Seriously disagreement

franktaw at franktaw at
Wed Sep 3 01:33:09 CEST 2008

-----Original Message-----
From: Peter Pein <petsie at>

>The page starts (after a tble of contents) wit a table of x (propably 
>bound of x) in the left column and the right column has got the title 

Yes, but the title of the page is "Sieving for Primes ...", not 
Primes ...".  In fact, the column is a count of primes - as I stated, 
the number
of primes dividing 2x^2-1 for any x <= 10^n.  And 1 is not being 
counted as
a prime here.

>Near the bottom (numbered "4.") the first entry says that 1 is prime.

This is just sloppiness.  The program is outputting 1 when no new 
primes are
found, and the author has simply copied this to the web page.

>These are unmisunterstandable (is there such an word in english 
>statements which are wrong. There is enough space to write "prime 
divisors" if
>one wants. But the author wrote "Primes". Therefore it is nonsense.

>Sorry for my ignorance but I do not want to have to _guess_ or 
>the meaning of words  when reading websites concerning mathematics.

It nowhere states that the numbers are the numbers of primes for x <= 
It implies that these are numbers of primes in some way associated with
2x^2-1 for x <= 10^n.  It would be (much) better if there was some
explanation for exactly what is being counted; but what is there is not 

Showing "1" in section 4 instead of blank, or perhaps the word "none", 
wrong -- but doesn't mean that the author thinks 1 is prime.

I agree that the page is far from ideal, but to simply dismiss it as 
"nonsense" is
short-sighted.  There is something of value here.  The effort required 
to figure
it out is much less than what is required to understand a typical 
paper.  And I see much worse in this mailing list on a regular basis.

(And no, there is no such word as "unmisunderstandable".  Say "not
misunderstandable" instead.)


franktaw at schrieb:
> A closer look at this web page shows that this is counting the number 
> distinct prime divisors of numbers of the form 2x^2-1 for x <= 10^n, 
> the number of primes.
> Note that there can be at most one prime divisor of 2x^2-1 that does
> not divide 2y^2-1 for some y < x.  Every prime divisor p except 
> one must be < 2x (in fact, p < sqrt(2) x), at which point p divides
> 2 |x-p|^2 - 1.
> Franklin T. Adams-Watters
> -----Original Message-----
> From: Artur <grafix at>
> Dear Seqfans,
> On www page
> we can read that number of primes of the form 2x^2-1 for x equal or 
> than 10^n is
> 8, 84, 815, 7922, 77250, 759077, 7492588, 74198995, 736401956,
> 7319543971, 72834161467
> ...

Franklin T. Adams-Watters

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