Abstract
This paper reports on some interesting properties of the natural number system which may interest mathematicians, scientists and engineers. In a recently published paper, a geometrical model in the form of a 2‐dimensional matrix map of the distribution of divisibles and indivisibles of the natural number sequence was constructed and on that basis, it was possible to derive an analytical expression which describes globally the distribution of primes and nonprimes. This equation is called the equation of divisibles.By predicting the presence of divisibles against each integer position, this equation also at the same time predicts the absence of indivisibles in the remaining positions. This approach is rather unusual but it works. Many interesting geometrical properties of the natural number system were discovered using the matrix map model which would be difficult to unravel by focussing on the prime number series alone. Two mathematical problems are posed which at this stage the author finds no proofs or solutions.
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