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

With no annotations and no substantive description, the behavioral burden falls entirely on the description, which says nothing about inputs, side effects, return type, or failure modes. The text merely echoes the tool's name and reveals no behavior beyond what the identifier already implies.

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 text is short but not meaningfully concise: it is a redundant label prefix plus the same phrase repeated. 'Is Mersenne Prime: Is Mersenne Prime' reads as under-specification rather than efficient communication, and no useful information is front-loaded because there is none.

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?

Given no output schema, no annotations, and an empty input schema, the description is the only source of context and it supplies almost none. An agent cannot tell how the candidate number is supplied, what the tool returns, or how this differs from x402-is-mersenne or x402-is-prime.

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?

The input schema contains zero parameters and 100% schema description coverage, so there are no parameters for the description to document. By the rule of thumb, zero-param tools receive a baseline of 4 even though the description itself adds no parameter clarification.

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?

The description is 'Is Mersenne Prime: Is Mersenne Prime', which is a tautology that only restates the tool name. It provides no verb, object, or explanation of what the tool actually does, and does nothing to distinguish it from the many same-type siblings.

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 guidance about when to use this tool or when to prefer an alternative. It does not mention the near-similarly named sibling x402-is-mersenne or any other comparison tool, so an agent receives no routing information.

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