> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/600-toc/634-primitive-recursive-functions/list-of-pr-functions.md). # The list of primitive recursive functions * addition * mul * exp * monus * abs * absolute difference * predecessor * factorial * primality testing * nth prime * divisibility, x-divides-y * EQ * LE * LT * GE * GT * α(x), `(== 0)`, isZero predicate * floor * integer division (with flooring) * pairing function (x,y) * Gödel's number (pairing function) * `Lt(x)` where x = \[a₁, …, aₙ] * projection, index `([a₁, …, aₙ])ᵢ` ## Operations on integers and rational numbers By using Gödel numberings, the PRFs can be extended to operate on other objects such as integers and rational numbers. If integers are encoded by Gödel numbers in a standard way, the arithmetic operations including addition, subtraction, and multiplication are all primitive recursive. Similarly, if the rationals are represented by Gödel numbers then the field operations are all primitive recursive. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/600-toc/634-primitive-recursive-functions/list-of-pr-functions.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.