Find the largest known prime number
The research team led by Curtis Cooper, a mathematician from the University of Central Missouri in the United States, discovered the largest known prime number-257885161-1(that is, 2 5788565438) by participating in an international cooperation project called GIMPS. The prime number is the 48th mersenne prime of 17425 170 digits; If you print continuously with ordinary font size, its length can exceed 65 kilometers! Mike brin, a spokesman for the American Mathematical Society, declared that this was a major breakthrough in the study of number theory.
The research team ran GIMPS software on about 65,438+0,000 university computers, and each computer spent 39 consecutive days to prove that 2578,856,5438+0-65,438+0 is a prime number. Later, other researchers independently verified this result. In recent years, Cooper discovered three mersenne prime by participating in the GIMPS project.
Finding mersenne prime has become the most effective way to find the largest known prime number. Today, nearly 280,000 people from more than 180 countries and regions around the world have participated in the GIMPS project, and more than 790,000 computers are networked to find the new mersenne prime. Is there an infinite number of mersenne prime? This is a famous unsolved mathematical problem.
Prove "weak twin prime conjecture"
After years of hard work, Zhang, a mathematician at the University of New Hampshire in the United States, took the lead in proving a "weak twin prime conjecture", that is, "there are infinite prime pairs with a difference of less than 70 million". /kloc-in April of 0/7, he contributed to the world's top periodical Mathematics of the Year. One of the judges, American mathematician Henrik Avenico, commented: "This is a first-class mathematical work." He believes that many people will soon "shrink" to the number of "70 million".
Although there is still a long way to go from proving the weak twin prime conjecture to proving the twin prime conjecture, the online report of the British magazine Nature called Zhang's proof an "important milestone". Because the twin prime conjecture is closely related to Goldbach conjecture (sister problem), many mathematicians hope to overcome Goldbach conjecture by solving this conjecture.
It is worth mentioning that British mathematicians godfrey hardy and John Littlewood once put forward a "strong twin prime conjecture". This conjecture not only puts forward that twin prime numbers have infinite pairs, but also gives its asymptotic distribution form. Zhou Haizhong, a mathematician in China, pointed out that people have to face many great difficulties to prove the conjecture of strong twin prime numbers.
Solve the "Weak Goldbach Conjecture"
/kloc-In May of 0/3, the Peruvian mathematician harald Jelf declared at the Paris Teachers College that he had proved a "weak Goldbach conjecture", that is, "any odd number greater than 7 can be expressed as the sum of three odd prime numbers". He submitted the paper to the world's largest pre-printed website (ARXIV); Some experts believe that this is an important achievement of Goldbach's conjecture research. However, whether the proof is established remains to be further verified.
Jelf Gott mainly uses the Hardy-Littlewood-vinogradov cycle method in his argumentation techniques. In this circle method, mathematicians created a periodic function whose range includes all prime numbers. In 1923, Hardy and Littlewood proved that if the generalized Riemann conjecture holds, the ternary Goldbach conjecture is correct for sufficiently large odd numbers; 1937, the Soviet mathematician Ivan vinogradov went one step further and directly proved that an odd number large enough can be expressed as the sum of three prime numbers without generalized Riemann conjecture.
Andrew glanville, a British mathematician, said that, unfortunately, due to technical reasons, it is difficult to prove the "strong Goldbach conjecture" by Jelf Gott's method, that is, "Goldbach conjecture on even numbers". At present, the mainstream opinion in the field of mathematics believes that to prove the strong Goldbach conjecture, new ideas and tools are needed, or the existing methods are greatly improved. (Zheng Hui is a professor at Nanyang Technological University)