Positive odd numbers: 1, 3, 5, 7, 9,1,13, 15, 17, 19, 2/kloc-. .........
Negative odd numbers:-1, -3, -5, -7, -9,-1,-13,-15,-17,-/kloc. .........
2. Even number: The number divisible by 2 is even. If 4 is an even number.
In decimal system, you can judge whether the number is odd (singular) or even (even) by looking at the single digits: 1, 3, 5, 7 and 9 are odd (singular); Numbers with digits 0, 2, 4, 6 and 8 are even (even).
3. Composite number: A number that can be decomposed into two numbers (except 1) and then multiplied is a composite number. If 6 is a composite number.
The composite number within 100 is:
4、6、8、9、 10、 12、 14、 15、 16、 18、20、2 1、22、24、25、26、27、28、30、32、33、34、35、36、38、39、40、42、44、45、46、48、 49、50、5 1、 52、54、55、56、57、58、60、62、63、64、65、66、68、69、70、72、74、75、76、77、78、80、8 1、82、84、85、86、87、88、90、9 1、92、93、94、95、96、98、99、 100
4. Prime numbers: Except 1, numbers that can only be divisible by themselves and 1 are prime numbers. If 7 is a prime number.
The prime numbers within 100 are 2,3,5,7, 1 1 3, 17,19,23,29,31.
Extended data:
The related properties of 1, odd number and even number;
(1) Two consecutive integers must have an odd number and an even number;
(2) Odd number+odd number = even number; Even+odd = odd; Even number+even number+...+even number = even number;
(3) Odd-odd = even; Parity = odd number; Odd-even = odd;
(4) If A and B are integers, the parity of a+b and a-b is the same, that is, a+b and a-b are both odd or even;
(5) The product of n odd numbers is odd, and the product of n even numbers is even; If one of the formulas is even, the product is even;
(6) Odd numbers are 1, 3, 5, 7 and 9; Even numbers are 0, 2, 4, 6, 8;
(7) Divide the square of odd numbers by 2, 4 and 8, and the remainder is1;
(8) The square difference of any two odd numbers is a multiple of 2, 4 and 8.
(9) The odd number divided by 2 is 1.
2, the nature of the composite number:
(1) All even numbers greater than 2 are composite numbers.
(2) In all odd numbers greater than 5, all numbers with 5 are composite numbers.
(3) Except 0, all natural numbers whose unit is 0 are composite numbers.
(4) All natural numbers with units of 4, 6 and 8 are composite numbers.
(5) The minimum (even) composite number is 4 and the minimum odd composite number is 9.
(6) Every composite number can be written as the unique form of the product of prime numbers, that is, the factorization of prime factors. (fundamental theorem of arithmetic)
(7) For any composite number greater than 5 (Wilson's theorem):
3, the nature 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 the order from small to large as p 1, p2, ..., pn, and let n = P 1× P2×...× PN, then,
Is it a prime number?
if
Is a prime number.
It is greater than p 1, p2, ..., pn, so it is not in the assumed prime set.
1, if it 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 it is impossible to be divisible by p 1, p2, ..., pn, so the prime factor obtained by this complex number decomposition is definitely not in the assumed prime number 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.
2. 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 proved more succinctly, and harry Furstenberg proved by topology.
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