What are the prime numbers and why should we know us?

Surely you have heard about it at least once, if not at school in other areas. For example, we find the two words ” prime numbers ” in a book’s title from a few years ago. Staying within the boundaries of the subject we are dealing with ( mathematics). You may have known, just in these days, of the discovery of a new prime number. The largest among all those identified to date. The milestone was achieved, of course, by an American (from Missouri, United States) mathematician named Curtis Cooper. He found one (even if it was a computer that calculated it, in about 31 days of processing) made up of more than 22 million digits! The previous “record number” was 5 million fewer digits. As a prize, Mr. Cooper won $ 3,000. From here,  you will know what are the prime numbers! So, Let’s start. 

 

But what are the prime numbers? How are they recognized, and what are they for?

 

In mathematics, it is called ” prime number,” which is divisible only by itself and by one, considering as results only integers without “remainder” and the comma. For example, there are three prime number because it is divisible only by three and by 1. If we divide three by two, we have as a result 1 with the remainder 1, or, in decimals, we get 1.5. As written above, the divisions with “remainder,” or quotients with a comma, we are not interested).

 

 

4, on the other site, it is not a prime number. In fact, besides being divisible by 4 and by 1 it is also divisible by 2. Numbers that are divisible by other numbers besides themselves. 

 

What are the prime numbers?

 

Starting from the beginning, from zero, and proceeding up to 100, we know with certainty that they are prime numbers. Going in order of magnitude As you progress, it becomes difficult to find a prime number.

 

For simplicity, we can exclude all numbers that are already multiples of a prime number. 

For example, all multiples of 2 (i.e. 4, 6, 8, 10, 12, 14, … etc) are not prime numbers. The same goes for 5 (10, 15, 20, … etc) or 13 (26, 39, 52, 65, 78, … etc). 

 

All multiples of a prime number are divisible by themselves, by one, and by that prime number, so they are “compound” and not “prime.” The method that allows us to remove all the multiple numbers of a prime number is called ” Sieve of Eratosthenes ” (Eratosthenes was a philosopher-mathematician who lived between 275 and 194 BC).

 

 Another facts we have to know? 

 

Besides, we can eliminate all even numbers because they will always be divisible by two. So the prime numbers (apart from 2) are all odd. Since there are no limits to numbers in general, we can also say that there is no prime number greater than all because prime numbers are also infinite, unlimited. The one discovered by Mr. Cooper is only the largest known found so far, but others exist, and more and more powerful computers will be needed to identify new ones. To know the largest prime numbers, we usually use tables, tables.

 

How to calculate a prime number

 

If you want to know whether a number is prime or not, you can calculate it yourself: just divide this number by the other prime numbers, starting from the smallest, then from 2, then 3, 5, 7, 11, and so on away, until you find an integer as a result. Continue until the product (quotient) is not less than the divisor: if you do not see a divisible number, then you are facing a prime number.

 

Example: Is 2029 a prime number? We calculate immediately.  We divide by two and find that it is not divisible (2029: 2 = 1014 with remainder 1).

 

Let’s try with 3, nothing to do (2029: 3 = 676 with remainder 1). It is not divisible by five either (2029: 5 = 405 with rest 4).  Moving forward, we arrive at 43 (2029: 43 = 47 with remainder 8) and then, to the prime number 47: here too, it is not divisible (2029: 47 = 43 with rest 8. 

 

Why did we stop at number 47 as a divisor?

 

As written before, we have to stop when the divisor is greater than the quotient (result). 2029: 47 = 43 with the remainder of 8. Since 47> 43 is not necessary to continue, 2029 is a prime number. You may also interested in Decomposing dialed numbers into prime numbers.

 

What are the prime numbers for?

 

There are several practical uses of these numbers. For example, thinking of today’s world, full of technology, personal data, current accounts, online profiles (on the internet). These figures are particularly useful for memorizing codes, passwords, which are difficult to discover. The bigger the prime number, the safer our data, our emails, our profiles on the web, our mobile phone, … etcetera will be.

 

Bonus part

 

 The first approach to mathematics may also depend on whether or not you understand the concept of a prime number. We would like to try to explain it to you in a simple way, so as not to arouse your hostility and help the children.

 

 By prime numbers, we mean all positive integers that have only two divisors. A prime number, therefore, is simply a natural number greater than one and divisible by one and itself. Conversely, all those numbers greater than one with more than two divisors cannot be called primes but composite numbers. Now that we have given the exact definition of a prime number, let’s better explain what they are and why they take this name.