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One of the typical categories of numerical analysis is that of the group of Prime numbers, defined as one composed of numbers that are only divisible by themselves (resulting in 1) and by 1 (resulting in themselves).
When you talk about 'be divisible'It is referring to that the result has to be a whole number, because in truth, all numbers are divisible by all numbers (except for 0) yielding integer or fractional results.
From the above, some important conclusions can be drawn:
- Even numbers cannot be prime, since all even numbers are divisible, in addition to two, by a certain number that results in two. An exception to this is the number two itself., which is prime by fulfilling the essential condition of being only divisible by itself and by the unit.
- Odd numbers, instead, yes they can be cousins, to the extent that they cannot be expressed as the product of two other numbers.
Examples of prime numbers
The first twenty prime numbers are listed below as an example (note that number 1 is not included in this list, as it does not meet the prime number condition).
| 2 | 31 |
| 3 | 37 |
| 5 | 41 |
| 7 | 43 |
| 11 | 47 |
| 13 | 53 |
| 17 | 59 |
| 19 | 61 |
| 23 | 67 |
| 29 | 71 |
Prime number applications
The Prime numbers are of great importance in the field of mathematical applications, especially in the field ofcomputing Y communications security virtual.
It happens that all the encryption system it is built on the basis of prime numbers, since the condition of primality makes it impossible to decompose these numbers; which means that the combination of digits under which a password is hidden is much more difficult to crack.
Distribution of prime numbers
Working with prime numbers has a particular characteristic that is rare in mathematics, which makes it exciting for many mathematical experts: the fact that most theoretical elaborations do not exceed the category of guess.
Although prime numbers have been shown to be infinite, there is no concrete proof of the distribution of them among the whole numbers: the general enunciation of the prime number theorem states that the larger the numbers, the lower the chance of meeting a prime, but there are no theoretical elaborations that specifically explain what this distribution is like, so that all prime numbers can be identified.
The combination between the functionality of prime numbers and riddles Around them, their analysis is of great interest to mathematics, and computers are programmed to find ever larger prime numbers. At the moment, the largest known prime number has more than 17 million digits, a figure that can only be calculated by means of computers that respond to very complex algorithms.
