Question

What is the value of x for which $x, x+1, x+3$ are all prime numbers?
A. $0$
B. $1$
C. $2$
D. $101$

Answer 1

Hint: In this question we are asked to find the value of \[x\] so that \[x,x+1\] and \[x+3\] are prime numbers. Prime numbers are those numbers which have only two factors i.e, \[1\] and the number itself. We have to assume x as 2 and then we will find each value x, x+1, x+3. Once we get the values, we have to check if they are all prime numbers

Complete step-by-step solution:
This question is based on the concept of prime numbers. As we can see the two numbers \[x\] and \[x+1\] will be consecutive numbers and according to the question they must be prime numbers too.
The numbers which can follow both the conditions will be 2 and 3 as these are consecutive numbers which also follows the condition for prime numbers
So, the value of \[x\] and \[x+1\] can be 2 and 3.
Now we have the third number\[x+3\] .
If \[x\] is equal to 2 then \[x+3\] will be
\[2+3=5\]
We know that \[5\] is also a prime number.
Now all conditions are satisfied if we have substituted \[2\] in place of \[x\].
So, value of \[x\] will be \[2\],
Option (c) is the correct answer.

Note: Some students think that \[1\] is a prime number and they substitute it in place of \[x\] but it is not true. The fact that should be kept in mind is that \[1\] is neither prime nor composite. This question can also be solved by substituting the options in place of \[x\] and then eliminating the wrong ones and this will not be that much lengthy. The only concepts to remember are the definition of prime number and \[1\] is not a prime number.