Primes: routine unsolved mysteries

Primes are one of the most interesting mathematical phenomenon that has attracted the attention of scientists and citizens for more than two millennia.Despite the fact that we now live in an age of computers and the latest information programs, many mysteries of prime numbers to be resolved until now, there are even some which scientists do not know how to approach.

Primes - this is known even from the course of elementary arithmetic, those natural numbers, which are divided evenly only by one and itself.By the way, if a natural number is divisible, except the above, further to any number, then it is called composite.One of the most popular theory is that any composite number can be represented as the only possible product of primes.

few curious facts.Firstly, the unit is unique in the sense that, in fact, does not belong to simple or to a composite number.At the same time the scientific community nevertheless it is usually referred to the first group, since formally it fully meets its requirements.

Secondly, only even number wormed group "primes" is naturally deuce.Any other even number to get here simply can not, because by definition, in addition to myself and the unit is divided into two even.

prime number, a list of which, as mentioned above, you can start with one, represent an infinite series, such as endless as the number of positive integers.Based on the fundamental theorem of arithmetic, we can conclude that primes never interrupted, and never end, because otherwise it will inevitably be interrupted, and a series of natural numbers.

Simple numbers do not appear in the natural numbers at random as it may seem at first glance.Carefully analyzing them, you can immediately notice a few features, the most interesting of which are associated with so-called chislami- "twins."Call them so because in some mysterious way they were next door to each other, separated only even delimiter (five, seven, seventeen and nineteen).

If we carefully look at them, we can see that the sum of these numbers is always a multiple of three.Moreover, when divided by three fellow left in the residue is always two, and right - a unit.Furthermore, the very distribution of these numbers by natural numbers can be predicted if you imagine all this in the form of a series of sine waves oscillating, the main points of which are formed by dividing the number by three and two.

Primes are not only the object of careful consideration by the mathematicians of the world, but has long and successfully used in the preparation of different series of numbers, which is the basis, inter alia, for shifrografii.It should be recognized that a huge number of puzzles associated with these wonderful elements, still waiting for their clues, many questions are not just philosophical, but practical significance.