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    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?
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    Actually, forget about full proofs... is proving this possible or does one even exist?
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    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.
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    (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.
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    (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).
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    Yes, the proof given on Wikipedia doesn't need anything beyond A-level
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    Thanks
 
 
 
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