Re: Minimum Prime Gap?

In article <44FA7F02.326291DE@xxxxxxxx>,
James Waldby <j-waldby@xxxxxxxx> wrote:
Gerry Myerson wrote:
..."Jules" ... wrote:
Gerry wrote:
does anyone know the minimum values {a,b,c} of a
quadratic function
f(x)=ax^2+bx+c
such that there is at least one prime between the values
f(x) and
f(x+1).
I just tested {1/5,3/5,1/5} which seems to be good up to 9901.
...
Isn't it still unknown if there is always a prime between two
consecutive squares?

Yes. Or perhaps I should say it is well-known that there is always
a prime between consecutive squares (omitting the squares 0 and 1)
but not yet proved.

So it seems safe to say that there is no quadratic f for which
it has been proved that there is always a prime between successive
values of f.

By Bertrand's Postulate (proven by Chebyshev) we
can take a=0, b=2, c=0, for x>3,

No, we can't. There isn't necessarily a prime between 2 x and
2 (x+1).

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


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Relevant Pages

  • Re: Minimum Prime Gap?
    ... Isn't it still unknown if there is always a prime between two ... So it seems safe to say that there is no quadratic f for which ... Gerry Myerson ...
    (sci.math)
  • Re: Minimum Prime Gap?
    ... Gerry Myerson wrote: ... a prime between consecutive squares ... By Bertrand's Postulate (proven by Chebyshev) we ...
    (sci.math)