Prime numbers are those natural numbers greater than 1 that cannot be divided by any other natural number except 1 and themselves. So, is 1 a prime number? Let p be a natural number greater than 1. If p only has two factors, 1 and p, then p is called a prime number (or a prime). That is, a prime number cannot be decomposed into the product of two factors that are smaller than it. The sequence of prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, ...
Prime numbers are important because any natural number greater than 1 can be decomposed into the product of some prime numbers, and this product is unique (if we don't consider the order). This conclusion is called the "Fundamental Theorem of Arithmetic". For example, 7623 can be decomposed into 3^2 × 7 × 11^2, and the uniqueness means that the prime factors 3, 7, and 11, and their corresponding square powers 2, 1, and 2 are all unique and cannot be replaced by other numbers. We know that any square power of 1 is equal to 1, and if 1 is also considered a prime number, any power of 1 can be inserted into the decomposition of 7623, and the uniqueness of the decomposition will be destroyed, which will cause unnecessary trouble. Therefore, mathematicians have clearly stipulated that 1 is not a prime number.
The Fundamental Theorem of Arithmetic shows that prime numbers are the "basic elements" that make up integers. The prime number table is to number theory what the periodic table is to chemistry, but with one major difference: the prime number table is infinite.