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Prime numbers are also called prime numbers. Refers to a natural number greater than 1, except 1 and the integer itself, which cannot be divisible by other natural numbers. In other words, a natural number with only two positive factors (1 and itself) is a prime number. Numbers greater than 1 but not prime numbers are called composite numbers. 1 and 0 are neither prime numbers nor composite numbers. Prime numbers play an important role in number theory.

Prime formula, also called prime formula, is a formula that can only produce prime numbers in the field of mathematics. That is to say, this formula can generate all prime numbers without omission, and the result produced by this formula is a prime number for each input value. Because the number of prime numbers is countable.

Therefore, it is generally assumed that the input value is a natural number set (or a countable set such as an integer set). So far, people have not found a prime formula that is easy to calculate and meets the above conditions, but they know a lot about the nature that prime formula should have. Some elementary proofs of the prime number theorem only need the method of number theory.

The first elementary proof was obtained in 1949 by Hungarian mathematician Paul Edith ("Erdos" or "Erdoshi") and Norwegian mathematician Atree Silberg. Before this, some mathematicians did not believe that elementary proofs could be found without the help of difficult mathematics. British mathematician Hardy said that the prime number theorem must be proved by complex analysis, which shows the "depth" of the theorem result.

He believes that only using real numbers is not enough to solve some problems, and complex numbers must be introduced to solve them. This is based on the feeling that some methods are more advanced and powerful than others, and the elementary proof of prime number theorem shakes this argument. Selberg-Edith's proof just shows that seemingly elementary combinatorial mathematics can also be very powerful.

However, it should be pointed out that although this kind of elementary proof only uses elementary methods, it is even more difficult than using complex analysis.