Yesterday I was 23505 days old. This number is triprime with factors of 2, 3 and 1567. I'm not sure how widely the term "triprime" is used in the mathematical community but it follows on logically enough from the term "biprime". One way of visualising a triprime number is to associate it with a rectangular prism whose length, breadth and height correspond to the three factors. Suppose we want to create a rectangular prism with a volume of 23505 cubic metres using only square plates with sides of one metre. There is only one way to do this and that is with a prism whose sides measure 2, 3 and 1567 metres (or 1.567 kilometres).
Viewed in one way, this prism has a very narrow cross-section of 2 metres by 3 metres and it is very inefficient in terms of the surface areas required to enclose the volume. The most efficient shape would be a cube with a side of \(23505^{1/3}\) metres. This cube would have a surface area of \(6 \times 23505^{2/3} \) square metres as opposed to our prism with a surface area of$$(2 \times 3 + 3 \times 1567 + 2 \times 1567) \times 2 \text{ m}^2 $$As was done with biprimes earlier, we could then determine the percentage "surface area efficiency" of our prism according to the formula:$$ \text{efficiency}=\frac{\text{surface area of cube}}{ \text{surface area of rectangular prism}} \times 100$$In the case of 23505, the efficiency turns out to be a little over 31.39% by my calculations.
So biprimes can be visualised as unique rectangles (that in some cases can be squares) and triprimes can be visualised as unique rectangular prisms (that in some cases can be cubes). Tetraprimes and beyond of course can have no visualisation in 3-dimensional space.
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