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-   -   Status of general solution for IFP and prime number sequence? (https://www.mersenneforum.org/showthread.php?t=23516)

 jwaltos 2018-07-20 15:11

Status of general solution for IFP and prime number sequence?

Is anyone trying to solve or resolve these two questions in general?
There is a lot of action regarding aspects of these questions but I haven't been able to find much in the way of complete descriptions encapsulating their manner of resolution...other than by quantum computation...and that is not a complete solution since there is much beyond that.

 jwaltos 2018-07-24 14:56

I've been searching for a deterministic form of integer factorization for a while because I strongly believe that
like the other basic mathematical operations there should be a step-by-step process. And I believe that this is a fundamental
question worthy of anyone's attention. I also believe there is an ordered and predictable distribution of the prime numbers.

Last November I determined a labyrinthine structure where each coordinate leads to every form of 2-element decomposition
and one aspect is exclusive of trivial forms. The best visual is that it resembles a vascular system composed of meshed building blocks of dendritic/fractal forms.
The easiest approach is to "zoom-in" to various locales within specific boundary parameters and search for a factorization
which is essentially a probabilistic approach which for me is very unsatisfactory.
The approach which I find most natural is Aurifeuillian as it is an expressly deterministic symbolic method. My next step is to start
mapping/indexing this structure which is daunting to say the least and one reason why I have not touched this since November.

The indexing which I am tryng to conceive of is something which probably doesn't fit the accepted definition.

 CRGreathouse 2018-07-24 15:24

[QUOTE=jwaltos;492189]Is anyone trying to solve or resolve these two questions in general?[/QUOTE]

Why don't you start by defining what you mean by those two problems, since I don't find it clear at all. I'm interested in integer factorization, prime numbers, and quantum computation, and more informed than most on those subjects, but before we can talk about resolving questions we need to know what the questions are.

 jwaltos 2018-07-24 19:46

[QUOTE=CRGreathouse;492404]Why don't you start by defining what you mean by those two problems, since I don't find it clear at all. I'm interested in integer factorization, prime numbers, and quantum computation, and more informed than most on those subjects, but before we can talk about resolving questions we need to know what the questions are.[/QUOTE]

CR, you are very knowledgeable and I respect your statements most of the time.
The IFP is the IFP with no further clarity required. The prime number sequence refers to content rather than cause and the question is causation.

I too am more knowledgeable than most and I look to people like yourself within this forum to steer me in the right direction. Based on your response I have a question for you.
Looking at the content of this forum, aside from the non-mathematical portions, what questions need to be resolved to eliminate the "raison d'etre" for the forum? An analogy would be being hired for a job and doing it so well that you eliminate the need for your position as well as others. I see a great deal of work within the state-of-the-art but not much beyond it.

My latest posts may be considered something of a rant and stem from my own inability to distill much of the results presented within the forum into something that does not require a computer to process.

 chris2be8 2018-07-25 16:04

By IFP I assume you mean the Integer Factorization Problem. But exactly what do you mean by that?

Are you asking if it's in P (solvable in polynomial time) or not?

If it is do you want to know how to solve it?

If it's not in P do you want a proof it's in NP (takes an exponential function of the length of the number)? Or could it be of intermediate difficulty?

AFAIK it's not NP-complete because it can be solved in probably polynomial time by a quantum computer running Shor's algorithm. So if IFP is NP-complete a quantum computer can solve any NP-complete problem which is unlikely.

Chris

 CRGreathouse 2018-07-25 16:28

[QUOTE=jwaltos;492421]The IFP is the IFP with no further clarity required.[/QUOTE]

I feel a great deal more clarity is required. You say you're searching for a deterministic form of integer factorization, and by the standard definitions of those words we already have one. There are great minds on this forum but without a clear definition of the problem you're attacking I can hardly imagine them putting forth effort on a goose chase.

[QUOTE=jwaltos;492421]The prime number sequence refers to content rather than cause and the question is causation.[/QUOTE]

One of the great minds who once posted here would have called this "word salad". Perhaps there is meaning deep inside it but I cannot coax it out.

I am trying to engage your ideas in good faith. Please don't make me look like a fool for having done so.

 jwaltos 2018-07-25 19:20

[QUOTE=chris2be8;492478]By IFP I assume you mean the Integer Factorization Problem. But exactly what do you mean by that?

Are you asking if it's in P (solvable in polynomial time) or not?

If it is do you want to know how to solve it?

If it's not in P do you want a proof it's in NP (takes an exponential function of the length of the number)? Or could it be of intermediate difficulty?

AFAIK it's not NP-complete because it can be solved in probably polynomial time by a quantum computer running Shor's algorithm. So if IFP is NP-complete a quantum computer can solve any NP-complete problem which is unlikely.

Chris[/QUOTE]

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

[QUOTE=CRGreathouse;492482]I feel a great deal more clarity is required. You say you're searching for a deterministic form of integer factorization, and by the standard definitions of those words we already have one. There are great minds on this forum but without a clear definition of the problem you're attacking I can hardly imagine them putting forth effort on a goose chase.

One of the great minds who once posted here would have called this "word salad". Perhaps there is meaning deep inside it but I cannot coax it out.

I am trying to engage your ideas in good faith. Please don't make me look like a fool for having done so.[/QUOTE]

Fair enough. As I stated before I respect your opinion. However, have the balls to quote your source and don't pretend to engage in good faith when employing sarcasm and playing the false victim. Silverman, if that is who you meant is the "great mind" could have said many things. And please don't try to engage these "unripe" (or ripe, however you prefer) statements as they will only waste your time. Gauss had an aversion to Boetians for good reason. I thought what I had written was clear enough in lay terms but obviously not and despite the presentation the input was appreciated.

 bsquared 2018-07-25 19:47

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.

 CRGreathouse 2018-07-26 13:31

Let's take stock. Right now we have one well-defined problem:
[INDENT]Can numbers be factored in polynomial time?[/INDENT]
or to be pedantic
[INDENT]Is there a deterministic (that is, no randomness) classical (that is, non-quantum) procedure to find a nontrivial (that is, greater than 1 and less than the absolute value of the number) factor of a composite number in time polynomial in the number of base-2 digits of the number to be factored?[/INDENT]
You also wanted to know something about prime numbers. bsquared and I don't know what problem you have in mind, but I'd be happy to consider it if you would explain which problem you mean.

 CRGreathouse 2018-07-26 13:41

[QUOTE=jwaltos;492487]However, have the balls to quote your source and don't pretend to engage in good faith when employing sarcasm and playing the false victim.[/QUOTE]

I'm genuinely hurt -- I am acting in good faith and not playing the victim. It takes time and energy to write these posts and try to interpret what is written here.

[QUOTE=jwaltos;492487]Silverman, if that is who you meant is the "great mind"[/QUOTE]

He's the one from whom I lifted the phase "word salad".

[QUOTE=jwaltos;492487]And please don't try to engage these "unripe" (or ripe, however you prefer) statements as they will only waste your time. Gauss had an aversion to Boetians for good reason. I thought what I had written was clear enough in lay terms but obviously not and despite the presentation the input was appreciated.[/QUOTE]

At least three members are confused as to what problem(s) you are speculating about. Speaking for myself only, I would prefer to discuss a mathematical problem than to attempt to intuit which problem was intended.

 Dr Sardonicus 2018-07-26 14:40