Determining if $973$ is prime Without a calculator, determine if $973$ is prime or not


I was given this question to solve. I know $973$ is not prime. I was told a strategy to solve whether a number is prime or not is to test all the numbers less than the square root of $973$

So I would have to test till $32$

and i find $1,7,139$ and $973$ are factors of this number.  Basically, what I want to find out is are there any other strategies to solve this question? then i wouldn't have to check till 1-32 to see if any of the numbers are factors.
Another method is $973 = 1000-27$ which can be represented as $(10)^3-(3)^3$

Therefore, applying the identity that $(a)^3-(b)^3=(a-b)(a^2+b^2+ab)$, we see that

$973=(10)^3-(3)^3=(10-3)(100+9+30)=7\cdot139$
If you're good at arithmetic, you can try this without a calculator $:)$

Wilson's theorem:

$p$ prime $\iff$ $(p-1)! \equiv -1 \pmod p$. 

Else, pocklington's test could be fast.