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Charles said:a_i is not defined. "Continual number" is not defined.
The "Proof of Goldbach, Polignac, Legendre, Sophie Germain conjecture" is a mathematical proof that provides evidence for the validity of four conjectures in number theory. These conjectures include the Goldbach conjecture, the Polignac conjecture, the Legendre conjecture, and the Sophie Germain conjecture. They all relate to the distribution and properties of prime numbers.
The proof was published in 2013 by mathematician Harald Andrés Helfgott from the University of Göttingen in Germany. Helfgott's proof is considered a significant achievement in the field of number theory.
The significance of this proof lies in the fact that it provides evidence for the validity of four long-standing conjectures in number theory, which have been studied and debated by mathematicians for centuries. It also helps to advance our understanding of prime numbers and their properties.
The proof was met with a mix of excitement and skepticism from the mathematical community. While some praised Helfgott's achievement, others raised concerns about the complexity and validity of the proof. Further research and analysis are still ongoing.
The proof opens up new avenues for future research in number theory and prime numbers. It also highlights the importance of rigorous and thorough mathematical proof, as well as the ongoing search for deeper insights into the properties and behavior of prime numbers.