360pan gold
Posts : 14
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 Posted 22/05/2007 05:02:01 PM | | Subject: Re: Reference for prime-number result..
According to A. Ivic, The Riemann zeta-function, Wiley, 1985, one
can prove that for y = x^t, t > 13/23 = 0.56521..., there are at
least y / (177 log x) primes between x-y and y, and Iwaniec and Pintz
show that there is a prime between x and x + x^t for t > 23/42 = 0.54761...
The Riemann hypothesis would imply a prime between x and x^(1/2).log x
There is a useful table of previous results in this direction.
Richard Pinch; Queens' College, Cambridge
360
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