Life inside the spaceship is boring and warm.

In addition to completing the daily observation tasks of the Centauri Constellation Samsung through the telescope, Pang Xuelin spent the rest of his time planting things in the plant cabin with Mu Qingqing, in addition to engaging in Riemann conjecture research.

Due to the crew's long-term hibernation, the ship's plant pods will only activate if the crew is awake.

Pang Xuelin and Mu Qingqing planted potatoes, cucumbers, eggplants, tomatoes, corn, rice and other crops in the plant cabin, and also raised a lot of bread worms as a source of animal protein.

This kind of life reminded Pang Xuelin of the days when he was in the Martian world.

But there's no doubt that life on a spaceship is much more fun than life on Mars.

Not only because of the diversity of food, but more importantly, because I am accompanied by beautiful people.

The only thing that gave Pang Xuelin a bit of a headache was that in the process of studying Riemann's conjecture, he still couldn't find any clues.

But this is not surprising.

From Hilbert's 23 questions in 1900 to the seven major problems of world mathematics proposed by the Clay Institute in 2000.

A century later, the Riemann conjecture still stands at the top of the world's mathematics.

The reason for this, of course, is not only because of the difficulty of the Riemann conjecture, but also because of the significance of the Riemann conjecture itself.

The first reason is that it is inextricably linked to other mathematical propositions.

According to statistics, there are already more than 1,000 mathematical propositions in today's mathematical literature that presuppose the establishment of the Riemann hypothesis (or its generalized form).

This shows that the Riemann hypothesis, once proven, and its generalized form, will have a tremendous impact on mathematics, and all the more than a thousand mathematical propositions can be elevated to theorems.

Conversely, if the Riemann conjecture is overturned, it will almost inevitably become a funeral for the more than 1,000 mathematical propositions.

The fact that a mathematical conjecture is closely related to so many mathematical propositions is unique in the history of mathematics.

Secondly, the Riemann conjecture is closely related to the distribution of prime numbers in number theory.

Number theory is an extremely important traditional branch of mathematics, and was called "the queen of mathematics" by the German mathematician Gauss.

The distribution of prime numbers is an important traditional topic in number theory, which has always attracted the interest of many mathematicians.

This kind of "noble lineage" deeply rooted in tradition has also increased the status and importance of the Riemann hypothesis in the hearts of mathematicians to a certain extent.

Furthermore, the importance of a mathematical conjecture is measured by whether the study of the conjecture produces results that contribute to other aspects of mathematics.

By this standard, the Riemann conjecture is also extremely important.

In fact, one of the early results of mathematicians in the study of the Riemann conjecture led directly to the proof of an important proposition about the distribution of prime numbers, the prime number theorem.

And the prime number theorem, before it was proven, was itself an important conjecture with a history of more than 100 years.

Finally, the Riemann conjecture has in some senses gone beyond the realm of mathematics.

In the early seventies of the twentieth century, it was discovered that some studies related to the Riemann conjecture were significantly related to some very complex physical phenomena.

The reason for this association remains a mystery to this day.

But its very existence undoubtedly further increases the importance of the Riemann hypothesis.

Because of this, the Riemann conjecture has attracted countless mathematicians to climb it for more than 100 years.

Although these efforts have not been fully successful so far, they have achieved some milestones along the way.

The first of these results appeared in 1896, 37 years after the Riemann conjecture was introduced.

There is only one easy to prove the non-trivial zero points of the Riemann ζ function, and that is that they are all distributed in a banded region.

The French mathematician Hadama and the Belgian mathematician Poussin eliminated the boundaries of the strip by independent means.

That is, the non-trivial zeros of the Riemann ζ function are distributed only in the interior of that band, and do not include boundaries.

At first glance, this may seem insignificant, but the boundaries of a strip area are actually zero in terms of area compared to its interior.

But it is only a small step for the study of the Riemann hypothesis, but it is a huge leap for the study of another mathematical conjecture, because it leads directly to the proof of the latter.

That mathematical conjecture is now known as the prime number theorem, which describes the law of a large distribution of prime numbers.

