13175Re: Prime Number Progresions
- Aug 5, 2003--- Mark Underwood wrote:
> Perhaps 2x^2 + 29 generates the longest sequence of consecutiveIf you believe the first Hardy-Littlewood Conjecture (also known
> primes of any two term equation.
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 toAgain, the same conjecture implies that arbitrarily long sequences
> look for a longer one since it has been shown that p = 41
> generates the longest one.
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.
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