What does prime number mean?

A prime number is a prime number. A natural number greater than 1. A number that cannot be divided by other natural numbers except 1 and itself is called a prime number, that is, a prime number; otherwise it is called a composite number.

1. There must be at least one prime number between a number a greater than 1 and its 2 times. An even number can be written as the sum of two composite numbers, each of which has at most 9 prime factors. (Norwegian mathematician Brown, 1920)

2. An even number can definitely be written as a prime number plus a composite number, where the number of factors of the composite number has an upper bound. (Raney, 1948)

3. An even number can definitely be written as a prime number plus a composite number composed of up to 5 factors.

4. A sufficiently large even number can definitely be written as a prime number plus a composite number consisting of at most 2 prime factors.

Related knowledge:

1. Primeness detection is generally used in the fields of mathematics or cryptography. Use a certain algorithm to determine whether the input number is prime. Unlike integer decomposition, primality testing generally cannot obtain the prime factors of the input number, but only indicates whether the input number is a prime number. Factorization of large integers is a computationally difficult problem, whereas primality testing is relatively easy (its running time is a polynomial dependence on the size of the input number).

2. Primeness tests are usually probability tests (cannot give 100% correct results). These tests use numbers randomly drawn from some sample space in addition to the input numbers; usually, a random primality test will never misclassify a prime number as a composite number, but it may misclassify a composite number as a prime number.

3. Numbers are used in cryptography. The so-called public key is to add a prime number to the information you want to transmit when encoding it. After encoding, it is sent to the recipient. After anyone receives this information, if there is no If the key possessed by the recipient is used in the decryption process (actually the process of finding prime numbers), the process of finding prime numbers (decomposing prime factors) will take too long, making even obtaining the information meaningless.

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