After four years, Professor Yitang Zhang of the University of California, Santa Barbara, a famous mathematician, recently returned to his alma mater. On the afternoon of December 25, 2023, Yitang Zhang gave a public talk entitled "New Development in Prime Distribution" at the Wenyuan Hall of Zhihua Building, Peking University, sharing his research work around the twin prime conjecture. Professor Chen Dayue, Dean of the School of Mathematical Sciences of Peking University, presided over the report and awarded the certificate of "Outstanding Alumni of Peking University" to Zhang Yitang.
Report to the scene. 
Chen Dayue presided over the report and presented Zhang Yitang with the certificate of "Outstanding Alumni of Peking University".
Ten years ago, a weak form of the twin prime conjecture was proved, and later, this result was greatly improved by Maynard et al., in this report, Zhang Yitang briefly reviews the relevant history and summarizes the idea of proof. Goldston, Pintz, and Yildrim in their early work introduced the eigenfunction of prime numbers to indicate whether a number is prime or not. Thus, the twin prime conjecture that there are infinitely many pairs of primes such that the difference between the two primes is 2, i.e., to prove that there are infinitely many n such that there is.
The twin prime conjecture is one of the most famous propositions in number theory, and it is the dream of many number theorists.
Goldston et al., after a series of variations, turned to trying to prove a weakened version of the twin prime conjecture by fixing a set of positive integers.
After that, look for a non-negative group.
Make a sum.
to an infinite number of them.
True, thus achieving proof that there are infinitely many differences that are controlled in.
The following pairs of prime numbers. They carried out a series of constructions and found a set.
In the form of: 
Thereinto. is pending.
power. Combined with the famous.
Theorem,
The trickiest part of the story.
Zhang Yitang combines various classical results of analytic number theory and uses some new techniques in algebraic geometry, such as the Riemann hypothesis on finite fields, through variables.
, successfully controlling the error term in the equation to be demonstrated, proved.
to some. can make the original proposition true. This was a great breakthrough in the mathematical community, which attracted the attention of the majority of number theorists, and was later used to advance the exploration of the twin prime conjecture. Subsequently, Tao Zhexuan organized an online project to use Zhang Yitang's results to find the best result for the difference between prime pairs. So far, a case with a proof difference of 246 has been achieved. That is, there are an infinite number of pairs of prime numbers such that their difference is no greater than 246.
Report to the scene. In the ensuing Q&A and tea break, the participating teachers and students had a heated discussion with Zhang Yitang on the content of the report and related mathematical problems.
Zhang Yitang interacted with teachers and students.
During the visit, Zhang Yitang communicated with Academician Tian Gang and Wei Dongyi.