Orion Crest, Series_1

Chapter 85: Proof of the Polignac conjecture

　　When the inspiration came, the pen could not stop, Orion, whose whole body had been filled with spiritual food, only felt energised, and taking that pen, he began to write down lines of arithmetic on the paper in a sprawling manner.

　　[Let the finite group G and |G| = p1α1p2α2 - piαi, where pi is a prime and αi is a positive integer. Let p ∈ π(G), define deg(p) = |{q ∈ π(G)|p~q)|

　　Call deg(p) the number of times vertex p. Then define C(G) = ......

　　......

　　]

　　Time passed by, and the feeling of the text flowing didn't stop for a moment.

　　This feeling was different from last time.

　　Last time, the inspiration was borrowed, but this time, it was birthed by himself.

　　The tip of the pen travelled over the paper.

　　Without realising it, five sheets of draft paper had already been written.

　　Sorting out the steps and thoughts, Orion rubbed his stomach, leaned back in his chair, and pulled out his mobile phone.

　　He thought it hadn't been long, but he was shocked when he looked at the time.

　　" Shit, it's already five o'clock?!"

　　Orion eventually couldn't hold out any longer and hurriedly ate his dinner, returning to continue his hard work.

　　......

　　Rome wasn't built in a day, a perfect theory not only needs inspiration, but also the accumulation of time.

　　For several consecutive days, Orion almost always soaked in the library during the day, and continued to delve into it after returning to his dormitory at night.

　　Occasionally, he also had to take time to reply to Professor Frank's emails. Although there was no new data coming from CERN for the time being, the work of perfecting the theory also required calculations.

　　Every day, Orion enjoyed himself.

　　In the second week of September, on a breezy morning, Orion, sitting in the library, stretched out and looked at the more than ten pages spilling out in front of him, and let out a sigh in his heart.

　　"It's finally fucking done!"

　　When the sensitivity was drained, all the work was done to pave the way for the moment when the inspiration came. And when he truly figured out the solution to this problem, finding the exit to the labyrinth seemed to be right in front of his eyes.

　　At the moment, Orion was indescribably happy.

　　Not just because he had solved yet another mathematical puzzle, but precisely because in solving this mathematical puzzle, he had gained a deeper understanding of group theory and had worked out a whole new set of mathematical methods based on it.

　　And this discovery, even more than solving the mathematical conjecture itself, put him in an excited mood.

　　Hilbert once remarked that Fermat's Last Theorem is a chicken that lays golden eggs, not because the hen has fed a large number of mathematicians or given many journals the opportunity to publish papers, but because many novel mathematical methods have been derived from the study of number theory problems.

　　Inspired by Fermat's problem, for example, Kummer introduced the notion of an ideal number and discovered the unique decomposition theorem for decomposing a number in a cyclic domain into ideal prime factors, which has today been generalised to arbitrary algebraic domains by Dedekind and Kronecker, occupies a central place in recent number theory, and whose significance extends far beyond the scope of number theory into the realm of function theory of algebra.