--- 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.