document.write( "Question 1207226: 3-digit number to be the
\n" ); document.write( "largest prime number less than 1000. What is this
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Algebra.Com's Answer #844981 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Answer: 997 \r
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\n" ); document.write( "\n" ); document.write( "Explanation\r
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\n" ); document.write( "\n" ); document.write( "One method is to look at a list of primes. There's not much else to say about this method.\r
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\n" ); document.write( "\n" ); document.write( "Another method would be to start at 999 and count down until finding the prime we're after.
\n" ); document.write( "We see that 999 is not prime because the digits add to a multiple of 3, so 3 is a factor.
\n" ); document.write( "998 isn't prime either since it is even (2 is a factor).\r
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\n" ); document.write( "\n" ); document.write( "Now to check 997.
\n" ); document.write( "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.
\n" ); document.write( "sqrt(997) = 31.575 approximately
\n" ); document.write( "We need to check all primes up to 31. Those primes are:
\n" ); document.write( "2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
\n" ); document.write( "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 997 is prime. It's the largest prime smaller than 1000.\r
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\n" ); document.write( "\n" ); document.write( "One tool that can be used to confirm is WolframAlpha
\n" ); document.write( "https://www.wolframalpha.com/input?i=largest+prime+number+less+than+1000
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