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 $$3,13,17,$$ 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 –
$$13-7=6.$$ 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 –
$$23-17=6.$$ 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.