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As discussed above, Prime numbers are only divisible by one and by the number itself. This article will discuss all the divisibility rules to check prime numbers. When prime numbers are divided by numerals other than one or its exact positive divisor, its product has a remainder or exists as a fraction. An example of a prime number is eleven. The only divisors of 11 include 1 and 11. A number that is not prime is referred to as a composite number. We will further read about the smallest prime number in detail. We will also discuss the concepts of twin prime numbers.
Prime Number Definition
The numbers having two factors only are known to be prime numbers. Examples of prime numbers are three, five, seven, eleven, thirteen, etc. These numbers have two factors, i.e., one and the number itself. For example, one factor is one for the number three, and another is the number three itself. An example of a composite number is six. The factors of six are one, two, three, and six. The number one is the factor of every number. It is neither prime nor composite.
Prime numbers in between 1 and 100 are 2, 5, 3, 7, 11, 19, 17, 15, 23, 29, 37, 31, 41, 43, 53, 47, 59, 67, 61, 73, 71, 79, 89, 87, 97.
Smallest Prime Number
Now, as we know, prime numbers have two factors. The smallest prime number is two, as two have factors 1 and 2 only. The number 1 is the smallest. Still, it isn’t prime numbers. Because 1 has only one factor, it is the number 1 itself. Therefore two is the smallest prime number with factors 1 and 2. A co-prime number is a pair of numbers whose HCF of 1. Two numbers are co-prime to one another if they share no common factors, except for 1. For example, the co-primes of 11 are 5 and 7.
Conversely, two numbers are relatively prime to one another if their greatest common factor is 1 (or they are co-prime). On the other hand, Twin prime numbers are prime numbers whose difference is always 2. Three and five, for example, are twin prime numbers. Let us see about twin prime numbers in detail.
Twin Prime Numbers
The prime numbers whose difference comes to be two are known as twin prime numbers. We can also say that the number is a twin prime if only one composite number is in between them.
List of twin prime numbers between 1 and 100:
{3, 5}, {5, 7}, {11, 13}, {17, 19}, {29, 31}, {41, 43}, {59, 61}, {71, 73}
List of twin prime numbers between 100 and 500:
{101, 103}, {107, 109}, {137, 139}, {149, 151}, {179, 181}, {191, 193}, {197, 199}, {227, 229}, {239, 241}, {269, 271}, {281, 283}, {311, 313}, {347, 349}, {419, 421}, {431, 433}, {461, 463}
List of twin prime numbers between 500 and 1000:
{521, 523}, {569, 571}, {599, 601}, {617, 619}, {641, 643}, {659, 661}, {809, 811}, {821, 823}, {827, 829}, {857, 859}, {881, 883}
Divisibility Rules for Prime Numbers
Divisibility rules for some prime numbers are listed below:
For checking divisibility by 2, we need to keep in mind that even numbers are always divisible by two.
For checking divisibility by 3, add all the digits. After that, if the sum comes to be divisible by three, then the number is also divisible by the table of three.
For checking divisibility by 5, check if the end of the number is 0 or 5.
For checking divisibility by 7, you need to double the last digits of the given number. Then subtract it from the remaining number. The answer came that if divisible by seven, the number is divisible by seven.
For checking divisibility by 11, add the digits in an alternate position. Then subtract it from the difference obtained by the sum of the next alternate digits. If the difference is divisible by eleven, then the given number is also divisible by 11. An example is if the number is 574652, add 5+4+5=14 and 7+6+2=15. Its difference will not be divisible by 11. Therefore the given number is also not divisible by 11.
Conclusion
Hence, it is concluded that different ways can check the divisibility of prime numbers in different ways. The smallest prime number is two, as two have factors 1 and 2 only. The prime numbers whose difference comes to be two are called twin prime numbers. In this article, we discussed the concepts of prime numbers. We also discussed the smallest prime number and twin prime numbers. After reading this article, I hope all the concepts related to prime numbers will be clear.
