Right Gary, I guess that would be the transformation. Actually I just

checked out the progression in the sequence starting with 29, 31,

37 ... and it was easy to see it was of this form. I now see from

http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
that Legendre is the first reported to have seen this one. Perhaps

2x^2 + 29 generates the longest sequence of consecutive primes of any

two term equation.

And I see that Virginia's sequence of primes is reported in the

Encyclopedia on Integer Sequences as sequence A060834.

The Mathworld link above has alot of informative things to say about

the matter. (Virginia would like to read this!) I agree with you Gary

that there are other polynomials out there that can generate even

longer sequences. How to cleverly find them, that is the question.

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.

Mark

--- In

primenumbers@yahoogroups.com, Gary Chaffey <garychaffey@y...>

wrote:

> > I just figured that Gary's equation can be reduced

> > to 2x^2 + 29 to

> > generate his 29 distinct primes from x=0 to x=28 !

> >

> > Mark

> I have just spotted this too.. make y=x-22...(is this

> the transformation you have spotted Mark???)

> Gary

>

>

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