A quick memory method of prime number table within 100: prime formula within 100.
Two, three, five, seven, eleven;
13, 19, 17;
23, 29, 37;
Three one, four one, forty seven;
43, 53, 59;
6 1, 7 1, 67;
73, 83, 89;
Add 79, 97;
25 prime numbers cannot be less;
Remember the prime numbers within 100.
Method 2: Reciting children's songs:
2, 3, 5, 7, 1 1 (two, three, five, seven and eleven)
13, 17 (thirteen followed by seventeen)
19，23，29( 19，23，29)
3 1, 37,41(Sany, Sanqi, Forty-one)
43, 47, 53 (43, 47, 53)
59, 6 1, 67 (59, 6 1, 67)
7 1, 73,79 (July 73,79 1 day)
83, 89, 97 (83, 97)
Method 3:
I don't think 2, 3, 5 and 7 need to be remembered.
I made up a story: prime number climbing mountains and drinking.
Chopsticks on Tianping Mountain (1 1) and doctors (13) use instruments (17) to make medicinal liquor (19). I met Jordan (23) and Uncle (29) with Chinese yam (3 1) and pheasant (37). The master of ceremonies (4 1) below said that there was a driver (47) wearing a black veil (53) hat at the foot of Shishan Mountain. When they climbed the mountain (83), they also brought a bottle of white wine (89). After drinking, they will go back to Hong Kong together (97). Transfer from: high mountains and flowing water.
There are two kinds of numbers in English: cardinal number and ordinal number. Cardinal number means number, ordinal number means order. In the English test questions of senior high school entrance examination in various places, the examination of numerals is the focus of the proposition (prime number), also known as prime number, which is endless. A natural number greater than 1 cannot be divisible by other natural numbers except 1 and itself, in other words, this number has no other factors except 1 and itself; Otherwise it is called a composite number.
According to fundamental theorem of arithmetic, every integer greater than 1 is either a prime number itself or a product of a series of prime numbers; If the order of these prime numbers in the product is not considered, then the writing form is unique. The smallest prime number is 2.
So far, people have not found a formula for finding all prime numbers.
In 2065438+2006 10 month and 65438+2006, the largest prime number in the world was found, with a length of 22.33 million digits. If printed in ordinary font, its length will exceed 65 kilometers.
Number of prime numbers
The number of prime numbers is infinite. There is a classic proof in Euclid's Elements of Geometry. It uses a common proof method: reduction to absurdity. The concrete proof is as follows: suppose there are only a limited number of n prime numbers, which are arranged in order from small to large as p 1, p2, pn, and let N=p 1? P2pn, then, is N+ 1 a prime number?
If N+ 1 is a prime number, then N+ 1 is greater than p 1, p2, pn, so it is not in those assumed prime numbers.
If N+ 1 is a composite number, because any composite number can be decomposed into the product of several prime numbers; The greatest common divisor of n and N+ 1 is 1, so N+ 1 cannot be divisible by p 1, p2, pn, so the prime factor obtained by this complex decomposition is definitely not in the assumed prime set.
Therefore, whether the number is a prime number or a composite number, it means that there are other prime numbers besides the assumed finite number of prime numbers. So the original assumption doesn't hold water. In other words, there are infinitely many prime numbers.
Other mathematicians have given some different proofs. Euler proved by Riemann function that the sum of reciprocal of all prime numbers is divergent, Ernst? Cuomo's proof is more concise, and HillelFurstenberg uses topology to prove it.
Used to calculate the number of prime numbers in a certain range.
Although the whole prime number is infinite, some people will ask? How many prime numbers are there below 100000? What is the possibility that a random number with 100 digits is a prime number? The prime number theorem can answer this question.
Correlation theorem
There must be at least one prime number between the number A greater than 1 and its twice (that is, within the interval (a, 2a)).
There is a prime arithmetic progression of arbitrary length. (Green and Tao Zhexuan, 2004)
An even number can be written as the sum of two numbers, and each number has at most nine prime factors. (Brown, Norway, 1920)
Even numbers must be written as prime addition numbers, where there is an upper limit on the number of factors. (Renee, 1948)
Even numbers must be written as a prime number plus a composite number consisting of at most five factors. Later, someone called this result (1+5) (China, 1968).
A sufficiently large even number must be written as a prime number plus a composite number consisting of at most two prime factors. The abbreviation is (1+2) (Chen Jingrun, China).
Famous conjecture
Goldbach conjecture: Can every even number greater than 2 be written as the sum of two prime numbers?
Twin prime conjecture: Twin prime numbers are a pair of prime numbers with a difference of 2, such as 1 1 and 13. Are there infinitely many twin prime numbers?
Does Fibonacci sequence have infinite prime numbers? Is there an infinite number of mersenne prime? Is there a prime number every n between n2 and (n+ 1)2? X2+ 1 Is there an infinite number of such prime numbers?
Introduction to nature
Prime numbers have many unique properties:
The (1) prime p has 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.
(3) The number of prime numbers is infinite.
(4) The number formula of prime numbers? (n) is an irreducible function.
(5) If n is a positive integer, there is at least one prime number between the quadratic power of n and the quadratic power of (n+ 1).
(6) If n is a positive integer greater than or equal to 2, it is between n and n! There is at least one prime number between.
(7) If the prime number P is the largest prime number not exceeding n (n is greater than or equal to 4), then p> is not applicable.