Question 1207226
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Answer: <font color=red>997</font> 


Explanation


One method is to look at a list of primes. There's not much else to say about this method.


Another method would be to start at 999 and count down until finding the prime we're after.
We see that 999 is not prime because the digits add to a multiple of 3, so 3 is a factor.
998 isn't prime either since it is even (2 is a factor).


Now to check 997.
This number isn't even, so we rule 2 out as a factor. The digits do not add to a multiple of 3, so that is ruled out as well.
sqrt(997) = 31.575 approximately
We need to check all primes up to 31. Those primes are: 
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
This is a fairly short list to work with. You should find that none of these values are a factor of 997, which lets us conclude that <font color=red>997 is prime</font>. It's the <font color=red>largest prime smaller than 1000</font>.


One tool that can be used to confirm is WolframAlpha
<a href="https://www.wolframalpha.com/input?i=largest+prime+number+less+than+1000">https://www.wolframalpha.com/input?i=largest+prime+number+less+than+1000</a>
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