Question

What is a prime triplet? Give an example.

Answer 1

Hint: Prime numbers are the numbers which are only divisible by $1$ and themselves. Thus, they have only two factors ($1$ and themselves). For example- $5$ is a prime number because it is only divisible by $1$ and 5 itself. Other examples of prime numbers are \[3,{\text{ }}13,{\text{ }}17,\] etc.
$2$ is the smallest and only even prime number. $3$ is the smallest odd prime number.

Complete step-by-step solution:
Prime triplet: Prime triplet is a set of three prime numbers in which the difference of smallest and largest prime numbers is $6$ . It means that the smallest and the largest number of the group is $6$. The prime numbers should be consecutive. They are generally of the form \[\left( {n,n+2, n+6} \right)\]or \[\left( {n,n+4, n+6} \right)\]with only two exceptions \[\left( {2,3,5} \right)\]and \[\left( {3,5,7} \right)\].
Examples of prime triplet: \[\left( {5,7,11} \right)\] Here the smallest number is $5$ and largest number is $11$. The difference between $11$ and $5$ is- \[11 - 5 = 6\]. Thus, it is a prime triplet.
Some other examples of prime triplet are –
\[\left( {7,11,13} \right)\]– here the difference between the smallest number ($7$) and the largest number \[\left( {13} \right)\] is –
\[13{\text{ }}-{\text{ }}7{\text{ }} = {\text{ }}6.\] So, it is a prime triplet.
 \[\left( {17,19,23} \right)\] – here the difference between the smallest number \[\left( {17} \right)\] and the largest number \[\left( {23} \right)\] is –
\[23{\text{ }}-{\text{ }}17{\text{ }} = {\text{ }}6.\] So, it is a prime triplet.

Note: Prime triplet should not be confused with twin primes in which two prime numbers differ by 2.
> Also, we will need to know about the prime numbers and composite numbers.
> Prime numbers are the numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself.
> But the composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
> Every composite number can be represented in the form of prime factorization.