"… Based on the paper published by Professor Zellberg in 1995, I further improved the large sieve theory using topology. Then, in order to expand the Polignac's conjecture, I introduced a group theory method.

"The main step is in the first three lines of the second thesis page. As for some of the group theory foundations, I will explain that later."

Pairs of eyes stared at Lu Zhou.

Lu Zhou sensed that people were looking at him. He turned the Powerpoint Page and continued to speak.

"We record S1(q,α)=∑e(αm3/q), C1(q,α)=∑e(αm3/q2), brought into Td(n,q)=∑S1(q,αd3) ·|C1(q,αd3)|·e(-an/q)/qψ2(q), the order δd(n)=∑Td(n,q) can be obtained."

"This step is crucial. It comes from the 2013 weak Goldbach's conjecture proof from Helfgott."

"However our goal is different than the circle method. We are not trying to perform Fourier analysis in the number theory function. Instead, we are trying to approximate the distribution of prime numbers."

"Next up is the "Group Structure Method"…"

Actual