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A prime number is a natural number that has no factors other than 1 and itself (excluding 1). Prime numbers are considered the basis of natural numbers, just like atoms in nature. All natural numbers greater than 1 can be represented by the product of several prime numbers, and this representation is unique (regardless of the order of prime numbers).

Some people may ask why it is in the context of multiplication, rather than more basic addition, such as decomposing natural numbers into the sum of several X numbers, which are more suitable as the basis of natural numbers. This is because if it is decomposed in this way, the final decomposition is the sum of several 1s, which becomes a simple counting and loses many rules. Of course, some numbers can also be set as basic numbers, such as 1, 2, 3, and 5, but there is no essential difference between decomposing 10 into 2+8 and 3+7. The selection of basic numbers is difficult to reflect some fundamental properties of numbers.

Back to the essence of numbers, numbers exist because things can be abstracted - there are no two things in the world that are exactly the same, but they can be considered the same and counted together. Multiplication actually extends this practice, dividing several things that have been considered the same into a group, and then repeating this process after treating multiple groups of the same number as the same. Therefore, the number obtained by multiplication is an extension of the number, and it is not surprising that multiplication has a unique position in calculation.

When two numbers have the same factors, it means that they can be obtained by repeating a certain grouping, for example, 4 and 6 can be repeated in groups of 2. It can be understood that they have some similarities and a certain ability to represent each other, so they are not so unique. The uniqueness of prime numbers is that they cannot be accumulated from smaller numbers (except 1), so each prime number is unique and does not contain each other. Precisely because of the irreplaceability of each prime number, the "uniqueness" of the fundamental theorem of arithmetic is obvious: for any natural number N greater than 1, if N is not a prime number, then N can be uniquely decomposed into the product of a finite number of prime numbers.

Each prime number is a representative of a class of numbers that are multiples of it, and this class of numbers has similar properties. The principle of the universe is "repetition but with change". As we have seen, the universe often repeats when creating things, such as having a large number of identical atoms and similar laws. This repetition makes it possible to understand the universe. After the prime numbers were created, all numbers can be obtained by repeating prime numbers continuously, which is undoubtedly simple and efficient. But why are there not finite prime numbers? From an intuitive understanding, although each prime number is repeated continuously and can cover a large number of larger numbers, it is multiplication after all, and the jump is relatively large, which will leave gaps. These gaps are new prime numbers. This means that there are always numbers that cannot be fully represented by previous numbers, leaving room for change in the universe.

Goldbach's conjecture can be understood as every natural number greater than 1 can be expressed as the sum of two prime numbers divided by 2. Although this representation method is not unique, it clearly gives people a vague sense of the deep connection between multiplication and addition. Prime numbers were originally used to represent all numbers in the form of multiplication, but they can also be represented by addition.

The twin prime conjecture can be understood as a special case of the Goldbach conjecture, that is, there are countless natural numbers n, 2n-1 and 2n+1 are both prime numbers, and 4n can be expressed as the sum of these two prime numbers. In other words, you can find prime numbers that differ by only 1 before and after a certain even number to represent this even number, and there are countless such even numbers.

As the German mathematician Kronecker said: "God created integers, and the rest are human creations." The concept of prime numbers is actually invented by humans, but it can effectively solve some problems. Multiplication is important not only because it is an efficient calculation method, but also because it is an extension of numbers.