Prime numbers can only be divided by 1 and themselves.
Each natural number that can only be divided by 1 and itself is known as a prime number . 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 cousin, the term primality is used. Since the only even prime number is 2, any prime number that is larger than this is usually cited as an odd prime number.
Goldbach's conjecture
The Goldbach conjecture , proposed by the mathematician Christian Goldbach in 1742 , states 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 the sum of two prime numbers, it is believed that the conjecture is true, although it could never be proven.
Some characteristics of prime numbers
Primality is very important since it implies that every number can be factored as a product of prime numbers. This factorization, on the other hand, will always be unique.
Around 300 BC , the Greek mathematician Euclid had already shown that prime numbers are infinite. There are some rules that allow you to check if a number is prime: for example, any number that ends in 0, 2, 4, 5, 6 or 8, or whose digits add up to a number divisible by 3, is not prime. On the other hand, numbers that end in 1, 3, 7 or 9 may or may not be prime.
Numbers that are not prime (that is, those that have natural divisors in addition to 1 and itself) are known as composite numbers . By convention, 1 is not defined as prime but it is not defined as composite either.
5 is a prime number.
Encryption techniques
The applications of prime numbers are many and they 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 large figure with conventional computers, it is very reliable.
Given the human need to protect certain information, encryption systems were created, which allow only those who know the specific instructions to decode it to be able to access a certain message. These cryptographic procedures date back to very ancient civilizations, although thanks to advances in mathematics and interest in these techniques on the part of the military, their complexity has grown considerably since their first forms.
To encrypt a message it is necessary to use a key that allows it to be converted into unreadable 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. The two known encryption systems are called symmetric and secret key .
The secret key system uses two same or different keys, while the decryption key can be deduced from the encryption key. The symmetric system , also known as public key, uses two different keys; It is absolutely necessary to know both, since they do not present any indication that allows us to logically intuit one having the other.
The secret of this last system is that it relies on the well-known cheat functions ; These are mathematical formulas whose direct calculation is easy, but which require a large number of operations to perform the inverse. Precisely, in the case of asymmetric cryptography, these functions are based on the multiplication of prime numbers.