1, odd number: refers to a number that is not divisible by 2. The mathematical expression is 2k+ 1, and odd numbers can be divided into positive odd numbers and negative odd numbers.

2. Prime number: refers to a natural number with no other factors except 1 and itself among natural numbers greater than 1.

Second, the mathematical characteristics are different.

1, odd number: there must be an odd number and an even number in two consecutive integers; Odd number+odd number = even number; Even+odd = odd; Even number+even number+...+even number = even number; Odd number-odd number = even number; Parity = odd number; Odd-even = odd; 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;

2. 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.

Third, the application is different.

1, odd number: add odd numbers continuously, and each number is exactly a square number. This is reflected in the close and important relationship between odd number and square number.

2. Prime numbers: Prime numbers are used in cryptography. The so-called public key is to add the prime number to the information to be transmitted when encoding, and then transmit it to the receiver after encoding. After anyone receives this information, if there is no key owned by the receiver, then the process of decryption (in fact, the process of finding prime numbers) is meaningless even if the information is obtained.

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