We explain what prime numbers are, their history and what their uses and applications are. Also, differences with composite numbers.
What are prime numbers?
In mathematics, prime numbers are the set of natural numbers greater than 1, which can only be divided by 1 and themselves. That is, they are numbers that cannot be broken down into smaller numbers exactly, and in this they differ from the rest of the natural numbers (that is, composite numbers). This condition is known as primality.
For example, 3 is a prime number, since it can only be divided by 1 and 3, while 4 can be divided by 2. Something similar happens with 7, a prime number, but not with 8, which is divisible by 2 and 4. You must read about Independence of Brazil once.
The list of prime numbers is infinite and seems to be subject to the laws of probability, that is, their frequency of appearance does not follow strict and regular rules.
That is why prime numbers have been the subject of study since ancient times by mathematicians and thinkers, many of whom have thought they could find some kind of revelation or divine message in the laws of their distribution. In fact, some of the most difficult mathematical problems to solve have to do with prime numbers, such as the Riemann hypothesis and the Goldbach conjecture.
History of prime numbers
The study of prime numbers had its beginnings in ancient times. Evidence of their knowledge has been found in civilizations long before the appearance of writing, around 20,000 years ago, as well as on clay tablets from ancient Mesopotamia. Both the Babylonians and the Egyptians developed a powerful mathematical knowledge in which prime numbers were contemplated.
However, the first formal study of prime numbers appeared in Ancient Greece around 300 BC, and it is in Euclid’s Elements (in volumes VII to IX). At that same time, the first useful algorithm for finding prime numbers arose, known as the Sieve of Eratosthenes.
However, it was not until the 17th century that these studies became relevant in the West again: the French jurist and mathematician Pierre de Fermat (1601-1665), for example, established his Fermat Theorem in 1640, and the French monk Marin Mersenne (1588-1648) devoted himself to prime numbers of the form 2p – 1, which is why they are known today as “Mersenne numbers”.
Thanks to these studies, added to those of Leonhard Euler, Bernhard Riemann, Adrien-Marie Legendre, Carl Friedrich Gauss and other European mathematicians, the first modern methods for finding prime numbers appeared in the 19th century, precursors of those used today by scientific computers. Maybe you should definitely read about Paralympic Games once.
Uses and applications of prime numbers
Prime numbers have the following applications and uses:
- In the field of numerical and mathematical studies, prime numbers are used to study complex numbers, using the concept of “relative primes”. They are also used in the formulation of “finite bodies” and in the geometry of star polygons of n
- In computing, prime numbers are used to formulate keys using calculation algorithms.
Table of prime numbers
Between the number 2 and the number 1013 there are 168 prime numbers, which are:
| 2 | 3 | 5 | 7 | 11 | 13 | 17 |
| 19 | ||||||
| 47 | ||||||
| 79 | ||||||
| 109 | ||||||
| 151 | ||||||
| 191 | ||||||
| 229 | ||||||
| 269 | ||||||
| 311 | ||||||
| 353 | ||||||
| 397 | ||||||
| 439 | ||||||
| 971 | 977 | 983 | 991 | 997 | 1009 | 1013 |
Difference between prime numbers and composite numbers
As the name suggests, composite numbers are made up of two other numbers in a perfect symmetrical manner. That is why composite numbers can be divided by other smaller numbers and obtain exact results. Prime numbers, on the other hand, are not divisible except by 1 and by themselves, so they are not really “composed” of other numbers, but rather constitute a singularity in themselves.
Thus, for example, the number 16 is composed of 8 (16 divided by 2), 4 (16 divided by 4) and 2 (16 divided by 8), while the number 13 is not composed of any other number, since it can only be divided by 1 and by itself.
The number 1
The number 1 is an exceptional case in mathematics, since today it is not considered a prime number, nor a composite number. Until the 19th century it was thought to be a prime number, even though it does not share most of the properties of prime numbers, such as the Euler function or the divisor function. The current trend, in this sense, is to exclude 1 from the list of prime numbers.
