When China discovered Chen Jingrun, it was because Chen Jingrun found a mistake in the theory of overlapping prime numbers written in China and wrote to him. At that time, Chen Jingrun was still a nobody. According to the statement here, it is a "folk researcher".

Number Theory and the Development of Probability Mathematics

7. 1 number theory

7. 1. 1 prime number distribution

Fermat number Fn =+1, n = 0, 1, 2, …

When n = 0, 1, 2, 3, 4, Fn is a prime number. The question people want to solve is whether there are infinite Fermat primes, which is also an unsolved problem.

Mason number Mp = 2p- 1, where p is a prime number.

There are 34 known mersenne prime * * *, among which the prime Mp with p =52 1 was discovered by computer after 1952.

The method of testing whether Mason number is a prime number is called Lucas-Lemmer test. For example, Lucas-Lemmer test is used to judge whether M5 is a prime number. Because M5=25- 1=3 1, the following calculation can be made:

U(0)=4，

u( 1)=(42-2)(mod 1)= 14(mod 3 1)= 14，

u(2)=( 142-2)(mod 3 1)= 194(mod 3 1)= 8，

u(3)=(82-2)(mod 3 1)= 62(mod 3 1)= 0

Because U(3)= 0, M5 must be a prime number.

Using factor table to study prime numbers

Rahn published the factor table within 24,000 in (1659);

Per (1668) has been expanded to 65438+ ten thousand;

Felkel (1776) gave the factor table of everything within 408000.

In the19th century, many scholars worked out the factor tables of all numbers within 10 billion, among which Culic of Prague University spent 20 years in his spare time.