Prime numbers represent one of the most interesting mathematical phenomena that has attracted the attention of scientists and ordinary citizens for more than two millennia. Despite the fact that we now live in the age of computers and the most modern information programs, many mysteries of prime numbers have not been solved so far, there are even those that scientists do not know how to approach.
Prime numbers are, as is already known from the course of elementary arithmetic, those natural numbers that are divisible without a remainder only by one and itself. By the way, if a natural number is divided, except for the above, into another number, then it is called a composite. One of the most famous theorems says that any compound number can be represented as the only possible product of primes.
Some interesting facts. First, the unit is unique in that it does not, in fact, belong to either prime or compound numbers. At the same time, it is still customary in the scientific community to attribute it to the first group, since formally it fully satisfies its requirements.
Secondly, the only even number that fit into the group of “primes” is, of course, a deuce. Any other even number simply cannot get here, since by definition, apart from itself and unity, it is also divided by two.
Prime numbers, the list of which, as indicated above, can be started from one, are an infinite series, as infinite as a series of natural numbers. Based on the main theorem of arithmetic, we can conclude that primes never interrupt and never end, because otherwise a series of natural numbers would inevitably be interrupted.
Prime numbers do not appear randomly in the natural order, as it might seem at first glance. After carefully analyzing them, you can immediately notice several features, the most interesting of which are associated with the so-called “twin” numbers. They are called so because in some incomprehensible way they were next door to each other, separated only by an even delimiter (five and seven, seventeen and nineteen).
If you look closely at them, you will notice that the sum of these numbers is always a multiple of three. Moreover, when dividing by three the left brother, the remainder always remains a deuce, and the right one. In addition, the very distribution of these numbers by the natural number can be predicted if we represent this entire series in the form of oscillatory sinusoids, the main points of which are formed when the numbers are divided into three and two.
Prime numbers are not only the subject of close scrutiny by mathematicians around the world, but have long and successfully been used in compiling various series of numbers, which is the basis, including for cipherography. It should be recognized that a huge number of mysteries associated with these wonderful elements are still waiting for their clues, many questions are not only philosophical, but also practical.