m=p^2+q^2, (p<q primes): number of presentations

[Richard Mathar]

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On Tue, 26 Feb 2008, Hans Havermann wrote:

> Max Alekseyev:
>
>> The values for pi(10^23) listed at
>> http://www.research.att.com/~njas/sequences/b006880.txt and at
>> http://mathworld.wolfram.com/PrimeCountingFunction.html differ
>> dramatically. Moreover, MathWorld claims that the exact value of
>> pi(10^23) is known only up to +/- 1.
>
> My guess is that Eric's value came from an old (2002) attempt (see 
> http://numbers.computation.free.fr/Constants/constants.html) that was 
> eventually abandoned because computational inconsistencies. The OEIS 10^23 
> value is Tomás Oliveira e Silva's (see http://www.ieeta.pt/~tos/primes.html).
>
> I'm not sure Eric puts a lot of effort into updating MathWorld anymore.

Hi, Hans.

Actually, I do.  Please observe the continuous stream of new and updated 
entries.  And OEIS links and new sequences based on my work on MathWorld. 
And my news story about the new MathWorld build system I recently 
unveiled.  ...

I think OEIS and MathWorld remain close to the 2 most tightly interlinked 
math sites on the web.  I find the two together an indispensable 
mathematical tool, and I hope other seqfans do as well.

> I emailed him one month ago about his incorrect 
> length-of-Gregorian-Easter cycle (see 
> http://scienceworld.wolfram.com/astronomy/Easter.html) and had neither 
> feedback nor seen a correction.

That's not MathWorld :)

But seriously, as Neil can attest to, keeping up with correspondence 
related to a large collection of information is always a challenge.

Every email is important, and I know it's annoying not to hear back.  I 
wish I could say I answer every email the day I get it.  The fact is I am 
doing the best I can (with help from Ed Pegg) in the face of many other 
professional duties (and recent happy developments in my personal life) 
that compete for my time.

BTW, I'm also in the process of preparing a 3rd printed edition of 
MathWorld which, at 4300 printed pages, another nontrivial amount of 
labor.  MathWorld is still a labor of love, and so you see I'm not exactly 
twiddling my thumbs...

Best,
-Eric
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