This is the most famous digital black hole. Its calculation is very simple, starting from any positive integer, according to a simple operation method: even number divided by 2, odd number multiplied by 3 plus 1, so it will eventually fall into the cycle of 4,2, 1.

Brief introduction to history

The origin of 3x+ 1 conjecture is confusing. One theory is that this game originated from Calaque (L.) of the University of Hamburg in 1930s. When he was studying the number theory function, he raised the second question, but it was not published. There is also a saying that this number game first appeared and was popular in a small town in the United States around World War II.

Later history is generally clear. In the 1950s, with the help of the International Mathematical Congress held in Cambridge, USA and the works of some mathematicians, the game was spread, and then it became all the rage in America and Europe. By about 1960, Japanese mathematician Kuo Kyoko brought this problem to Japan.

Kakudji wrote in his memoirs: "At one time, everyone in Yale University, a famous American university, was studying this problem, but there was no result. Some people joked that this is part of a big conspiracy by the enemy to stop the progress of American mathematics research. "

This game is also called angle conjecture, and it is even more called hail conjecture in the United States because the numbers in the operation are big and small, just like the ice particles are up and down when hail is produced. In fact, it also has the names of Sgrcuse, Hasse and Vlam.

status

People have done a lot of research on 3x+ 1 conjecture and verified it countless times. Tamishev of Tokyo University verified all the integers of 1-2 40 (about 1.2 * 10 12) by computer, and all the integers reached 4,2,1cycle without exception. Mathematicians have written about 20 papers on this problem, but this problem is far from being solved.

1970, bonuses to solve this problem were set up one after another.

H.S.Coxefex offered a reward of $50.

Page (abbreviation of page) Ordos offers a reward of $500.

B.Thwaifes offers a reward 1000.

This game has the conditions of guessing: it seems extremely simple, but in fact it is extremely difficult. So it will be all the rage. Until today, people (including middle school students, college students, or teachers) still claim to have proved the 3x+ 1 conjecture by elementary methods. Generally speaking, experts will not take these certificates seriously. Therefore, for us ordinary people, as a game, we can play, and at most we can consider small details, and don't try to prove it.

In fact, some people think that 3x+ 1 conjecture will be the next great achievement in mathematics after the proof of Fermat's last theorem.

123 digital black hole

Take any number, write down the number of even numbers, the number of odd numbers and the sum of these two numbers in turn, and you will get a positive integer. For this new number, put its even and odd numbers and its sum into another positive integer, and so on, it will inevitably stay on the number 123.

For example, the given number is 1474 1029.

The first calculation result 448

The second calculation result 303

The third result is 123.