Escape the Library

At 8:00 in the morning, the examination room for the compulsory course "Maze of Prime Numbers" of the School of Mathematics opened.

The four of Yue Xingwen were instantly pulled into a strange maze. The room of the labyrinth is a cube structure. The upper and lower, front and rear, left and right, the six walls are painted with special black paint, and there are many star-like embellishments, just like being in a dark, deep cosmic starry sky. Those "stars" emit a faint glow that illuminates the room.

There is a door on each of the four walls, and four digital cards are pasted with white fluorescent characters on the door.

Additional Question: Collect all twin primes.

They should take down all the "twin primes" cards posted on the wall to complete the extra questions.

Yue Xingwen's eyes quickly looked around, and the four numbers in the first room were very simple, 4, 5, 6, and 7.

It is easy to find prime numbers with one digit, 5 and 7 are a pair of twin primes. If you get the wrong card, you will definitely not get points for the additional questions, so you must count the cards before you get the cards.

Yue Xingwen looked at Jiang Pingce: "The 3-credit labyrinth class shouldn't be too easy, right?"

Jiang Pingce frowned and thought for a few seconds, then said: "There are 4 doors in each room. If there is a passage behind each door, then the number of doors in this maze is 4 to the nth power. The difficulty is not to find the twin prime numbers. , is to find the right path. We need to walk the maze while drawing and judging the direction.”

Ke Shaobin quickly took out his laptop: "I can write a piece of code to quickly figure out which prime numbers are, and build a maze model by the way... Wait, my laptop doesn't seem to be turned on?"

Liu Zhaoqing leaned over and looked at it: "It won't be broken, will it?"

Ke Shaobin put his fingerprint on the power button and pressed it for a long time. He asked in confusion, "Don't you allow the computer to be used?"

Yue Xingwen helped his forehead helplessly: "It seems that this test cannot be calculated by computer, we have to calculate it ourselves." He raised his head and glanced at the countdown in the upper right corner: "The test time is 4 hours, if there are many fork in the road, we will slowly Should the investigation be too late?"

Liu Zhaoqing spread his hands: "I haven't touched mathematics for many years. Let me do the division, and my mind is in a mess. In this class, you can treat me as a mobile pendant, and I will quietly follow you. of."

Yue Xingwen smiled and said, "I'm about the same."

Jiang Pingce suddenly said solemnly: "In order to clear the customs in the fastest time, we still explore the way in teams."

Ke Shaobin and Liu Zhaoqing looked at each other and said in unison, "Team?!"

He must be on the same team as Yue Xingwen, can the other two do it?

Ke Shaobin held up his glasses embarrassedly, and his ears were slightly red: "Although I am a science student, I have been used to using computers to solve all calculation problems since I was a freshman. I haven't done mathematics myself for a long time." For multiplication and division of more than 10 digits, I have to use pen and paper to calculate it several times before I can understand it. My team with Senior Brother Liu may be very inefficient, right?"

Jiang Pingce said: "It's not divided into two teams."

He turned his head to look at the teammates beside him, and said word by word, "It's divided into four teams, one for each person."

Three people: "..."

are you joking? Liu Zhaoqing looked terrified: "I'm really bad at math!"

Yue Xingwen quickly understood his thoughts: "What do you mean, the four of us are going to explore the road separately, and the calculation tasks are all handed over to you? Are you calculating the prime numbers of the four roads at the same time?!"

Sure enough, Xingwen knew him better, Jiang Pingce nodded calmly.

Ke Shaobin and Liu Zhaoqing stared at him with wide eyes.

I thought that the team he said was divided into two teams, but as a result, Jiang Pingce was more ruthless than everyone imagined - directly divided into four teams! He counts four at the same time!

Obviously, he has enough confidence in his computing power.

Jiang Pingce looked at Yue Xingwen and said seriously: "The research group channel can send messages during the exam. Every time you enter a labyrinth room, type the number on the door on the research group channel, and I will calculate and give the correct answer. ."

Yue Xingwen tried to post a line on the research group channel: "Can you see it?"

All four of them saw the information in the transparent floating frame in the upper left corner.

