Pääkuorilukuina

Pääkuorilukuina (literally “as primary shell numbers”) is a term found in Finnish mathematical literature describing a method of classifying natural numbers by a hierarchical shell decomposition. In this framework, integers are grouped into successive shells, with the outermost group called the head shell. A number is referred to as a pääkuoriluku in a given decomposition if it belongs to the head shell or if it serves as a defining representative for that shell.

Because the precise definition of shells and the rules for moving from one shell to the next vary between authors, there is no single universally accepted formal definition. In typical presentations, the outer shell is described as containing numbers that fail to satisfy a simpler rule, while inner shells contain numbers that progressively meet stricter criteria. The concept is used mostly in Finnish-language expository or recreational number theory to illustrate layered classifications of integers and to pose problems about the distribution of numbers across shells.

Use and scope: The notion is primarily found in didactic contexts, puzzles, and historical discussions of number classifications in Finnish texts. It is not a standard term in international number theory, and there is no universally accepted formalization. Researchers encountering the term should consult the specific source to understand the exact shell construction being used.

See also: Number classification, Shell decomposition, Layered structures in mathematics, Finnish mathematical terminology.