Question

What is the largest $4$ digit prime number?
$A)9973$
$B)9987$
$C)9991$
$D)9997$

Answer 1

Hint: First, 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 and $1$ and also with some other numbers (at least one number other than $1$ and itself)

Complete step-by-step solution:
Since from the given that we are asked to find the largest prime number which is a four digit number. Thus we will first see the four digit number. which are the numbers with four exact digits, they are $1000$ to $9999$
Thus now to check the largest prime number. We will take the given numbers and then try to eliminate the options.
Take the option $A)9973$ since the given number is the prime number because numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself. Also this number doesn’t have any other factors except $1,9973$ and hence the option A is correct. But I need to check all the options because the given question is about the largest prime.
Take the option $B)9987$ which is not the prime because $\dfrac{{9987}}{3} = 3329$ and thus which is the composite number, composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
Take the option $C)9991$ which is not the prime because $\dfrac{{9987}}{{97}} = 103$ and thus which is the composite number, composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
Take the option $D)9997$ which is not the prime because $\dfrac{{9987}}{{13}} = 769$ and thus which is the composite number, composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
Therefore the option $A)9973$ is the largest four digit prime number.

Note: We can find whether the given number is prime or composite by the trial-and-error methods. Divide the number with the prime numbers less than the given number. if the number is exactly divisible by the prime number, it is the composite number, if not then it is the prime number.
The only even prime number is $2$ and all other prime numbers are odd.