Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers

Abstract

In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P1 = 1 + 6 * n (n > 0, n is an integer) P5 = 5 + 6 * m (m ≥ 0, m is an integer) Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Twin prime numbers can only be formed between P1 and P5 prime numbers, n must be 1 greater than m. The largest prime number is known at the moment 2^(82,589,933) – 1 is a P1 prime number.