Here is a quite basic high-school problem that I couldn't solve.
So I was working through past papers from a competition I have been selected to go to, and here is the problem:
Which one of the following numbers are prime: A. 999973 B. 414577 C. 249951 D. 359919 E. 1000027
After a little bit of time, I figured that options $C$ and $D$ are definitely not the answer, as the numbers are divisible by $3$. This leaves us with choices of $A$, $B$, and $E$.
I tried seeing if the numbers satisfy the form $6n\pm1$ for some $n$, but all of them do, which make sense as none of the numbers are divisible by either $3$ or $2$.
I am left with the most stupid way I can find of doing this problem.
As we know, most of the numbers in options $A, B$ and $E$ are six-digit numbers, with exception to that of option $E$. This means that the numbers are mostly below $1000^2$. Thus, we know from the characteristics of prime numbers that as long as all of these numbers are not divisible by any primes less than $1000$, then it must be a prime. However, there are so many primes less than $1000$, and during the test, with roughly $40$ questions in $45$ minutes, it would be impractical and virtually impossible to test the divisibility of every prime and solve the problem.
Please tell me if there is an easier way.