Number theory is my favorite branch of mathematics. Mathematics is my favorite field of study.

This summer, I discovered the following fact:

The maximum distance from any given number n to the next prime is less than twice the square root of n.

For each primorial from 30 onward, there exists a pattern in the arrangement of the prime factors of the composite numbers which I call "the mirror patterns". For each of these mirror patterns, there is a set of five whole numbers to which I have assigned the names $Zero$, $the$ $Left$ $Mirror$ $Center$, $the$ $Central$ $Number$, $the$ $Right$ $Mirror$ $Center$, and $the$ $Product$. Here is the set of these five whole numbers for the primorial 30: $$0,4,15,26,30$$ Surrounding 4 are the prime numbers 3 and 5.

Surrounding 26 are the prime factors 5 and 3.

$$15=3·5$$

© 2014 Jeffrey Young The foregoing is from the summer of 2014 and is my original work. I have contacted the World Intellectual Property Organization. https://www3.wipo.int/contact/en/area.jsp