Some numbers are not sure whether they are prime numbers if they are just impressions. Some numbers can be immediately said to be not prime numbers. A number, no matter how big, can't be a prime number as long as its single digit is 2, 4, 5, 6, 8 or 0. In addition, if the sum of all digits of a number is divisible by 3, it cannot be a prime number. But if its unit number is 650. And the sum of its digits is not divisible by 3, so it may be a prime number (but it may not be a prime number). There is no ready-made formula to tell you whether a number is prime or not. You can only try to see if you can
A number is expressed as the product of two smaller numbers.
One way to find a prime number is to list all the numbers (until you don't want to go any further, for example, until 10000) by the method of "if it is, leave it, if not, remove it". The first number is 2, which is a prime number, so you should leave it and continue counting down, deleting every other number. In this way, all numbers that are divisible by 2 and are not prime numbers can be removed. In the smallest number left, 3 is the second prime number, so we have to leave it, and then count backwards from it, and delete one every two numbers, so that all numbers that can be divisible by 3 can be removed. The next digit that can't be deleted is 5, and then every four digits are deleted, and all digits that can be 5 are deleted. The next number is 1 1, and one will be deleted every 10. The next one is 13, and then one is deleted every 12. ................................................................................................................................................
You may think that if you delete it like this, as more and more people delete it, it will eventually happen; After a certain number, all the numbers will be deleted. After a certain maximum prime number, there will be no more prime numbers. But in fact, such a situation will never happen. No matter what number you take, millions or millions, there will always be a greater prime number.
In fact, as early as 300 BC, the Greek mathematician Euclid proved that no matter how big a number you take, there must be a prime number bigger than it. Suppose you take out the first six prime numbers and multiply them: 2 * 3 * 5 * 7 *11*13 = 30030, and then you get 3003 1. This number cannot be divisible by 2,3,5,7, 1 1, 13, because the result of each division will be 1. If 3003 1 is not divisible by any number except itself, it is a prime number.
This can be done for pre 100, pre 1 100 million or any number of prime numbers. If 1 is added after calculating their product, then the number obtained is either a prime number or the product of several prime numbers larger than the listed number. No matter how big the number is, there is always a prime number bigger than it. Therefore, prime numbers.
The number of numbers is infinite.
With the increase of numbers, we will repeatedly encounter two adjacent odd pairs that are prime numbers, such as 5, 7; 1 1, 13; 17, 19; 29,3 1; 4 1,43; Wait a minute. Mathematicians can always find such a prime pair as much as possible. Is there an infinite number of such prime pairs? Nobody knows. Mathematicians think it is infinite, but they have never been able to prove it. This is why mathematicians are interested in prime numbers. Prime numbers provide mathematicians with some seemingly simple questions, but the facts are very difficult to understand. They are not yet able to meet this challenge.
Up to now, the largest prime number discovered by human beings is 224036583- 1, which is 4 1 mersenne prime.
A prime number, also called a prime number, is a number that can only be divisible by itself and 1, such as 2, 3, 5, 7, 1 1 and so on. 2500 years ago, the Greek mathematician Euclid proved that prime numbers are infinite, and proposed that a few prime numbers can be written as "2 to the nth power minus 1", where n is also 1. /kloc-Martin Mei Sen, a French priest in the 7th century, was one of them. He made outstanding achievements, so later generations called this prime number mersenne prime in the form of "2 minus 1".