--- 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)

>

> into quadratics?

? 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.

>

Please see:

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

quadratic race.[2]

Paul

[1]

http://mathworld.wolfram.com/MonicPolynomial.html
[2]

http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
> Aldrich Stevens

>