--- In

primenumbers@yahoogroups.com, "Mark Underwood"

<mark.underwood@...> wrote:

>

>

> 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.)

>

Another example: Consider the (already known) prime poly

36x^2 - 810x + 2753

which produces 45 consecutive primes (including negatives) from x=0 to

x=44.

This poly can be reduced to

36x^2 + 18x - 1801

which is prime from x=-33 to x=11.

Notice how b is positive and no more than a. Also notice how b contains

all the prime factors of a. It must, or else the poly is forced to

contain the prime factors of a which b doesn't have.

Mark