How do I show that except for 5039, there is no prime between 5033 and 5047. I just need a nudge in the right direction, no idea how to start the problem :(
Show there is no prime in a range of numbers
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prime-numbers
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2That's a rather small range of numbers (just ~15 of them). Why don't you look for small factors of them, one number at a time? As a start, all even numbers in that list are divisible by 2. :) – 2011-11-08
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1Recall that a number is divisible by $3$ if and only if the sum of the digits is divisible by $3$. If you write down each number between those two, that is $5034, 5035, \dots , 5046$ you'll notice that each one is either even, divisible by $3$ or divisible by $5$ except 5039. That completes proof. – 2011-11-08
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1@EricNaslund How about 5041? It turns out to be $71^2$, but I know of no easy way to get that result. Of course, if you have a calculator handy, that changes everything. – 2011-11-09
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2@Arthur: Eric’s argument takes care of everything but $5041$. When it doesn’t succumb to the easy tests for $2,3,5$, and $11$, the fact that $50$ is just a little over $7^2$ and the number ends in $1$ could suggest trying $71^2$. Even if you think that you’ll have to test everything the hard way, you’ll want to know how far you need to go, so you’ll want $\sqrt{5041}$ anyway. – 2011-11-09