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Re: Andrica

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  • djbroadhurst
    Let p and q be successive primes. Andrica conjectures that q - p
    Message 1 of 2 , Aug 3, 2002
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      Let p and q be successive primes.
      Andrica conjectures that
      q - p < sqrt(q) + sqrt(p)
      whereas Tschebysheff proved merely that
      q - p < p
      which is far weaker.
    • Jon Perry
      ... Andrica conjectures that q - p
      Message 2 of 2 , Aug 3, 2002
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        >>>Let p and q be successive primes.
        Andrica conjectures that
        q - p < sqrt(q) + sqrt(p)
        whereas Tschebysheff proved merely that
        q - p < p
        which is far weaker.<<<

        Andrica's conjecture doesn't seem very tight compared to the two:

        x^2 < p < (x+1)^2

        x^2 < p < x^2 + x

        Andrica's conjecture looks comparable to the first one.

        Can it be tightened?

        Jon Perry
        perry@...
        http://www.users.globalnet.co.uk/~perry/maths
        BrainBench MVP for HTML and JavaScript
        http://www.brainbench.com
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