Mainly refers to the "quality table". The process of compiling a prime number table is: according to the order of natural numbers, the first number 1 is not a prime number, so it should be excluded, and then all natural numbers from 2 to 100 are written in order, where 2 is a prime number, and the rest, all multiples of 2 after 2 are crossed out, and then all multiples of 3 after 2 are crossed out, and so on.

2. Trial Chamber:

When there is no prime number table at hand, we can judge whether a natural number is a prime number by trial and error division. For example, if we judge whether 143 and 179 are prime numbers, we can try to divide them by prime numbers such as 2, 3, 5, 7, 1 1 ... in descending order. Generally speaking, 8 prime numbers within 20, namely 2, 3, 5, 7, 1 1 3, 17, 19, can be removed.

For example, 143, the unit of this number is 3, which excludes the possibility of being divisible by 2 and 5. The sum of its digits is 1+4+3=8, which cannot be divisible by 3. It is also proved by oral calculation that it cannot be divisible by 7. Divided by 1 1, the quotient is exactly 65438.

Extended data:

First, the related properties of prime numbers

1 and prime number p have only two divisors: 1 and p.

2. Basic theorem of elementary mathematics: Any natural number greater than 1 is either a prime number itself or can be decomposed into the product of several prime numbers, and this decomposition is unique.

The number of prime numbers is infinite.

4. The number formula π(n) of prime numbers is an irreducible function.

5, if n is a positive integer, in n? To (n+ 1)? There is at least one prime number between.

6. If the prime number P is the largest prime number not exceeding n(n≥4), then p> is not applicable.

7. Among all prime numbers greater than 10, the unit number is only 1, 3, 7, 9.

Second, related applications

Prime numbers are used in cryptography. The so-called public key is to add a prime number to the information to be transmitted when encoding, and then transmit it to the receiver after encoding. If anyone receives this information without the key possessed by the receiver, the process of decryption (actually the process of finding prime numbers (decomposing prime factors)) will be too long, even making it meaningless to obtain information.

In the design of automobile gearbox gears, the number of teeth of two adjacent gears is designed as prime numbers, so as to increase the least common multiple of the number of encounters and meshing of two identical teeth in two gears, which can enhance durability and reduce failures.

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