## What are the Things Which Make Prime Numbers so Unique?

Prime numbers have attracted the attention of the house of human beings since the early days of civilisation and this is one of the most exciting topics of mathematics that everybody should master. From the beginning of human history, prime number have aroused a good amount of human curiosity and the appearance of prime numbers might seem to be very much random on a large scale but actually, it always comes with a good amount of logic in terms of finding out the numbers.

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Prime numbers are fundamentally very much important in the world of mathematics and help in solving different kinds of problems very easily. On a generic basis, the prime numbers are the positive integers that have only two factors one and the integer itself. A very common example is the seven because it has only two common factors which will be one and number seven itself. On the other hand, the prime numbers can be considered as the numbers which are divisible by number one or number itself. Another way of defining it will be that it will be a positive number or integer which will be a product of any two kinds of positive integers. There is no specific defined formula to find out the prime numbers apart from finding out the factors of the number. Any number which does not follow this will be termed as the co-prime numbers and which means that they can be factored into other positive integers as well.

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The first 10 prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

The prime number was introduced in 275-194BC, Greece and it was based upon the example of sieving out the prime numbers from the list of natural numbers and draining out the composite numbers. Students can also practice this particular method by writing out the numbers from one-hundred and circling the prime numbers and putting across marks across all the composite numbers. Before the introduction of the concept of calculators and computers, the numerical tables were utilised for recording all the prime numbers and prime factorisation up to a specific limit which was usually printed. The concept of producing a list of prime numbers was based upon the sieving method in Greece. This particular method resulted in a chart which was referred to as the Eratosthenes chart and it showed the list of prime numbers of 200 which were represented in the coloured boxes. Following are some of the most common properties of the prime numbers:

- Every number is greater than one can be divided by at least one prime number.
- Every even positive integer greater than two can be expressed as the sum of two primes.
- Except to all prime numbers will be odd and in other words, one can even say that two is the only even prime number.
- Two prime numbers are always co-prime to each other
- Every composite number can even be factored into prime numbers and individually everybody will be very much unique. The methods of finding out the prime numbers are explained as follows:

Normally people know that 2 is the only even prime number and only two prime numbers are two and three apart from all of them can be based upon utilisation of the formula 6n +1 or 6n -1. In this case, n will be a natural number.

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On the other hand to know the prime numbers which are greater than 40 then people can depend upon this particular formula which has been explained as follows: n square plus n plus 1

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With the help of the above-mentioned formulas, students will be very much successful in terms of finding out the prime numbers without any kind of problem. Hence, it is also very much important for the students to get themselves registered on the platforms like cuemath.com so that they can become experts in the field of prime numbers and composite numbers.