Orion Crest, Series_1

Chapter 34: I don't want to go to heaven yet

          At 8.30am, the classroom was nearly full. Orion found a seat in the back row.

　　By 8:50am, the lecture theatre was full, and some people even sat on the aisle to listen to the lecture. Not only from the university, but also from several other colleges and universities next door.

　　It is obvious that Professor Thomas is really popular.

　　At 9:00, the lecture officially began, looking at the old gentleman on the podium, Orion looked more and more familiar, and always felt that he had met him before. But the distance is too far, plus may have changed clothes, he really can't remember where he has seen.

　　"...... We all know that prime numbers are natural numbers that contain only two factors, and twin prime numbers, are pairs of prime numbers with a difference of 2, i.e., p and p+2 are the same as a pair of prime numbers. Examples are 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc. As the number gets larger, fewer and fewer twin prime pairs can be observed."

　　"There are 8 twin prime pairs up to 100, while in the interval 501 to 600, there are only 2 pairs. As the prime numbers increase, the next prime should get further and further away from the previous one, but, as famous and important as Goldbach's Conjecture, a conjecture claimed that there existed an infinite number of pairs of prime numbers that differed by only 2, such as 3 and 5, 5 and 7, and even this ......"

　　Speaking of this, Professor Thomas, on the blackboard, wrote a line of numbers.

　　[2003663613 x 2195000-1 and 2003663613 x 2195000+1].

　　He smiled and continued.

　　"The existence of infinitely many prime numbers with a difference of 2 is the famous twin prime conjecture."

　　So far, what Professor Thomas had said was so elementary that even Orion, who hadn't studied the twin prime number problem in depth, could easily follow along.

　　The rest of the freshmen, as well, both maths and non-maths amateurs, listened attentively and with interest.

　　Soon, though, the lectures began to go deeper.

　　"The ...... twin prime conjecture has long been a problem that has plagued the mathematical community. But just recently, there has been a breakthrough in the research for this problem." Professor Thomas smiled, flipped to the next page of the PPT, and continued, "Chinese mathematician, Mr Zhang Yitang proved a weaker form of the twin prime number, and found that there are infinitely many pairs of prime numbers with a difference of less than 70 million, thus achieving a breakthrough from nothing on the path to this important problem. "

　　Having said that, Professor Thomas pushed up his glasses and wrote down Zhang's proof process on the blackboard.

　　[Define theta(n)=lnn, if n is a prime number; define theta(n)=0, if n is a composite number. Take the function lambda(n)=...... define S1(x)=......S2(x)=......]

　　[Prove that S2-(log3x)S > 0 ......]

　　[......]

　　Looking at the ever-increasing number of formulas on that blackboard, the students who were previously able to understand them were instantly confused.

　　For example, the girl sitting next to Orion was all "Who am I?" "Where am I?" "What am I listening to?" She looked as if she had just missed a second.

　　Orion was able to follow Professor Thomas' thoughts.

　　In simple terms, that Mr Zhang cleverly chose a lambda function and successfully proved that the conclusion S2-(log3x)S1 > 0 valid for k >= 3.5*10^6.