The prime number theorem has been pending for more than 100 years since it was proposed, and at the time it was something more anticipated by the mathematical community than the Riemann conjecture.

Eighteen years later, in 1914, the Danish mathematician Bohr and the German mathematician Landau achieved another phase of their work, which was to prove that the non-trivial zeros of the Riemann ζ function tend to be "tightly united" around the critical line.

In mathematical terms, the result is that the narrowest strip region containing the critical line contains almost all the nontrivial zeros of the Riemann ζ function.

However, the result that "close solidarity" is "close solidarity" is not enough to prove that any zero point happens to be on the critical line, so it is still far from the requirements of the Riemann conjecture.

But in the same year, another milestone appeared: the British mathematician Hardy finally planted the "red flag" on the critical line – he proved that the Riemann ζ function has an infinite number of non-trivial zeros on the critical line.

At first glance, this seems to be a remarkable result, since the non-trivial zeros of the Riemann ζ function are infinitely many in total, and Hardy proved that there are infinitely many zeros on the critical line, which is literally identical.

Unfortunately, "infinity" is a very subtle concept in mathematics, and the same infinity is not necessarily the same thing.

In 1921, Hardy collaborated with the British mathematician Littlewood to make a concrete estimate of the "infinity" in his result seven years earlier.

According to their specific estimates, what percentage of the "infinitely many non-trivial zeros" that have been shown to be on the critical line compared to all the non-trivial zeros?

The answer is frustrating to them: zero percent!

Mathematicians advanced this percentage to a number greater than zero twenty-one years later, in 1942.

That year, the Norwegian mathematician Selberg finally proved that the percentage was greater than zero.

Selberg's work came at a time when the smoke of World War II was sweeping across Europe, and the University of Oslo, Norway, where he worked, was almost an island of math journals.

Perhaps that's why Selberg was able to accomplish such a remarkable feat.

However, although Selberg proved that the percentage was greater than zero, he did not give a specific number in the paper.

After Selberg, mathematicians began to study the specific values of this ratio, among which the American mathematician Levinson was the most notable.

He proved that at least 34% of the zero points are on the critical line.

Levinson achieved this in 1974, when he was past the age of sixteen and nearing the end of his life (died in 1975), but he was still tenacious in his mathematical research.

After Levinson, progress has been slow, and several mathematicians, including the Chinese mathematicians Lou Shituo and Yao Qi (who proved in 1980 that at least 35 percent of zeros are on the critical line), have struggled to settle for the second digit of the percentage.

It wasn't until 1989 that the first number of percentages was shaken: the American mathematician Con Ray proved that at least 40% of zeros were on the critical line.

This is also one of the strongest results in the entire study of the Riemann conjecture, after which there has been almost no progress in the mathematical community.

Two years passed unconsciously.

On this day, Pang Xuelin floated in front of the porthole of the command and control cabin, looking at the starry sky in the distance.

For two years, Pang Xuelin's research on the Riemann conjecture has been stagnant.

This made him a little helpless.

Mathematics is sometimes like this, no matter how agile you are, when faced with a problem, if you can't find a suitable breakthrough, it's basically a blind eye.

Now Pang Xuelin has entered this situation when facing the Riemann conjecture.

Pang Xuelin took a deep breath and turned his gaze to the upper right corner of the porthole.

On one side of the starry sky, a fireball the size of a tennis ball had appeared, spewing hot flames into the universe, it was Alpha Centauri B.

On the other side, there is a bright star that is many times brighter than Venus, the brightest star seen on Earth, and that is Alpha Centauri.

In the past two years of observation, Pang Xuelin has a relatively clear understanding of the situation in the Centauri α.

There is only one terrestrial planet in the Alpha Centauri A/B binary system, which is about the size of Venus.

This planet orbits around the A/B binary star in a figure-8 shape, and its orbit is stable, but this planet is not in the habitable zone of the two stars, and through spectral analysis and various band observations, it is shown that the planet's basic mountain does not have an atmosphere, and the surface is densely covered with impact craters, which is basically meaningless to humans.

