Talk:Goldbach's comet

Bounds
There are many approximations to the comet bounds (lower,upper). One lower bound is On Partitions of Goldbach's Conjecture by Woon, which is

Gº(n) ~ S[1/(ln(k)*ln(n-k))], for k=3 to n/2, for n=even=>6.

Carlos Rivera claims it fails only 5 times for n<130000 (at n=332,398,632,992 and 2672)--Billymac00 (talk) 03:15, 5 November 2009 (UTC)

&Pi;2
Uppercase pi Π in a sans-serif font looks like a geometric drawing: the top, left, and right sides of a rectangle somewhat taller than it is wide. To an amateur not very advanced in math, like me, this shape might very well be an unfamiliar math or set operator; cf. the analogous curved shape, the intersection operator ∩. And in fact there is such a symbol, ⨅ (U+2A05 ). So I am changing the sentence
 * For this range of E values, the peak location is within 0.03% of the ideal Π2.

in the Anatomy section to use  (which I guess uses ∏ (U+220F )), as in the rest of the article, rather than a directly typed capital pi Π2. --Thnidu (talk) 19:50, 18 February 2015 (UTC)

An interesting potential update for this wiki page: a generalization of the binary Goldbach's conjecture (BGC) applied on primes with prime-indexes of any order
I've recently found this interesting (so-called "vertical") generalization of the binary Goldbach's conjecture (aka "VBGC") applied on primes with prime-indexes of any order. Its Romanian author (who isn’t a mathematician, however, but collaborated with some other Romanian mathematicians who are listed in MathSci: PhD George Anescu and prof. Toma Albu who are mentioned in the Acknowledgements section of the main article dedicated to VBGC and the latex preprint) called it a "meta-conjecture" and defined it as an infinite class of conjectures stronger than BGC: the author verified VBGC up to the limit 10^10 (VBGC was also independently verified by many OEIS reviewers who approved two proposed sequences of that author http://oeis.org/A316460 and https://oeis.org/A282251, both sequences based on VBGC as their main reference). Some other mathematicians also cited VBGC (as shown by the VBGC-dedicated Vixrapedia page https://www.vixrapedia.org/wiki/VBGC), including by the well-known Chinese mathematician Zhi-Wei Sun (URL2 URL3) (as a reference of an integer sequence he has submitted to OEIS in 2014 (and then updated it by linking VBGC as a main reference): A218829) and by the Portuguese mathematician and researcher dr. Carla Santos PhD in her relatively recent article called "Os números primos de Ishango". See URLs: URL1 and URL2''' Here are the ArXiv preprints on this “VBGC”: https://arxiv.org/abs/2009.12949v1 https://arxiv.org/abs/2009.12949 https://arxiv.org/a/dragoi_a_1.html The potential infinite number of Goldbach-like comets generated by this “VBGC” are much narrow and stricter than the standard/classical Goldbach comet. I think this “VBGC” would be an interesting potential update for this Wiki page 82.79.100.137 (talk) 20:06, 31 October 2020 (UTC)