Pls tell what are

1. Co-prime numbers
2. Perfect numbers
3. Twin primes
4. Prime-triplets

Pls explain this in a simple language and with an example????

Dear Student, 

1. Co-prime numbers are numbers who have only 1 as a common factor. Therefore, HCF of such numbers is 1.

$$\begin{gathered} \text{Eg: 6, 25} \\ \text{Factors of 6 = }\left\{1,2,3,6\right\} \\ \text{Factors of 25 =}\left\{1,5, 25\right\} \\ \text{So, 1 is the only common factor between 6 and 25} \end{gathered}$$

2. A perfect number 'n' is a positive integer which is equal to the sum of its factors, excluding 'n' itself.

$$\begin{gathered} \text{Eg: 28} \\ \text{Factors of 28 = }\left\{1, 2, 4, 7, 14, 28\right\} \\ \text{Sum of factors of 28 (except 28) =}1+ 2+ 4+ 7+ 14=28 \end{gathered}$$

3. If only one composite number is present between two prime numbers, then such numbers are called twin prime numbers. So, the difference between twin prime numbers is always two.

$$\begin{gathered} \text{Eg: 3 and 5} \\ \text{Only 1 composite number i.e 4 is present between 3 and 5.} \\ \text{Also, 5 - 3 = 2} \end{gathered}$$

4. A set of three consecutive prime numbers, differing by 2  is called a prime triplet. 

$$\begin{gathered} \text{Eg: 3, 5 and 7} \\ \text{5-3 = 2 , 7-5 = 2} \\ 3,\text{5 and 7 are the only known prime triplet.} \end{gathered}$$

Regards,