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# Prime Number Proof? watch

1. Firstly, this isn't homework, just something I was thinking about so I don't mind full proofs

It seems that for an integer a > 2, there always exists a prime number p such that sqrt(a) < p < a.

I don't know any maths beyond A2 level, but I was wondering if there was a way of proving this?
2. Actually, forget about full proofs... is proving this possible or does one even exist?
3. Yes, this is always true. In fact something stronger is true: http://en.wikipedia.org/wiki/Bertrand's_postulate - there is a prime between n and 2n.
4. (Original post by SimonM)
Yes, this is always true. In fact something stronger is true: http://en.wikipedia.org/wiki/Bertrand's_postulate - there is a prime between n and 2n.
Thanks Simon. Would a proof of these kinds of things be too advanced for me to understand? The article seems quite advanced.
5. (Original post by IceWater)
Thanks Simon. Would a proof of these kinds of things be too advanced for me to understand? The article seems quite advanced.
Have a go at the one on wikipedia. It's elementary so there won't be any advanced machinery involved.

http://en.wikipedia.org/wiki/Proof_o...%27s_postulate

Don't give up if you don't first understand it. Even if it takes time to go from line to line (I'm pretty sure it would take me a while to go through it properly).
6. Yes, the proof given on Wikipedia doesn't need anything beyond A-level
7. Thanks

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