I call n2 + m a “multi-dimensional” sum, because:-
- n x n = n2 calculates the size of a square 2D area
- and m quantifies the length of a 1D line.
In fact, these kinds of sums could be called “3D”, since m could ‘go vertical’ to ‘add’ to n2 geometrically!
Adding a 1D value to a 2D value, is like adding sticks to squares. We can only count them as objects. By calculating arithmetically we mix dimensional qualities to achieve one numerical value.
But conventional wisdom allows for this ‘dimensional mix’ with the definition of
these arithmetical units: 13 = 12 = 11 = 10 = 11/2 = SQRT (1)
The fact that n2 + m leads to “Diagonals of Primes” was as unsuspected as all my other discoveries. Maybe PhD texts will be written about “multi-dimensional sums and their relevance to prime numbers?” Meanwhile here’s what excited me: a “Diagonal of Prime Numbers” that I ‘mirrored’ such that it forms a “Prime Diamond”. The store has both picture and workbook available for you to experiment with.
This diagonal is the longest I found. Its Primes end only with Last Digits 1, 3 and 7:
NEXT: “DIAGONAL Prime Numbers”