Lubina J. Symmetry of prime numbers and their products

No publisher info, 2023. — 34 p."The mathematical sciences particularly demonstrate symmetry and order constraints; and these are the greatest forms of beauty". Aristotle
In the previous chapter, we were delighted with the forms of beauty of an equilateral triangle, which represents the symmetrical transformation of natural numbers into quadratic numbers using triangular numbers as their sums 3 = 6 ± 3 = 9, 1 + 2 = 3 + 3 = 6 + 4 = 10.
All prime numbers and their products are built symmetrically, and therefore they are arranged symmetrically. In fact, the arrangement of prime numbers depends on a strict relationship to their products, which results from the ability to create identical intermediate sums to a given quantity. Up to 10 we have 4 prime numbers (2 + 3 + 5 + 7) = 17, they form 4 identical intermediate sums up to 10 [2 + 8 = 10, 3 + 7 = 10, 5 + 5 = 10, 7 + 3 = 10, (8 + 7 + 5 + 3) = 23, 17 + 23 = 40/4 = 10]. According to this scheme, the ratio of prime numbers to their products will be formed, i.e. out of 40 odd numbers in a given interval, there may be 17 prime numbers and 23 their products. This is what it looks like on a line chart. Here, the sum of 4 prime numbers (2 + 3 + 5 + 7 = 17), complemented by the sum of the differences to 10 (8 + 7 + 5 + 3 = 23), shows the ratio of 17 prime.