--- In

primenumbers@yahoogroups.com, "Mark Underwood"

<mark.underwood@...> wrote:

>

>

> Put differently, any sequence which is found in

> ax^2 + sx + t

> where s >= 2a,

> can be found in the simpler

> ax^2 + bx + c

> where b < 2a.

>

A modification is in order. Any prime sequence which is found in

ax^2 + sx + t where s>=2a

can be found in the simpler

ax^2 + bx + c

where b <= a and both a and b are positive.

For instance, consider 5 polys which generate 40 consecutive primes

from x=0 to x=39.

x^2 + x + 41

4x^2 - 154x + 1523

4x^2 - 158x + 1601

9x^2 - 231x + 1523

9x^2 - 471x + 1603

The second and third polys generate the same sequence (in reverse),

and so does the fourth and fifth polys.

So really there are three:

x^2 + x + 41

4x^2 - 154x + 1523

9x^2 - 231 + 1523.

But these three can be simplified to

x^2 + x + 41 (prime from x=0 to x=39)

4x^2 + 2x + 41 (prime from x=-20 to x=19)

9x^2 + 3x + 41 (prime from x=-20 to x=19)

Here's another 40 I stumbled upon, but which dips into the negatives

in the middle of the sequence:

8x^2 + 6x - 661 (prime from x=-19 to x=20)

Anyways, the point I wanted to reiterate is that if one is searching

for prime polys of the form

ax^2 + bx + c

such that x roams in a certain range, one need only consider positive

b's from 0 to a. (Otherwise there is redundancy.)

Mark