Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are supplied, so the description carries the full behavioral burden. It does disclose the monetization/auth trait (5 free trial calls per signed wallet), which is genuinely useful, but it says nothing about how check/generate/factorize are dispatched from a single input, what output each mode returns, or how failures or exhausted trials surface.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The definition is one compact sentence plus a pricing note, front-loading the capability before the trial terms. Nothing is padded, though the emoji and marketing phrasing sit oddly next to a technical utility description.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a multi-mode tool with an opaque string parameter, zero annotation coverage, and no output schema, an agent needs to know how to select a mode and what comes back. Neither is addressed, leaving the dispatch model and return shapes entirely unspecified.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0% for the single "number" parameter, which is typed as a string with no description or constraints. The description does not clarify whether the value is an integer, how large it may be (string suggests big-number support), or what format factorize/generate expect, so it adds essentially nothing beyond the bare schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

"Prime number utilities — check, generate, factorize" names three distinct verbs and the resource, so the general domain is clear. However, the sibling list contains dedicated tools like x402-is-prime, x402-prime-factors, and x402-prime-series that map to exactly those three verbs, and the description never explains whether this tool subsumes them or how it differs.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no when-to-use guidance at all: no statement of which operation runs, whether an operation selector exists, or when an agent should pick this over the specialized prime siblings. The only extra sentence is billing information, which is not usage guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.