If $$k$$​, $$(k^2 +3)$$​and ($$k^3 +5 )$$​ are prime numbers, then what will be the value of k?

Correct option is D

Given:

​$$k, (k^2 +3)\ and\ (k^3 +5 )$$​ are prime numbers

Solution:

Checking the options:

1. Putting the values of k = 4

k = 4,

Now k itself is not a prime number hence it is not the answer

2. Putting k =3

k=3

​$$k^2+3 = 9+3 = 12$$​​

12 is not a prime number

3. Using k = 7

k=7

​$$K^2+3 = 49+52$$​

52 is not a prime number

4. Using k =2

k =2

​$$k^2 +3 =4+3 =7$$​​

​$$k^3+5 =8+5 =13$$​​

Hence correct answer is option(d) 2