# Discrete math induction proof

• kai89

#### kai89

Could someone help me with this induction proof. I know its true.

given any integer m is greater than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain

any help is greatly appreciated thanks

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Is 5! prime?

I'm sorry, Ziox, I really don't see what that has to do with the problem. Please enlighten me.

How do you know this is true?

My teacher only gave us true proofs so we wouldn't be able to prove it wrong by counter example.

I'm sorry, Ziox, I really don't see what that has to do with the problem. Please enlighten me.

5!+i has divisors 2,3,4,5 for i=2,...,5. Paired up respectively.

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Oh, of course! That answers the whole question. I was focusing on the "5" and didn't think about doing the same thing for n in general. Very nice.

kai89, do you understand what ZioX is saying?

Oh, of course! That answers the whole question. I was focusing on the "5" and didn't think about doing the same thing for n in general. Very nice.

kai89, do you understand what ZioX is saying?

You're right though, I was being pretty vague and probably would've only made sense if someone has seen it before. Should've said something about divisibility when adding.

kai89, since it has been a couple of days now, I will give detail on what ZioX hinted at: For any positive integer n, n! is obviously divisible by every integer up to and including n. Therefore, n!+ 2 is divisible by 2, n!+ 3 is divisible by 3, up to n!+ n is divisible by by n. You have n-1 consecutive integers that are not prime.

As I said before, very nice!

Primes are so unpredictable.

;-p