20200826, 14:26  #23  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}×5×167 Posts 
Quote:


20200826, 14:35  #24 
Jul 2014
60_{10} Posts 
If you read my statement before, I already said that what you just stated would be what some people would say about counting the (2,n) tuples up to some finite number.
If you aren't going to actually read, and understand, anything I write why comment on it? Last fiddled with by jzakiya on 20200826 at 14:35 
20200826, 14:43  #25 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}×5×167 Posts 
I only commented on the part I quoted. And that part I quoted was either attempting to mislead, or shows a basic misunderstanding you have. Either way it was wrong to say it IMO.

20200826, 15:15  #26  
Dec 2008
you know...around...
2^{4}×53 Posts 
Quote:
I did just about the same calculations two years ago until I concocted a Pari program that lets you find the number of gaps up to gap size = 212 in "prime generators", as I understand it, the ring of integers coprime to p#. If you want to do some number crunching, I've attached the program (Pari code together with three data files for the code). Note that the algorithm doesn't work when gap > 2*p. (The data for "a_z.txt" was taken from S. Herzog, I think it was http://zigherzog.net/primes/mathconstants/trk.html, a link which is now dead. Similar data can be found under http://pauillac.inria.fr/~harley/brent.html) Alas, though, it won't actually prove Polignac's conjecture. Sorry I can't give any details, as I'm not deep enough into the matter. But I'm sure if it was proven, you'd read it in the newspapers (yes, I'm a child of the 20th century...). 

20200826, 15:27  #27  
Aug 2006
13543_{8} Posts 
Quote:
I don't say this to be unkind, but merely to explain why no one will be able to give you what you would like. Normally I'd glance at a proof to see if I could find a telltale mistake, but here there isn't even an attempt to prove the proposition at hand. 

20200826, 16:17  #28  
"Ben"
Feb 2007
7223_{8} Posts 
Quote:
[edit] I am intrigued by the thought of packing the residueclass bits contiguously, and then sieving at fixed bitpositions for each class. Yafu makes independent arrays for each class and sieves each in turn. There are pros and cons to each approach. Independent array pros: * trivial to parallelize across classes * fewer segments to represent a given numberline range, per class Cons: * variablebit memory access per sieve step (so that one must compute a bitoffset in the current byte for each step). I'm actually not sure this is a bottleneck though, because the computation is so much faster than the memory access. Bitpacked pros: * fixedbit sieving (perhaps an improvement, see cons above) * a given segment remains cached throughout class sieving (this is probably a bigger win) * primes can be generated inorder Cons: * more segments to represent a given numberline range * parallelization would probably be best done across subsegments of the range I might have to play around with some code to see how things compare Last fiddled with by bsquared on 20200826 at 16:54 

20200826, 17:40  #29  
Jul 2014
2^{2}·3·5 Posts 
Quote:
Also its interesting that apparently the Sieve of Eratosthenes, Sieve of Atkin, and Sieve of Sundaram are totally good form, but the Sieve of Zakiya somehow is not. Why? Who should my sieves and techniques be named after? So only certain types of people have work named after them? https://en.wikipedia.org/wiki/Generation_of_primes Thankfully, thousands of people have downloaded my Rubygems, read my papers, and are using my work. 

20200826, 18:38  #30  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10,891 Posts 
Quote:
Eratosthenes came up with the idea. It was a good one, people called it after him. 

20200826, 18:45  #31  
"Oliver"
Sep 2017
Porta Westfalica, DE
1,319 Posts 
Quote:
You could even have had a great breakthrough once and your next proposal could as well be rubbish. But vice versa is of course also possible. In all cases, we need facts, at best a mathematical proof. CRGreathouse is really trying to push you forward in a friendly manner! 

20200826, 19:00  #32  
Aug 2006
1763_{16} Posts 
Quote:
https://oeis.org/wiki/User:Charles_R...ouse_IV/Vanity It needs vastly more work than I am able to provide, but it does give some kind of an idea of the norms and expectations in the OEIS, which are somewhat more relaxed than those of academic mathematics, which in turn is less cutthroat than many (most?) other academic disciplines. Incidentally I would be happy to receive feedback (by private message or email) on this or any of my other projects. 

20200826, 19:01  #33 
Jul 2014
2^{2}×3×5 Posts 
Well, since you aren't going to address any of the "facts" presented in the paper there's little else left for me to say to you. For others who are interested/curious I can answer their questions to help them understand.

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