primenumbered

Primenumbered is an informal term used to describe mathematical objects that are organized according to prime numbers. It is not a standard term in formal number theory, but it appears in blogs, puzzle literature, and exploratory papers to indicate cases where primes govern labeling, indexing, or construction.

Common interpretations include prime-indexed sequences, where a sequence is formed by taking terms at prime positions. For example, the subsequence of the primes p_k with prime indices k yields p_2, p_3, p_5, p_7, p_11, ... = 3, 5, 11, 17, 31, ... Another interpretation is prime-labeled structures, in which the elements of a combinatorial object carry labels drawn from the sequence of primes, such as assigning primes to the vertices of a graph in a uniform or rule-based way.

In both senses, the primenumbered property emphasizes the role of primality either in selecting elements or in labeling. Analyses of primenumbered objects often focus on how prime distribution affects structure, such as density of selected terms or labeling constraints, and may connect with related ideas like prime-indexed sequences and prime labelings in combinatorics.

Because primenumbered lacks a fixed formal definition, precise statements depend on context. It remains primarily a descriptive badge rather than a formal classification.

See also: Prime numbers, Prime-indexed sequences, Prime labeling, Number theory.