Yue Xingwen's eyes lit up: "This method is amazing! The four people walk forward in four ways, which can greatly save the time to explore the maze, and the number of wrong ways to go back and forth will also be reduced." He paused, a little worried Looking at Jiang Pingce, "But then you will be under a lot of pressure, right? There are four roads. In case of chaos at the back, can you tell the direction?"

If Jiang Pingce's judgment is correct, and there are four doors and four paths in each labyrinth room, then there are as many correct paths as 4 to the nth power. Can he remember the exponentially increasing path?

Jiang Pingce looked at Yue Xingwen, his eyes full of seriousness: "Trust me."

When he met his gaze, Yue Xingwen immediately nodded: "Okay, I believe you, just do as you say!"

Jiang Pingce said: "Take out your dictionary first, tear some paper for me, and I will draw a map of the maze path."

Yue Xingwen did as he did, and took out a pen from his pocket and handed it to Jiang Pingce.

Jiang Pingce walked to the wall with the number [5] pasted, opened the door, and the next room was exactly the same as this room, with four numbers on four walls.

Jiang Pingce tried to open the other three doors [4] [6] [7] again, and came to the same conclusion.

Prove his reasoning - every room has four doors and four exits. Some of the rooms in the back are sure to turn into dead ends. If you want to find the right exit of the maze, if the four of them are together, and they slowly check the rooms one by one, of course they can walk out in 4 hours. However, if you want to get a high score in this class, you must not use this The dumbest way.

Jiang Pingce quickly drew a few squares on the paper and explained: "Everyone has traveled a lot and can't remember the direction. For example, in the current room, there are four numbers 4, 5, 6, and 7. After the door of 5], you will enter the next room, and remember the number of the other door connected to [5]. When reporting the number, start from the door you entered, and follow the The hour hand counts, do you understand what I mean?"

Yue Xingwen saw him draw five consecutive rooms on the paper, all square, with a number on each side. As he said, when there are many paths behind, the sense of direction becomes a floating cloud, east, west, north, south, and so on. It must be hard to tell, what's more, all the walls inside this maze have been painted into starry sky, so it's no wonder if you don't get dizzy.

If you want to locate the exact direction, you must use the rooms of the previous maze.

For example, the door directly in front of room a is marked with [5], which is regarded as [door 5]. After opening this door, it is room b. Since room b is also a square, two squares will share a side when connected together. That is, on the four walls of room b, there must be a door directly connected to [door 5] in room a.

The logic used by Jiang Pingce is that "two rooms share a door, and the front and back of the door are pasted with different numbers." Then, starting from the first room and continuing to reason down, the complete maze graph can be derived.

This kind of reasoning method does not need to care about east, west, north and south. As long as every room is correct, his diagram will not go wrong.

Jiang Pingce looked at the three teammates and warned again: "Be sure to remember the number on the door that you pushed open, immediately look at the number on the back of the same door after entering the next room, and report the number clockwise, don't report the wrong number. If you make one mistake, you will make a series of mistakes later, do you understand?"

The three looked at each other and nodded in unison: "Understood!"

They can't tell the difference between east, west, north and south, and they can still tell the difference between clockwise and counterclockwise!

Jiang Pingce said: "Prepare for a team. Ke Shao goes to gate 4, I go to gate 5, Xingwen 6, Liu senior 7."

Yue Xingwen took the initiative to reach out: "Come on, let's cheer for Xueba."

Liu Zhaoqing and Ke Shaobin consciously put their hands up, Jiang Pingce glanced at Yue Xingwen, and also put their hands up, Yue Xingwen gently placed his other hand on the back of his hand, smiling brightly: "Come on, Don't put too much pressure on yourself, we can pass the test, there is no need to rush for the first place, you know?"

Jiang Pingce warmed his heart and nodded at him: "Well, don't take the wrong card. The standard for scoring additional questions must be that all the cards we collect must be twin prime numbers, and points will be deducted if you take the wrong card."

The four of them looked at each other, walked into the four doors separately, and the numbers appeared again in the next room.

Double digits this time.

Yue Xingwen’s room is 11, 12, 13, 14; Ke Shaobin’s room is 16, 17, 18, 19, Liu Zhaoqing’s room is 28, 29, 30, 31, and Jiang Pingce’s room is 40, 41, 42, 43.

