Applied Mathematics & Information Sciences

Author Country (or Countries)



We present a certain geometrical interpretation of the natural numbers, where these numbers appear as joint products of 5- and 3-multiples located at specified positions in a revolving chamber. Numbers without factors 2, 3 or 5 appear at one of eight such positions, after a specified amount of rotations of the chamber. Our approach determines the sets of rotations constituting primes at the respective eight positions, as the complements of the sets of rotations constituting composite numbers at the respective eight positions. These sets of rotations constituting composite numbers are exhibited in strict rotation regularities from a basic 8£8-matrix of the mutual products originating from the eight prime numbers located at the eight positions in the original chamber. These regularities are expressed in relation to the multiple 112 as an anchoring reference point. The complete set of composite numbers located at the eight positions is exposed as eight such sets of eight series. Each of the series is completely characterized by four simple variables when compared to a reference series anchored in 112. Ad negativo this also represents an exact and complete generation of all prime numbers as the union of the eight complement sets for these eight non-prime sets of eight series. By this an exact and complete pattern in composite numbers, as well as in prime numbers, are exhibited in the maximum sense of a pattern.

Suggested Reviewers