Seriously disagreement
Artur
grafix at csl.pl
Wed Sep 3 10:07:58 CEST 2008
Dear Seqfans,
I was write mathematica procedure follow Franklin sugestion that numbers
aren't number of primes but number of prime divisors for numbers of the
form 2x^2-1 and x<=10^n.
My result is fllowing
*10, 154, 1904, 21741, 238392*
Mathematica codes:
l = 0; p = 2; a = {}; Do[k = p x^2 - 1; m = Divisors[k];
Do[If[PrimeQ[m[[y]]], l = l + 1], {y, 1,
Length[m]}];If[N[Log[x]/Log[10]] == Round[N[Log[x]/Log[10]]], Print[l];
AppendTo[a, l]], {x, 1, 100000}]; a
Mayby on mentioned www is nothing wrong (as Franklin belive) but what
author was mean are difficult puzzle to deknotting.
Best wishes
ARTUR
franktaw at netscape.net pisze:
> -----Original Message-----
> From: Peter Pein <petsie at dordos.net>
>
>> The page starts (after a tble of contents) wit a table of x (propably
> upper
>> bound of x) in the left column and the right column has got the title
> "Primes".
>
> Yes, but the title of the page is "Sieving for Primes ...", not "Counting
> 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
> language?)
>> 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
> _search_for_
>> the meaning of words when reading websites concerning mathematics.
>
> It nowhere states that the numbers are the numbers of primes for x <=
> 10^n.
> 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 wrong.
>
> Showing "1" in section 4 instead of blank, or perhaps the word "none", is
> 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
> mathematical
> 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.)
>
>> Peter
>
> franktaw at netscape.net schrieb:
>> A closer look at this web page shows that this is counting the number
> of
>> distinct prime divisors of numbers of the form 2x^2-1 for x <= 10^n,
> not
>> 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
> possibly
>> 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 csl.pl>
>>
>> Dear Seqfans,
>>
>> On www page
>> http://www.devalco.de/quadr_Sieb_2x%5E2-1.htm
>> we can read that number of primes of the form 2x^2-1 for x equal or
> less
>> than 10^n is
>>
>> 8, 84, 815, 7922, 77250, 759077, 7492588, 74198995, 736401956,
>> 7319543971, 72834161467
>>
>> ...
>>
>
> Franklin T. Adams-Watters
>
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>
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>
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