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Topic: polynomials can't give only primes - sci.math #54025
Replies: 5   Last Post: Sep 13, 1996 5:00 PM

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Tord Kallqvist Romstad

Posts: 13
Registered: 12/12/04
Re: polynomials can't give only primes - sci.math #54025
Posted: Sep 6, 1996 1:19 PM
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Richard Pinch (rgep@dpmms.cam.ac.uk) wrote:
: In article <50odl2$ecr@nuscc.nus.sg>,
: sci50090@leonis.nus.sg (VeLaGaMist) writes:
: |> In anycase, it has been proved that there is indeed an integral
: |> polynomial that gives primes whenever it takes positive values.
: |>
: |> I do not have an idea of the explicit form of the polynomial. Could
: |> anyone enlighten me on this?

: Accoring to my notes, it is

: (k+2){1-([wz+h+j-q]^2 + [(gk+2g+k+1)(h+j)+h-z]^2 +
: [16(k+1)^3 (k+2) (n+1)^2 +1-f^2]^2 + [ 2n+p+q+z-e ]^2 +
: [ e^3 (e+2)(a+1)^2 + 1 - o^2]^2 + [(a^2-1)y^2 + 1 - x^2]^2 +
: [16r^2 y^4 (a^2-1) + 1-u^2]^2 +
: [ ( (a+u^2 (u^2-a))^2 - 1 ) (n+4dy)^2 + 1 - (x+cu)^2]^2 +
: [(a^2-1)l^2 + 1 - m^2]^2 + [ai+k+1-l-i]^2 + [n+l+v-y]^2 +
: [p+l(a-n-1)+b(2an+2a-n^2-2n-2)-m]^2 +
: [q+y(a-p-1)+s(2ap+2a-p^2-2p-2)-x]^2 +
: [z+pl(a-p)+t(2ap-p^2-1)-pm]^2
: ) }

: (the layout may help show why it is not of much practical use!).

There is one more reason it is not very practical:
Most of the time, the formula just give you the primes 2 and 3!
(Please don't flame me if this is wrong. I haven't tested it myself,
but think I remember having read it somewhere).

Tord Romstad







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