It is known as **Prime number** to each **Natural number** that can only be divided **for 1** and **itself** . To cite an example: 3 is a prime number, while 6 is not since 6/2 = 3 and 6/3 = 2.

To refer to the quality of being a cousin, the term is used **primality** . Since the only even prime number is 2, any prime number that is larger than this is usually cited as an odd prime number.

The **goldbach conjecture** , proposed by the mathematician **Christian Goldbach** in **1742** , points out that any even number greater than two can be expressed as the **sum** of two prime digits (4 = 2 + 2; 6 = 3 + 3; 8 = 5 + 3). Since no mathematician has been able to find an even number greater than 2 that could not be expressed by adding two prime numbers, it is believed that the conjecture is true, although it could never be proven.

Primality is very important since it implies that everything **number** may **factor** as a product of prime numbers. This factorization, on the other hand, will always be unique.

Close to the year **300 BC** the Greek mathematician **Euclid** I had already shown that prime numbers are infinite. There are some rules that allow you to check if a number is a prime: for example, any number ending in 0, 2, 4, 5, 6 or 8, or whose digits add up to a number divisible by 3, is not a prime. Instead, numbers ending in 1, 3, 7 or 9 may be cousins or not.

Numbers that are not cousins (that is, those that possess **dividers** natural in addition to 1 and himself) are known as **composed numbers** . By convention, 1 is not defined as a cousin but is not defined as a compound.

The applications of prime numbers are many and are usually related to encryption techniques. For example, in the case of the algorithm called RSA, a key is obtained through the **multiplication** of two prime numbers greater than 10100; Since there are no ways to quickly factor such a high number with conventional computers, it is very reliable.

**Encryption systems**

Given the need of the human being to protect certain information, the encryption systems were created, which allow only a person who knows to access a certain message **specific instructions to decode it**. These cryptographic procedures date back to very ancient civilizations, although thanks to advances in **mathematics** and the interest in these techniques by the military, its complexity has grown considerably since its first forms.

To encrypt a message it is necessary to use a **key** that allows to convert it into illegible text. Once received, depending on the technique used, to decrypt it it will be necessary to use another key, which may or may not be the same as the first one. The two known encryption systems are called *symmetrical* and *secret key*.

The secret key system uses two identical or different keys, while the decryption key can be deduced from the encryption key. He **system** symmetric, also known as a public key, uses two different keys; It is absolutely necessary to know both, since they do not present any evidence that allows one to logically intuit one having the other.

The secret of this last system is that it relies on the known **trap functions**; these are mathematical formulas whose **calculation** Direct is easy, but they require a lot of operations to perform the inverse. Precisely, in the case of asymmetric type cryptography, these functions are based on the multiplication of prime numbers.