## Re: RE 40 prime polynomials

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• ... 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.
Message 1 of 12 , Apr 5, 2006
<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
• ... wrote: ... Correction: 9x^2 + 3x + 41 is prime from x=-13 to x=26 Mark (no alcohol required to goof up) Underwood
Message 2 of 12 , Apr 5, 2006