20180726, 15:39  #12 
Sep 2009
2^{2}·3^{2}·5·11 Posts 

20180730, 17:27  #13  
Apr 2012
168_{16} Posts 
Quote:
CR, thank you for clarifying your intent. When I take exception to someone's statements I have started addressing them rather than letting them pass as I have in the past. I didn't like your wording but I acknowledge that it wasn't mean spirited so I apologize for my retaliatory comments. Bsq'd, I don't get emotional about this kind of thing for this and future reference because it's a waste of time and I much prefer addressing the issue rather than any accompanying baggage. I'm not too keen on gratuitous statements that add nothing to an issue as well. I don't believe I asked for help of any kind with the initial post in this thread. If I do have a problem where I am soliciting help/advice I will ask for it explicitly as I had done so in the past. Regarding the questions of the "general solution of the integer factorization problem" and the "distribution of the prime numbers", these are tough questions and I was wondering if there was any noteworthy conceptual breakthrough of any kind regarding these questions. I thought my subsequent comments/statements were declarative rather than something asking for help. Anything I would post within a forum that could have great significance would be buried within several layers of abstraction at the very least or would be of such generality or specificity as to be useless without other components. As a public forum providing a public service (and I have been helped immensely from various members of this forum both past and present through their posts) I interact accordingly. I have PM'd members in the past delving a little deeper into certain things (including Silverman who I found to be a very nice and helpful gentleman) but again only to a certain threshold. Last fiddled with by jwaltos on 20180730 at 17:45 

20180730, 17:46  #14  
Apr 2012
101101000_{2} Posts 
Quote:
The paths taken within the successive general solutions found and the number of iterations required to obtain a specific factorization are more easily calculated by randomizing which general solution tree to traverse. A GPUcentric environment works for these kinds of computations but what I am looking for is that single thread that will work every time for every factorization. The polynomial form that I have considered is always composite and will never consist of a single prime. Last fiddled with by jwaltos on 20180730 at 18:30 

20180730, 18:41  #15  
Aug 2006
3×1,987 Posts 
Quote:
For an overview of the first see https://www.ams.org/notices/199612/pomerance.pdf After that I think https://mathspeople.anu.edu.au/~bre...phythesis.pdf is standard, perhaps with something like http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf as a gentler transition. Once you've absorbed Murphy's thesis there are several people here who can advise on the best papers to read to better understand stateoftheart integer factorization.  As for the distribution of prime numbers, that's a much broader subject. The first major result was the Prime Number Theorem at the close of the 19th century. A recent breakthrough was Zhang's bounded gap theorem. I wrote a post diagramming its relationship to other results; you might find it useful. 

20180730, 21:52  #16 
Apr 2012
550_{8} Posts 
CR, thank you for the pointers to the articles in your post.
With the exception of Zhang's paper I had looked at the others years ago. I haven't factored a single noteworthy number so my track record is equivalent to my credibility, zero. Last fiddled with by jwaltos on 20180730 at 22:05 
20180731, 12:46  #17  
Aug 2006
3×1,987 Posts 
Quote:
Maynard (2015) Ford, Maynard, & Tao (2015) Ford, Konyagin, Maynard, Pomerance, & Tao (2018) 

20180801, 20:44  #18 
Apr 2012
168_{16} Posts 
Thank you again for the links and I appreciate the time taken to provide them.
I'll PM you with a result I have that will clarify why I initiated this thread. Last fiddled with by jwaltos on 20180801 at 20:46 
20180802, 13:16  #19 
Aug 2006
3·1,987 Posts 

20180803, 17:32  #20 
Apr 2012
2^{3}×3^{2}×5 Posts 
Sorry for the delay.
I recently returned from a trip to L.A. and am playing catchup. The PM will be sent within two days when I can redact the example I have in mind and send it off as a text file. 
20180803, 19:05  #21 
Aug 2006
3·1,987 Posts 

20180804, 06:03  #22 
Apr 2012
2^{3}×3^{2}×5 Posts 
Rather than send a text file I prepared a maple worksheet (mws).
Unfortunately I could not find a way to send that to you via PM so I provided something else instead. 
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