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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It does not state the input type expected (the schema says string) or what a failed/unparseable input does, whether it returns a boolean, or how it treats single-digit reversals (which are trivially palindromic and should not count as emirps). For a predicate tool with zero annotation coverage, this is a meaningful gap.

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 sentence is tight and front-loaded, but the trailing 'Provide value.' is filler that adds no information and weakens an otherwise clean sentence.

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?

With no annotations, no output schema, and a one-parameter predicate tool whose result type is never stated, the description leaves the agent unsure what comes back (boolean vs. formatted text) and how edge inputs are handled. It defines the concept well but is not complete enough for correct invocation.

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 100%, so the single 'value' parameter is already documented ('Value to process'). The description adds the semantic intent of that value (a number to test) but no format or type detail beyond the schema, so the baseline of 3 applies.

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 gives a specific verb+resource ('Check whether a number is an emirp') and immediately defines the concept ('a prime whose reversal is also a different prime'), which distinguishes it from siblings like x402-is-prime or x402-is-palindromic-prime. An agent can tell exactly what this tool does and how it differs from other number-property checks in the list.

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?

The definition of an emirp implies the usage context (applying it to candidate integers to test the property), so an agent can infer when to call it. But there is no explicit guidance about when NOT to use it or which sibling (e.g., x402-is-prime) to prefer for the simpler question, so it stops at implied usage.

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