Expand Messages
• ... When X is odd the expressions are even. They are not equal to 2, so they are then composite. ... ? factor(x^4-97*x^3+3294*x^2-45458*x+213589) [x^4 -
Message 1 of 2 , May 25, 2008
--- In primenumbers@yahoogroups.com, "aldrich617" <aldrich617@...> wrote:
>
> Well, got the official word from D.B.:
> linear transforms are of no value and
> egregious factors are annoying. But
> then again he says that about
> almost everything. I really thought
> I was on to something with
>
> X^2 - 80X + 1763 --- 79 consecutive primes
> X^2 - 237X + 14409 --- 76 consecutive primes
>

When "X" is odd the expressions are even. They are not equal to 2, so
they are then composite.

> but apparently, no.
>
> I still want to try to beat the limit though,
> and use transforms
> to find a way to make longer prime chains.
>
> Can anyone factor
>
> X^4 - 97X^3 + 3294X^2 -45458X + 213589
> (49 consecutive primes)
>

? factor(x^4-97*x^3+3294*x^2-45458*x+213589)
[x^4 - 97*x^3 + 3294*x^2 - 45458*x + 213589 1]

Of course this is factored into linear factors over the complex
numbers ;-)

>
> Now that is an equation that really looks like
> fun to me, and a factorization would be a good
> place to start.
>

http://www.maa.org/editorial/mathgames/mathgames_07_17_06.html

As far as I can tell, if only monic polynomials[1] with unique
positive values were permissible, then Euler would have won the