Is there an equation that can find whether a number is prime or not?

It seems that no, mathematicians and their computers in various countries are still trying to find larger prime numbers. If there is an equation, do you still have to find it this way?

ps: I'll give you some more information, the "maximum prime" from the encyclopedia

To date, the largest prime number ever discovered by man is 2 32582657-1, which is the 44th Mersenne prime number.

In 1995, George Waterman, an American programmer, compiled a program for calculating Mersenne primes and placed them on the Internet for use by math enthusiasts. More than 60,000 volunteers and more than 200,000 computers are currently participating in the program. The project takes a distributed computing approach, using the idle time of a large number of ordinary computers to obtain the computing power equivalent to that of a supercomputer, and the 39th Mersenne prime number is found in this way.

A ** club in the United States has also set up a $100,000 prize to encourage the first person to find more than 10 million primes.

This also proves that there are no so-called "equations" for prime numbers to follow, and they need to be discovered one by one by a computer.

You can just go down to "Maximum Prime Number" to find out. The information there is very complete, so I won't copy it.

Please search in the encyclopedia: Tai Chi Calculation, which contains a prime number equation.

1. Find the square root of this number m = m

2. Find all prime numbers that are not greater than m.

3. Cross out the integer multiples of all prime numbers on a table of natural numbers (the prime numbers themselves are not crossed out) 4. Cross out 1.

5. Numbers that are not crossed out are prime numbers.

For example, if we want to find all prime numbers within 100, we just need to follow the steps below:

1. Calculate the square root of 100, which is 10.

There are prime numbers within

3. Cross out integer multiples. First of all, the bucket rises to a multiple of 2, such as , and then crosses out a multiple of 3, such as , and the duplicate does not need to be crossed out again. Then cross out multiples of 5, multiples of 7.

4. Cross out 1 at the end.

The sum of several prime numbers must be odd or even.

For example, the rentable chain is: 2 3+5=10, 10 is an even number; 3 5+7=15, 15 is an odd number; Summoning.

So the sum of several prime numbers must be odd or even.

The sum of several prime numbers must be a composite number, which is the result of experiments.

The sum of a prime number, and any other prime number, is an odd number. I am (2).

Because any even number except round 2 has at least 1 next to it, and it itself is 2, so any prime number except 2 is odd, and even and odd are added to give an odd number.

So the answer is 2

A prime number is noisy, and the sum of any other prime number is odd. I am (2) because any even number except 2 has at least 1, which itself is 2, so any prime number except 2 is odd, and even and odd are added to get an odd number, so the answer is 2

Prime numbers are also known as prime numbers. A natural number greater than 1, except for Chunda 1 and itself, is not divisible by other natural numbers is called a prime number; Otherwise, it is called a composite number.

The vertical method of tossing and dividing is to determine whether two numbers are mutually primary, rather than being applied to one number, and is to find the major common divisor of two numbers.

The specific method of tossing and dividing is to divide the smaller number by the larger number, then remove the divisor with the remaining number that appears (the first remainder), and then remove the first remainder with the remaining number that appears (the second remainder), and so on until the final remainder is 0. If you are finding the greatest common divisor of two numbers, then the final divisor is the greatest common divisor of the two numbers.

This is a specific flowchart, to determine whether a number is prime or not is to see if it is divisible by a number other than 1.

Prime numbers are an important part of mathematics, and the so-called prime numbers are numbers that do not have any factors except 1 and itself. The following is a summary of how to find prime numbers in C.

Problem: Enter a positive integer n(n>=2) and find all prime numbers not greater than n.

Method 1: Round-robin method.

Idea: To determine whether a number n is prime, you can use all integers between 2 and n to remove n, if none of them are divisible, then n is a prime number. Try to skip some unnecessary situations when designing nested loops.

1."2"It is a prime number that must be output, and can be output separately. This can be judged from 3 to n.

2.Why only the number to n is to be judged?

Since n = n * n, the factors of n exist in pairs except n, and there must be a factor greater than n and less than n, assuming n is not a prime number, and there is a factor greater than n (not n itself), then n must have a corresponding factor less than n.

3.Except for 2, there is no even prime number, so you can set the step to 2 when designing the loop.

Method 2: Sieve method (space for time).

Idea: List all the numbers from 2 to n, and then start with 2, first sift out all the multiples of 2 in n, and then start with the next remaining number (must be prime) each time, sift out all the multiples in n, and finally the remaining numbers are prime numbers.

1.Set an array a, where the value of a[i] is 1 to indicate that i is a prime number, and all elements are initialized to 1

2.Sieve out the multiples of m, i.e., put a[2*m], a[3*m]....Set to 0

3.Outputs an i with an a[i] value of 1.

Method.

1. When using trial division to determine whether a natural number a is a prime number, use each prime number to remove a in order from small to large, if a prime number is exactly divisible, this a can be concluded that it is not a prime number; If it is not divisible, when the incomplete quotient is less than this prime number, there is no need to continue the trial division, and it can be concluded that a must be a prime number method.

2. As long as x is found to be an odd number and an even number in the form of the square difference (which is certain), then a2-b2 = (a+b) (a-b) are the two factors. For example, 26341, first find an even square number larger than 26341, 26896, and the difference between it is 555, which is definitely not a square number, and then the next square number (in fact, considering (x+1) 2=x2+2x+1, so just add the original number to 2x+1, and don't need to calculate the square of x+1), 27556, the difference is 1215, and it is not, and then the difference between 28224 single digits and 1 is 3, directly excluded, The next 2559 is not either (one look knows that it is equal to 50 2+59). Then the next difference is 3 and it is directly discharged, and then the next one, and then the next ......It is very fast to find the pattern, and finally 221 2 = 48841, 48841-26341 = 22500, obviously 22500 = 150 2, and it is decomposed.

Definition: A number, if there are only two factors of 1 and itself, such a number is called a prime number, also known as a prime number. Even numbers have only 2 as prime numbers.

The experience is: 1 The simple sieve method is to directly test and remove.

2 If a is an n-factor, then n a is also an n-factor, then if n has a true factor greater than 1, then there must be a factor of 1 to the second power that is not greater than n.

3 Further, if n is a composite number, he must have a prime factor not greater than n to the 1 2nd power, and to detect whether a number within m is prime, a table of prime numbers within the 1 2nd power of m must be established in advance.

Therefore: first determine if n is even?

Next, find m to the 1 2nd power (take the whole number).

If n is not divisible by the prime number of a prime number table of 1 2nd power (taken as an integer) of m, then n is also a prime number.

o(∩_o

Let's start with prime numbers (prime numbers) and composite numbers.

A prime number is one that is only divisible by 1 and itself.

For example, 31*3=3

The factor of three has two 1s and 3s

Then three is a prime number.

Composite numbers are the opposite of prime numbers. For example, 15

The factor of 15 has 1513

5 four so 15 is a composite number, so to speak.

Prime numbers other than 2 are all odd numbers.

Just judge if he can find the third factor.

You can know if he is a prime number.