From child prodigy to chief scientist

Hearing the shopkeeper say that, Xu Xiao was both amused and exasperated.

He must have thought that he was also a kid who loved playing games, but Xu Lang just wouldn't let him.

Xu Xiao decided not to explain anymore, since even if he said he was using the computer to look up papers, the other party might not believe him anyway.

After confirming that there was no problem with the computer, Xu Xiao then let Xu Lang pay the remaining balance.

As he was leaving, the shopkeeper couldn't help but say to Xu Lang:

"You've raised your child so well; he understands everything at such a young age."

"I heard that Yucai University had a kid about his age who got a perfect score in some competition this year and was directly admitted to Tsinghua University."

"I think your child is no worse than that child!"

Upon hearing the shopkeeper's words, Xu Xiaoxin wondered, "Is it possible that we are the same person?"

Upon hearing this, Xu Lang was overjoyed and felt an urge to immediately reveal Xu Xiao's true identity.

However, neither of them actually did it, to avoid causing any unnecessary trouble.

On the way back, Xu Lang asked Xu Xiao curiously.

"Xiaoxiao, when did you become so knowledgeable about computers?"

If Xu Xiao hadn't been there today, Xu Lang would have been ripped off by these unscrupulous merchants countless times.

"I had learned some things from books and the internet before, and today I just happened to put them to use."

Xu Xiao did use the computer in Wang Ze's office to check the hardware configuration of this era, but he would definitely rely more on his experience from his previous life.

"Really? If you're smart, you can do everything better than the average person."

At this moment, Xu Lang felt that with such a son, what more could a husband ask for?

After delivering the computer to their home, Xu Lang immediately arranged for broadband internet to be installed, allowing their family to enter the internet age ahead of schedule.

When Xu Xiao checked the computer files, he indeed found several games that the store had installed for him.

Red Alert.

Age of Empires.

The Legend of Sword and Fairy.

Romance of the Three Kingdoms...

Many of these were games that Xu Xiao loved to play when she was a child, and seeing them now brings back a lot of memories.

However, Xu Xiao really has no interest in playing games anymore.

Xu Xiao closed the game folder, opened QQ, and logged into her account.

This account doesn't have any friends yet, but after successfully logging in, Xu Xiao quickly saw an email notification.

"Professor Yuan... replied to my email again as expected."

Xu Xiao keenly noticed that Yuan Jiyang replied to her email on the same day she sent it, with only an hour in between.

Looking at the contents of the email, Xu Xiao was in a relatively pleasant mood.

"It seems that Professor Yuan is quite positive about my topic selection and research progress."

Xu Xiao wasn't quite sure whether there was any element of encouragement involved.

Perhaps Yuan Jiyang, considering his young age, wouldn't really hold himself to the same standards as a graduate student.

However, Xu Xiao still felt that Yuan Jiyang's suggestion to try returning to elementary methods was very worth considering.

Recently, he has tried to use many advanced theories to prove it, but this only gives the impression of deliberately showing off his skills, and the actual effect is not very good.

Although Xu Xiao did use some basic methods at the beginning, he did not put in a lot of effort in them.

Since using advanced theories didn't yield any results, Xu Xiao could try to simplify the problem.

"Let's consider the special case of a=b=1 first. If we can prove it, then we can generalize to other cases."

After simplifying the problem, Xu Xiao first performed numerical calculations on some of the prime numbers and quickly discovered the pattern, leading to the development of a proof.

Using methods such as Fourier expansion, Passevar orthogonality, and van der Corput finite difference method, Xu Xiao successfully completed the proof.

Just as Xu Xiao was about to continue using the same method, she gradually realized a new problem.

If you are only performing numerical calculations on a specific case, it is indeed relatively easy to discover the patterns.

However, in reality, both a and b are variables, and the amount of computation required to calculate a sufficient number of numerical results is enormous.

Whether calculated manually or with a calculator, this is a task that would take at least several months to complete.

However, this problem ultimately did not stump Xu Xiao.

"You can just write a program. Judging from the computer's configuration, it should be able to handle it perfectly well."

Programming is Xu Xiao's specialty. Even if he wasn't a particularly outstanding programmer in his previous life, he could still easily solve this kind of small problem.

At that time, there were no scientific computing libraries such as NumPy and SymPy, but as long as the computing core was written in C and the architecture of scheduling and analysis scripts was written in Python, all the underlying operations could be implemented independently.

"First, we'll use C to build the underlying number theory operation library. It should only take about a hundred lines of code."

After determining the programming approach, Xu Xiao quickly got to work.

Actually, for relatively simple calculations, you can just use an Excel spreadsheet to solve the problem.

However, Excel is not a very professional calculation tool, especially the latest Excel 2003 version, which only supports a maximum of 60,000 rows.

To achieve better numerical calculation results, it is best to calculate all combinations of prime numbers less than 1000.

However, even with just a relatively large prime number, the number of combinations involved will exceed the maximum number of rows in Excel.

In addition, Excel 2003 does not have native support for large integers. When performing large integer operations, it will automatically convert them to double-precision floating-point numbers, resulting in a loss of precision.

In addition, Excel is very slow at calculating formulas, making it completely unsuitable for this kind of scientific research-level calculation work.

After writing about 150 lines of C language low-level library, Xu Xiao successfully constructed the three core functions for his research project.

In a previous life, many mathematical researchers would have been able to reach this level of programming skills, and could even have completed the programming directly using AI.

However, in this era, the overall programming level of mathematical researchers is still relatively low. Unless they are researchers who specialize in numerical analysis or mathematical modeling, most of them only know some basic scripts.

Xu Xiao's algorithm, on the other hand, is truly professional-grade, and in this day and age, it's almost like a game-changer.

After checking the code and confirming there were no problems, Xu Xiao began the calculations.

Because the combinations of the prime numbers are relatively few, the computer can calculate them very quickly, sometimes even within milliseconds.

However, as prime numbers continue to increase in size, the calculation speed has slowed down considerably.