Orion Crest, Series_1

Chapter 107: Ethereal sound

　　The sky outside the window dawned.

　　Orion, who was lying on his desk, slowly opened his eyes.

　　Rubbing his somewhat sore brow, he looked at the calendar placed on the corner of the desk.

　　It's already May ......

　　Orion shook his head with a slight headache.

　　From the time he came to Princeton in February until now, almost a large portion of his time had been spent in this ten square metre house, and apart from driving to the supermarket to buy groceries, he basically hadn't left the house.

　　What hurt him the most was the $10,000 club card, which he hadn't even used a few times.

　　For nearly half a year since he received that mission, he had been challenging Goldbach's Conjecture.

　　Now, it was finally coming to an end.

　　Taking a deep breath, Orion stood up from his chair.

　　Having come to the final step, he was rather less anxious.

　　Humming a little song, he walked into the kitchen and got himself something to eat, Orion even took out a bottle of champagne from the fridge and poured it for himself.

　　The champagne had been bought two months ago for this moment.

　　After a quiet dinner, Orion calmly went to the kitchen to wash his hands, and then returned to his desk to finish up his work for a while.

　　Crossing over nearly fifty pages of essay paper, he put pen to paper and continued writing where he had drifted off to sleep before finishing yesterday.

　　[...... Obviously, we have Px(1, 1) ≥ P(x, x^{1/16})-(1/2)∑Px(x, p, x)-Q/2-x^(log4)......(30)]

　　[...... From equation (30), citing Theorems 8, 9 and 10, it can be proved that Theorem 1 holds.]

　　The so-called Theorem 1 is the mathematical formulation of Goldbach's Conjecture, as defined in his paper.

　　That is, given a sufficiently large even number N, there exist prime numbers P1 and P2 satisfying N=P1+P2.

　　Similar to this is Chen's theorem N = P1 + P2 - P3, and a series of theorems about P(a, b).

　　Of course, although this formula is now called Theorem 1 in his paper, it may not be long before this theorem is upgraded to something like "Orion's Theorem" when the mathematical community generally accepts his proof process.

　　However, the review period for such major mathematical conjectures is generally long.

　　Perelman's proof of the Poincaré Conjecture took three years before it was recognised by the mathematical community, and Mochizuki Shinichi's proof of the ABC Conjecture, because of the large amount of "mysterious terminology", requires that one must at least read and understand his "Inter-universal Teichmüller" in order to have a basic understanding of it. So far no one has finished reading it, and it is likely to be difficult to do so in the future.

　　The speed with which a major conjecture is reviewed depends very much on how hot the proposition is and how "new" the work is.

　　In proving the twin prime theorem, Orion did not use any particularly novel theory, but only innovative topological methods, and those who have studied the paper can quickly see what he has done.

　　The review period for the paper proving the Polignac-Orion theorem, on the other hand, was significantly longer.

　　Even though his group construction method was already reflected in the proof of the twin prime theorem, the large number of changes made it so far out of the realm of the sieve theory that it took quite a bit of time for the reviewers, even if they were greats like Deligne, to come to a final conclusion.