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Maths > Number Systems > Prime Numbers – Definition, Importance and List
Number Systems

Prime Numbers – Definition, Importance and List

Ever since the very beginning, we have been very curious about what prime numbers are. One might wonder what they are and why are they so tough? These are quite interesting as their distribution among natural numbers is a wonder. When you look at them on a small scale, you might think they appear randomly. However, there is a pattern on a large scale. Let’s take a dive deep into what they are and understand them better.

Definition of Prime Numbers

Any whole number which is greater than 1 having precisely two factors, 1 and itself, is certified as a prime number. In other words, any whole number which is greater than 1 and is only divisible by 1 and itself will be referred to as a prime number.

An easier way to understand this can be that if you can divide a number into equal groups, it won’t be a prime number. It will be a composite number. Similarly, if you cannot divide the number into equal groups, it is going to be a prime number. On the other hand, any number which is greater than 1 and not a prime number will be a composite number. Thus, you see that a composite number will be having more than 2 factors.

For instance, 1 will be neither be prime nor composite. It is because any whole number being greater than 1 will be prime or composite. Let’s take 15 for example. As it has got more than 2 factors which are 1, 3, 5 and 15, it will be a composite number. Further, number 13 will have only 2 factors which are 1 and 13 so it is a prime number.

prime number

Importance of Prime Numbers

We can consider prime numbers as the building blocks of numbers. Any whole number is said to be either a prime number or we can build it by multiplication of unique combination of prime numbers. Thus, if you pick any whole number, it will either be a prime number or you can build it by making use of a unique combination of prime numbers. It also carries significance in maths and is referred to as the Fundamental Theorem of Arithmetic.

A little trick to identify these numbers is that an even number that is greater than 2 is always going to be composite. Thus, 2 will be the only even Prime number. Further, if you have a number that has 2 or more digits and is ending with 5 or 0, it won’t be a prime number. This is because these numbers will always be having 5 as their factor.

List of Prime Numbers from 1 to 100

You know by now that prime numbers are ones having only two factors that are 1 and the number itself. The number of systems comprises of a lot of prime numbers. So, now we will discuss the list of prime numbers from 1 to 100 to get a better understanding.

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Through this table, we see that the numbers in red are our prime numbers. So from 1 to 100, the prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

So, you see that 2 is a prime number as its factors are 1 and 2 and its prime factorisation will be 1 x 2. Similarly, 1 and 3 are factors of 3 where the prime factorisation is 1 x 3. Thus, the same goes on for the rest of our prime numbers.

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Amulya

Satisfied with the answer

Olak Jamoh
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Olak Jamoh

Very clear. ..thanks

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