At this time, Pang Xuelin suddenly shrugged his nose, and a fragrant wind came from behind him.

Immediately afterwards, a warm body hugged Pang Xuelin from behind.

"What's wrong?"

Pang Xuelin felt Mu Qingqing's delicate body tremble slightly, as if crying.

He hurriedly pulled the girl in front of him.

Mu Qingqing's eyes were a little red, and she sobbed: "Ah Lin, I just received news from Brother Shuiwa, Brother Liu Qi...... Let's go. ”

In the past two years, Pang Xuelin and Mu Qingqing have been able to receive information from the solar system almost every week.

All of this information was sent after the Earth estimated that Ark 1 had arrived in the Centauri α.

Naturally, it also includes the messages sent by Liu Qi and Shui Wa.

Pang Xuelin was stunned for a moment, and his mind was a little dazed: "Lao Liu, he ...... Passed away? ”

Mu Qingqing nodded and said, "It should have been four years ago, Brother Liu's heart has never been very good, plus he is over eighty years old, it is said that he suddenly walked when he was walking in the yard." ”

Pang Xuelin was in place.

In the past two years, I have been able to receive messages from Liu Qi and Shuiwa from time to time, which is the greatest comfort for Pang Xuelin.

The blue planet four light-years away has always had a hint of concern.

Now another person worth caring about is gone.

Although Pang Xuelin had been mentally prepared, at this moment, his heart was still panicked.

In the train carriage many years ago, the fat man who laughed cheaply still seemed to be in front of him.

In the blink of an eye, the Si people have passed away, and they are far away.

Pang Xuelin took a deep breath and said, "Qingqing, let's hibernate too." ”

Mu Qingqing looked up at Pang Xuelin, nodded, and said, "Okay!" ”

……

Passing α Centauri, Ark One's next target was Sirius.

Sirius, also known as α Canis Major, is the brightest star of the day except the Sun, and although it is fainter than Venus and Jupiter, it is brighter than Mars most of the time.

Sirius is a binary star system in which two white stars orbit each other about 20 AU apart (roughly the distance between the Sun and Uranus) with an orbital period of just over 50 years.

The brighter star (Sirius A) is an A1V-type main-sequence star with an estimated surface temperature of 9,940 K.

Its companion planet, Sirius B, has passed the process of being a main-sequence star and has become a white dwarf.

Although Sirius B is now 10,000 times darker than Sirius A, it was once the most massive of the two.

The age of this binary star system is estimated to be about 230 million years.

Early in their lives, it is assumed that two blue-white stars orbit each other in elliptical circles with a period of 9.1 years.

Sirius A is so bright not only because of its already high luminosity, but also because it is so close to the Sun, about 8.6 light-years, making it one of the closest stars.

Sirius A has about 2.1 times the mass of the Sun. Astronomers measured its radius using an optical interferometer and estimated the angular diameter to be 5.936±0.016 mas. Its star rotates at a slower speed of 16 kilometers per second, so the star is not visibly oblate.

Celestial models indicate that Sirius A was formed by a molecular cloud collapse, and that by 10 million years later, its energy generation had been entirely provided by nuclear fusion. Its core is the troposphere, which uses the carbon, nitrogen and oxygen cycle to produce energy.

Astronomers predict that Sirius A will run out of hydrogen stored in its core within 1 billion years of formation, at which point it will go through a red giant phase before mildly becoming a white dwarf.

Sirius B is one of the most massive white dwarfs known, with a mass almost equal to the mass of the Sun (0.98 M☉) and twice the average mass of white dwarfs of 0.5~0.6 M☉, but so much material is compressed to be as large as the Earth.

Sirius B currently has a surface temperature of 25,200 K.

However, since there is no energy generated inside, the remaining heat will be radiated in the form of radiation, and Sirius B will eventually cool down gradually, taking more than 2 billion years.

A star does not become a white dwarf until it passes through the main-sequence and red giant phases.

Sirius B became a white dwarf a little more than half its current age, about 120 million years ago.

When it was still a main-sequence star, it was estimated to have 5 solar masses and was a B-type star.