The two-digit number is very simple, and everyone can calculate it by themselves, but for the convenience of Jiang Pingce's drawing, the three of them still follow the rules he said and count clockwise from the door they entered.

Jiang Pingce gave instructions: "Take off the twin prime number card, Xingwen goes 13, Ke Shao 18, and Senior Brother 30."

All he chooses is the road in front of him. He walks in a straight line first. When he encounters a dead end, he steps back to the right and then to the left, so that there will be no confusion.

The four quickly entered the next room, this time the number became three digits.

Jiang Pingce: "Brother take 107 and 109 and go through the door of 111."

According to his instructions, Zhaoqing took down two number cards and moved on.

The research group channel kept popping up messages from Jiang Pingce: "Xingwen takes 137, 139, and goes to 133."

"Ke Shaona 179, 181, go through door 181."

In the next room, the prime numbers become four digits again.

Two-digit and three-digit numbers can be calculated by everyone. After reaching four-digit numbers, the three simply gave up thinking, and had time to do the calculations on their own. It is better to type quickly and wait for Jiang Pingce's result.

Jiang Pingce's brain speed is amazing, and he can even give an answer in seconds by calculating four paths at the same time!

"4019, 4021" "8969, 8971" "9281, 9283..."

Walking another room, the number rose to five again.

"16829, 16831" "31541, 31543..."

But for Jiang Pingce, five-digit numbers were not difficult, and he quickly and accurately reported a pair of twin prime numbers.

Teammates collect more and more prime cards in their hands. Jiang Pingce not only has to calculate the twin prime numbers of the four roads at the same time, but also draws a maze path while walking to ensure that the direction of his teammates is correct...

In this maze full of numbers, other people's eyes were black and they didn't know how to walk, but Jiang Pingce was like a duck to water-these numbers were his closest friends since childhood. He participated in the National Mathematics Competition in high school, and he liked mathematics from the bottom of his heart, and liked the wonderful, rich and rigorous world of numbers.

In the world of mathematics, he is like a born king. Others are afraid of numbers, but he can control them.

The numbers in the room are getting more and more complex, and the amount of calculation is increasing like crazy.

Jiang Pingce is like a high-speed computing machine. As he calculates, he gradually draws a maze in his mind. As soon as his teammates type the numbers, he can always give the correct answer as soon as possible.

Yue Xingwen: "The front room is a dead end, and there is no door."

Jiang Pingce instructed: "Go back one room and go to door 8861."

Ke Shaobin also quickly said: "I have encountered a dead end."

Jiang Pingce: "Go back and go to gate 9657."

"Brother come back, door 9861."

Under the command of Jiang Pingce, everyone repeatedly explored the road, and the number of forks in the entire math maze was almost innumerable. Yue Xingwen alone took eight forks. It is hard to imagine that Jiang Pingce did not go wrong.

I thought that if they continued to investigate like this, they would soon be able to check all the fork in the road. However, when the number of twin prime cards collected by Yue Xingwen reached 30, a message from Liu Zhaoqing suddenly appeared on the research group channel: "I rely on , there was an elevator in the room I entered, and up and down buttons."

After a few seconds, Ke Shaobin also sent a message: "I entered the door of 24189, and there is also an elevator inside."

Liftable elevator?

Yue Xingwen said, "Could it be that this maze has at least three layers?"

Jiang Pingce said: "I expected it a long time ago. The course description says that this is a three-dimensional maze. No matter how many forks in a plane maze, it is not difficult to make marks and explore slowly, and the difficulty of the three-dimensional maze will be doubled."

Yue Xingwen said worriedly: "Three-dimensional maze, your calculation will be doubled, right?"

Jiang Pingce said: "It's okay, go back first, we will collect the twin prime numbers on this floor before going upstairs."

To do the extras, collect all the twin primes, that means they have to explore all the rooms in the maze. The three were already confused and couldn't tell the difference between north and south, but Jiang Pingce's calm and clear command gave them full confidence.

In this vast digital maze like a starry sky, it is not only necessary to calculate four lines at the same time, so that teammates can quickly find the twin prime numbers among the dense numbers, but also to ensure that teammates are not lost in the process of repeatedly pushing the door, exploring the way, and returning.

With such a difficult command, other teams may not even dare to think about it.

But Yue Xingwen believed that Jiang Pingce would definitely be able to do it.