## 17862Cubic x^3 + x^2 + x + t prime generators

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• Mar 28, 2006
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Date: Tue, 28 Mar 2006 03:59:23 -0000
From: "Mark Underwood" <mark.underwood@...>
Subject: Re: prime generating quadratic conjecture

Hello Patrick,
My guess is that many polynomials of degree 3 and up will be found
which yield over 40 positive and distinct prime numbers in a row. But
if the coefficients are made to equal one, like x^3 + x^2 + x + t, I'm
guessing that none will beat Euler's x^2 + x + 41.

Mark

From Kermit < kermit@... >

In order that x^3 + x^2 + x + t not have any positive prime factors < 43,

t must be

2 mod 3

and

3 or 4 mod 5

and

2 or 5 mod 7

and

2 or 3 or 7 or 9 mod 11

and

3 or 5 or 9 or 11 mod 13

and

2 or 5 or 7 or 8 or 10 or 13 mod 17

and

3 or 4 or 7 or 9 or 12 or 13 mod 19

and

3 or 4 or 5 or 10 or 11 or 12 or 16 or 22 mod 23

and

2 or 5 or 8 or 9 or 13 or 14 or 17 or 20 or 24 or 27 mod 29

and

2 or 10 or 13 or 14 or 16 or 19 or 24 or 27 or 29 or 30 mod 31

and

2 or 4 or 7 or 10 or 14 or 18 or 19 or 24 or 25 or 29 or 33 or 36 mod 37

and

3 or 4 or 7 or 10 or 12 or 15 or 16 or 24 or 25 or 28 or 30 or 33 or 36 or
37 mod 41
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