What geometric applications do prime numbers have?

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