Thanks for the correction Jack, I would not have discerned that

difference from what I read unless it was pointed out.

I remember the Hardy-Littlewood k tuple Conjecture but I never did

connect it to polynominals.

Whether the k tuple conjucture is true, I guess I believe it with a

condition, which is that the tuple does not occur if it does not

occur early on, or something like that...

Mark

--- In primenumbers@yahoogroups.com, "jbrennen" <jack@b...> wrote:

> --- Mark Underwood wrote:

>

> > Perhaps 2x^2 + 29 generates the longest sequence of consecutive

> > primes of any two term equation.

>

> If you believe the first Hardy-Littlewood Conjecture (also known

> as the k-tuple Conjecture), there exist arbitrarily long sequences

> of primes from two term equations.

>

> > But for expressions of the form x^2 + x + p there is no need to

> > look for a longer one since it has been shown that p = 41

> > generates the longest one.

>

> Again, the same conjecture implies that arbitrarily long sequences

> of primes exist of the form x^2+x+p.

>

> What has been shown is that p=41 is the largest prime such that

> x^2+x+p is prime for all x, 0 <= x <= p-2.

>

> It has not been shown that x^2+x+p is never prime for 0 <= x <= 40.