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Jul26-11, 12:57 PM
P: 460
Quote Quote by Robert1986 View Post
Well sure, what we said was a sharper result than Bertrand's Postulate. I still don't see how this is misleading (though I will agree it really doesn't have much to do with the the thread.) The fact that there is ALWAYS a prime between n and 2n for all n is interesting on its own, espicialy when you consider that I can give you an arbirarily long list of consecutive composite integers.

I just posted the quote as a joke in the first place.
Yes but that list of r consecutive composite integers must start at some integer n and my gut tells me that n is much larger than r for large r. For instance if r is 100 then n is going to be much larger than 100 and of course 2n-n is the number of integers in this interval. what would be 100/n? my gut tells me it's about 0

so in a simillar fashion r/n goes to zero as r goes to infinity. Remember that r is the number of consecutive composite integers and n is the integer where this sequence starts.

Is my gut mistaken?

It's all good, you don't have to see it my way, my opinions are not 'etched in stone'