Mathematics is often referred to as a study of patterns or sequences. Among the various patterns represented by mathematics, there has always been a basic and fascinating sequence of prime numbers, which has stirred up the attention of many mathematicians since the beginning. Along with prime numbers, composite numbers also come into the picture.
Mathematics has evolved into its own language, complete with its own collection of principles and symbols, capable of interpreting a wide range of naturally occurring events. The prime numbers are all those natural numbers that can only be divided by one and themselves. To put it another way, their factors would be one and the number itself, resulting in a total of two factors. A composite number is one that can be created by multiplying two or more numbers together. As a result, composite numbers have more than two factors, or at the very least three. One thing to keep in mind is that 1 is neither prime nor composite. It’s also worth remembering that numbers that aren’t composite numbers are known as prime numbers.
Let us have a look at a few of the examples to understand the concept of prime and composite numbers better. If we consider the number 2, its factors would be 1 and 2; 2 is an even number and is also considered a prime number as it has only two factors, 1 and itself.
Coming to the number 3, we again see that it has only two factors, 1 and 3, meaning it is divisible by only 1 and 3, which makes 3 a prime number.
Taking the example of number 4, we see that it is divisible by 1, 2, and 4. Since it has a minimum of three factors, it falls under the category of composite numbers.
Let us see the number 5, which is again divisible by only 1 and 5, making it a prime number again.
A divisibility test using the numbers 2, 3, 5, 7, 11, and 13 can be used to determine whether a number is prime or composite.
If a number is divisible by one of these, it is composite, and no further checks are needed.
We have seen some basic simple numbers above and how they are classified into composite and prime. Coming to larger numbers, if we consider 21, its factors being 1, 3, 7, and 21 makes it a composite number.
Prime factorization of any number is done by breaking it down into its factors until all of them are prime numbers. To do so, divide the given number by the smallest prime number and keep going until all of its factors are prime.
We know that 2 is the smallest prime number. 3, 5, 7, 11, and 13 are the other prime numbers. It’s also worth noting that there is no largest prime number.
Insight or predictions about nature can be achieved by mathematical logic. Mathematics is derived from counting, estimation, measurement, and numbers with the aid of abstraction and logic, and hence the numbers play an important role in mathematics. Mathematics is no longer a mystery if one is skilled at crunching numbers. As a result, being familiar with the different forms of numbers will help you gain a basic understanding of how mathematical logic works. To have some practice with numbers, visit the Cuemath website and look at some helpful mathematical worksheets available there.
In both mathematics and computer science, prime numbers play a crucial role. Since long numbers are challenging to work with and identifying prime factors is difficult, they are used for encryption and secret codes, which makes them useful for making cryptographic codes for ATMs in banks.