1742 On June 7th, German Goldbach put forward a mathematical problem in a letter to Euler, a great mathematician living in Russia at that time. Its essence is: can any even number not less than 6 be expressed as the sum of two odd prime numbers? A prime number is a natural number that cannot be divisible by any other integer except 1 and itself. For example, 2,3, 1 1 are all prime numbers that cannot be divisible by any other integer except 1 and itself. Odd prime numbers are other prime numbers except 2. ) This question is the famous Goldbach conjecture in the original sense!
19th century, mathematician cantor patiently experimented with all even numbers within 1000 (for example, 8 can be expressed as 3+5; 20 can be expressed as 3+17,7+13; 56 can be expressed as 3+53, 13+43, 19+37. All even numbers within 1000 can at least be expressed as the sum of prime numbers of 1). Opley tried all even numbers from 1000 to 2000, and confirmed that the conjecture was correct within the test range. 19 1 1 merry pointed out that most even numbers between 4 and 9,000,000 are the sum of two prime numbers, and only the number of 14 is unknown. Some people even spent almost their whole lives verifying it one by one, and the results of verification confirmed that this conjecture was correct. In June 2003, someone told me that Cray Computer Company had tested this conjecture to the 40th power of 10! I found this company on the Internet and asked about it, but I didn't get a reply. I just found it online. 10 year 10 on October 3rd, with the help of computer, Oliveira e Silva and others verified that it was 6× 10 to the power of 16, and all the guesses were correct. 20 12 on April 4th, Oliveira e Silva and others verified that the power of 4× 10 was 18.
More than one hundred years after Goldbach's conjecture was put forward, there is still no effective progress in its direct proof. Through previous experiments on small even numbers, many mathematicians believe that Goldbach conjecture is valid in small even numbers. Therefore, mathematicians have adopted a circuitous method, so that their research direction mainly follows two routes. Its basic approach is to turn Goldbach's conjecture into a weaker proposition, that is, to relax the requirements of the problem-exclude small even numbers and narrow the research on it to the scope of large even numbers.
The first route, initiated by Landau, is to prove that "there is such a positive integer e that every integer large enough can be expressed as the sum of not more than e prime numbers". The first major breakthrough on this route was made in 1930 by the 25-year-old Soviet mathematician Sini german, who proved the proposition that Landau predicted that mathematicians at that time could not achieve. He pointed out that any integer large enough can be expressed by the sum of some prime numbers, and the number of addends does not exceed 800,000, which is S.
The second route mainly adopts screening method, that is, it is proved that every even number large enough is the sum of the products of S prime numbers and T prime numbers (referred to as "s+t"). Goldbach's conjecture is "1+ 1". 1920, Bulun of Norway first proved "9+9" mainly by an ancient screening method. At present, the highest achievement recognized is "1+2" proved by China mathematician Chen Jingrun in 1966. For this achievement, Chen Jingrun has greatly improved the screening method, which has brought its effectiveness into full play, and thus shocked the international mathematics community. "1+2" is also called Chen theorem, that is, "any large enough even number can be expressed as" the product of one prime number plus two prime numbers ".
The schedule with even numbers as "s+t" is as follows:
1920, Bren of Norway proved "9+9".
1924, Rademacher proved "7+7".
1932, Esterman of England proved "6+6".
1937, Ricei of Italy proved "5+7", "4+9", "3+ 15" and "2+366" successively.
1938, Byxwrao of the Soviet Union proved "5+5".
1940, Byxwrao of the Soviet Union proved 4+4 ".
1948, Hungary's benevolence and righteousness proved "1+c", where c is the number of nature.
1956, Wang Yuan of China proved "3+4".
1957, China and Wang Yuan successively proved "3+3" and "2+3".
1962, Pan Chengdong of China and Barba of the Soviet Union proved "1+5", and Wang Yuan of China proved "1+4".
1965, Byxwrao and vinogradov Jr of the Soviet Union and Bombieri of Italy proved "1+3".
1966, China Chen Jingrun proved "1+2".
1978 1, Xu Chi published reportage Goldbach conjecture in People's Literature! Xu Chi showed Chen Jingrun's achievements and brought a strong sense of national pride to many people in China. At the same time, it also makes Goldbach conjecture a household name! Since then, many people in China have a special liking for Goldbach conjecture; Many ordinary people in China use their spare time to prove Goldbach conjecture! On March 18, 2000, the reference news reprinted the news that Faber Company of Britain offered a reward of 1 10,000 dollars to prove Goldbach's conjecture! This news inspired China people who were deeply influenced by Xu Chi's article Goldbach conjecture to prove it again, so that Journal of Mathematics, the top publication of mathematics in China, receives a large number of amateur papers proving Goldbach conjecture every year!
However, none of the amateur papers have been recognized by experts! Papers sent to math magazines are often as heavy as stones! Even if these papers are all wrong, folk scholars don't know where their papers are wrong! As a result, some people published papers online, and some people published papers in non-professional newspapers! However, the paper published in this way did not attract experts' comments with reasons as the author expected! (Note: Such comments sometimes appear, such as: Your article is wrong! But there is no explanation! Anyone can say! Some are accused by other amateurs of copying other people's achievements! Because the articles on the network can be deleted by the network administrator at any time, in the end, no one can tell who copied who. After a group of amateurs "learn that this problem has not been proved, enter the proof, get the excitement of the proof (most people may be eliminated after thinking fruitlessly before this link), expect after sending out the paper, publish the paper through the network or small journals, and finally get frustrated and helpless", another group of amateurs has entered the same infinite loop! (Note: There may be several amateurs who have been promoting themselves online! )
In recent ten years, some mathematics experts have appealed through the media, hoping that ordinary people will not spend futile time and energy to prove this Goldbach conjecture that ordinary people can't prove! However, I wonder if there are any wise mathematical experts who know something about psychology-is there any way for some people who think they are not weak in intelligence to admit that they are unable to prove Goldbach's conjecture before proving it? Even if the experts change the above appeal to all China in order to prevent people from entering the above-mentioned infinite loop, "Mathematics magazines will not accept all the papers that amateurs prove Goldbach's conjecture, and no matter whether your papers prove Goldbach's conjecture are correct or not, they will not be published", there will still be new people entering! Experts must understand that as long as Goldbach's conjecture is not proved, people will always believe that the correct proof will be published, and there will always be groups of ordinary China people coming one after another, repeating this seemingly endless cycle that will never be recognized by experts. Of course, the possibility of plagiarism is not ruled out!
2065438+01July 28th, the "Spark of Scientific Wisdom" column of Chinese Academy of Sciences was launched, and some fans felt hopeful! Did "fans" succeed? Some "fans" who think they have successfully proved their guesses are waiting for the day when they are recognized by the world. These people who are not weak in intelligence spend a lot of energy on publishing papers, but they lose the time to really seek benefits for themselves. In a society where people's success is measured by money and official position, they are very weak! And they often make themselves poor because they demand integrity and justice! It is said that only a few of the thousands of papers sent to the editorial department of Journal of Mathematics have been reviewed by experts! If most papers are really not audited, then who knows whether they are correct or not? If there is a correct paper, then Goldbach conjecture has been proved now, but it has not been recognized by the public!
It is said that today's great mathematicians want to prove that any big even number can at least be expressed as the sum of 1 pairs of prime numbers! When the photonic computer is successful, people will see that any even number greater than 10 to the power of 100 can at least be expressed as the sum of the 95th power pairs of prime numbers of 10!