Zero Centers: The Mental Math and Primality Guide

This paper introduces an innovative framework termed the “ Zero Center ” to facilitate mental arithmetic and explore prime numbers. The framework leverages numerical patterns centered around multiples of ten, hundreds, thousands, their halves, or quarters for mental arithmetic operations, while employing the 6k ± 1 form around the Zero Center at 6k and larger centers (e.g., 30 and 210) to address primality. For mental arithmetic, the Zero Center approach organizes operations such as multiplication, squaring, exponentiation, and root extraction (square, cube, fourth, and fifth roots), building on established references while introducing novel techniques. For prime numbers, the Zero Center innovates primality testing, iden- tification of twin primes, and the application of Goldbach’s Conjecture for even integers up to 1000. Through structured tables and simplified computational meth- ods, the study provides effective tools for analyzing prime numbers, establishing the Zero Center as a novel theoretical system. These contributions enhance the under- standing of prime numbers and pave the way for future research into conjectures such as the infinitude of twin primes and Goldbach’s Conjecture.