Perhaps best, before moving forward on a definition of Prime Numbers, is to briefly review the very concept of Natural Numbers, as these are the kind of numbers in which prime numbers are classified.
In this sense, one can begin by saying that Mathematics defines natural numbers as those numerical elements with which the elements of a set can be counted, express accounting amounts or even assign a number or position to the elements of a collection. They are also understood as elements representing whole quantities.
On the other hand, natural numbers will be considered as positive integers, as will the oldest numbers within Humanity, since as some specialists point out, these numbers were generated directly from the basic concept of amount that the primitive man handled, being the elements that allowed this individual to count and order the world around him.
As for prime numbers, these will be explained by Mathematics as any natural number – that is, whole and positive – that is greater than zero (0) and that has only two possible dividers, also natural, which will be number one and itself. The mathematical condition that makes a number a prime number is known as primality. They are also given the mathematical name of cousins, as this discipline considers that the rest of the numbers come from them.
Thus, Mathematics notes that a prime number must not only have the property of having only two natural dividers, but in turn will be characterized as any positive integer that is unable to express itself as a product of two numbers less valuable, that is, a prime number will be one that cannot be factored.
Although the definition of prime numbers indicates that any natural number greater than zero that cannot be expressed as the product of two smaller positive integers will be considered as such, by convention one is not taken as a prime number , nor is it assumed as whole. Thus, one (1) will not belong to either of these two categories, even if it will be considered one of the two dividers with which the prime numbers count.
For its part, it will also be necessary to review the situation of number two (2) within the set of Prime Numbers, since this natural number will be understood by Mathematics as the only even number that can be considered as a prime number. In this sense, when reviewing the nature of the two (2) you will see that certainly this number can only be divided between 1 and 2, while it cannot be expressed as a product of two minor natural numbers.
The first 25 prime numbers
Although prime numbers have been conceived as a set of infinite numbers, for practical terms the different sources almost always account for the first 25 prime numbers that exist between the 2 – which is considered the first prime number , in addition to the only par- and 100 prime number. Here are these numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97
Whenever you want to check whether a positive integer is a prime number, you should try to determine its possible dividers, knowing that if a number can only give as a quotient a positive integer when it is divided between one (1) or itself, then it is in presence of a Prime Number.
September 21, 2019