The infinite set of natural numbers is formed by infinite subsets of pairs of quadratic intervals [n(n-1)+1, n^2], [n^2+1, n(n+1)]. Each of these pairs of intervals is formed by increasing quantities of elements, all governed by their divisor, of value ≤ n, closest to n. By bringing together these individual divisors of each element, a scale is formed for each interval, including all values included in the interval [1, n]. By assigning the name Mm (Major than minor) to these particular divisors, we note that between the elements and their divisors Mm, there is a one-to-one group correspondence which always allows for each quadratic interval the presence of at least one element having the trivial divisor 1 , i.e. the presence of at least one prime number, as noted by Oppermann's conjecture of 1882. By extending Fermat's method of factoring natural numbers, through quadratic number lines, it is confirmed that each of the divisors Mm finds group correspondence with at least one of the elements of the quadratic intervals. The mathematical law that regulates the distribution of prime numbers, therefore, is expressed through the divisors Mm which, from time to time, depending on the occurrences of each quadratic interval, observe some fundamental rules common to all quadratic intervals. Furthermore, by observing the quadratic intervals arranged inside the Spiral of Ulam, one has the opportunity to observe that, in a fascinating way, Nature places all the quadratic intervals, assembling them according to their four different typologies, each in a different cardinal direction: quadratic intervals A of odd n, quadratic intervals B of odd n, quadratic intervals A of even n, quadratic intervals B of even n.