I want to prove that the it is not possible that when two prime numbers are subtracted, for them to result in 97: $$p-q=97$$
But honestly, I don't know how to go about it. Any suggestions?
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6What can you say about two numbers whose difference is odd? – Dan Uznanski May 04 '21 at 14:02
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1Ohh, that one of them is odd and one even, so both numbers cannot be prime! Thank you! – Nick Heumann May 04 '21 at 14:03
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Well, it would have worked with a difference of 95. Or 99. – Oscar Lanzi May 04 '21 at 14:38
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We know that all primes are odd except for $2$. If $p$ and $q$ are both odd, then the difference would be even, so it can't be $97$. Therefore, one of $p$ or $q$ must be $2$. If $p$ is $2$, then the difference would be negative. If $q$ was $2$, then $p$ would have to be $99$, which is not prime. Therefore, it is not possible.
Fatso Boo
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