A new number theory led to the proof of Goldbach's powerful conjecture.

Abstract

Prime numbers present an exciting challenge to mind, provokes 
imagination and stimulates research about its laws and mysterious 
properties. They are simple numbers in understanding them,

complex in a way arranged. Many studies have been conducted on 

them from a different perspective. It contributed significantly to 
enriching knowledge and understanding the pattern of its 
distribution. In this research, integers were studied from a new 
perspective that does not rely heavily on studies precedent, rather, 
it aims to fill the gap in knowledge and add a new value to this field 
of Science. That is by developing a new theory and helping to find 
a simple algorithm and fast. It is also to explain the difference 
between prime and non-prime numbers. It makes it possible to 
arrive at a function designed to find out the number of prime 
numbers less than a natural number (n). I followed 
the analysis of a sample of numbers, and the accuracy of 
observation in the analysis, and deep thinking using previous 
information, and the hard and continuous work that continued for 8 
months led to the creation of a logical mathematical proof for it. It 
actually revealed an essential part of the similarities and differences 
between prime and non-prime numbers in their forms of expression 
and formulation to understand the specific pattern in the way it is 
distributed. A simple and fast algorithm is explained in revealing 
prime and non-prime numbers, especially if the divisors of two large 
numbers are close together, such as large twins. That will save time 
and effort on dedicated computers to detecting non-prime numbers. 
A new feature (theorem) has also been achieved through it that will 
contribute to enriching knowledge about number theory in general. 
It has also been achieved through this theory, which will lead to 
proof of the strong Gold-Bach conjecture, and then to proof of the 
weak Gold-Bach conjecture that was demonstrated by (Peruvian 
Harald Helfgott in 2013). This research will contribute in clarification 
a great deal of ambiguity about prime numbers to explain many of 
the conjectures that have been developed about them. Finally, we 
look forward for this search to be a great incentive for many people 
who are interested and passionate about studying prime numbers to 
discover more and more of ambiguity to explain the strongest 
hypotheses made about primary numbers.