Status of general solution for IFP and prime number sequence?

[chris2be8]

Originally Posted by jwaltos

I'm looking for a polynomial time process. I found a probabilistic process which I am not satisfied with.

What process have you found? And why are you not satisfied with it?

Chris

Originally Posted by bsquared

Nobody can understand what you are asking for. If you want meaningful discussion, then the ball is in your court...

If what you want is to angrily wave your hands until this thread gets locked, then by all means continue.

I'm sincerely sorry for my unclear statements.
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.

Originally Posted by chris2be8

What process have you found? And why are you not satisfied with it?

Chris

The process is basically developing successive iterations of general solutions of a polynomial.
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 GPU-centric 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.

[CRGreathouse]

Originally Posted by jwaltos

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.

There have been tremendous breakthroughs, conceptual and otherwise, on both problems.

For an overview of the first see
https://www.ams.org/notices/199612/pomerance.pdf

After that I think
https://maths-people.anu.edu.au/~bre...phy-thesis.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 state-of-the-art 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.

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.

[CRGreathouse]

Originally Posted by jwaltos

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.

Some worthwhile papers related to prime gaps to have come out since Zhang's result include
Maynard (2015)
Ford, Maynard, & Tao (2015)
Ford, Konyagin, Maynard, Pomerance, & Tao (2018)

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.

[CRGreathouse]

Originally Posted by jwaltos

I'll PM you with a result I have that will clarify why I initiated this thread.

I didn't get a PM -- please resend or just post here.

Sorry for the delay.
I recently returned from a trip to L.A. and am playing catch-up.
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.

[CRGreathouse]

Originally Posted by jwaltos

Sorry for the delay.
I recently returned from a trip to L.A. and am playing catch-up.
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.

No rush, just making sure the message wasn't lost in the ether.

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.