or more positive integers (arbitrary precision).
POST/is-prime$0.004Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer. Returns { prime }.
POST/factorize$0.004Prime-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.
POST/gcd$0.004Greatest common divisor of two or more non-negative integers (arbitrary precision).
POST/modpow$0.004Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.
POST/totient$0.004Euler'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).

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Showing 6 of 6 listed endpoints.

Agents can find it through the Superstables MCP server and JSON API: GET /api/v1/services/numtheory.openverbs.com

Recent checks

28 Sept 2026One bar per check, showing up to 20 recent checks. Coloured bars show relative response time, with a minimum visible height; full-height grey bars mean no challenge was detected. “Challenge detected” means HTTP 402 or another detected payment-challenge signal.17 Oct 2026

All 10 checks

When (UTC)	Result	HTTP	Response
17 Oct, 09:26 UTC	Challenge detected	402	559ms
16 Oct, 08:13 UTC	Challenge detected	402	178ms
14 Oct, 23:56 UTC	Challenge detected	402	290ms
13 Oct, 10:39 UTC	Challenge detected	402	236ms
11 Oct, 10:02 UTC	Challenge detected	402	366ms
9 Oct, 21:31 UTC	Challenge detected	402	181ms
8 Oct, 18:39 UTC	Challenge detected	402	184ms
7 Oct, 15:42 UTC	Challenge detected	402	203ms
6 Oct, 15:31 UTC	Challenge detected	402	238ms
28 Sept, 17:02 UTC	Challenge detected	402	188ms

Questions

Did our last probe detect a payment challenge?

At our last probe on 17 Oct, 09:26 UTC, it returned HTTP 402 or another detected payment-challenge signal. This check did not test payment, delivery or compatibility with the Superstables client.

What price is recorded for Prime factorization?

Its listed price is $0.004.

What payment terms does Prime factorization advertise?

The listing advertises x402, Base and USDC. It names cdp as its facilitator. Check the seller's current payment challenge and authentication requirements before paying.

Where is Prime factorization listed?

In x402 Bazaar. Superstables first indexed it on 26 Sept 2026.

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