What geometric applications do prime numbers have?

[Loren Booda]

The Fibonacci numbers seem intimately connected with geometry. Prime numbers appear to avoid geometrics, however. Can you give some counterexamples of this latter statement?

 

[HallsofIvy]

A set of n objects can be place in an i by j rectangular array with i and j both greater than one if and only if n is NOT prime.

 

[Loren Booda]

Is the set of points constituting (n>1)-dimensional rectangular quadrilaterals and numbered non-prime larger than such a set numbered prime? Does this hold for both n real and n integer?

 

[Loren Booda]

Rectangles and prime cardinality

Sorry for the mix-up.

Please consider the special case:

"Is the count of all rectangles each containing a total non-prime number of points greater than the count of all rectangles each containing a total prime number of points?