On Feb 29, 8:30 pm, marcus_b
yahoo.com> wrote:> On Feb 28, 8:14 pm, JSH
gmail.com> wrote:
>
>
>>> On Feb 28, 9:14 am, marcus_b
yahoo.com> wrote:>
>>> On Feb 27, 7:46 pm, JSH
gmail.com> wrote:>
>>>> On Feb 27, 9:19 am, marcus_b
yahoo.com> wrote:>
>>>>> On Feb 26, 7:42 pm, JSH
gmail.com> wrote:>
>>>>>> On Feb 25, 8:48 pm, amzoti
gmail.com> wrote:>
>>>>>>> On Feb 25, 8:42 pm, JSH
gmail.com> wrote:>
>>>>>>>> On Feb 25, 8:31 pm, Rotwang
hotmail.co.uk> wrote:>
>>>>>>>>> On 26 Feb, 04:27, JSH
gmail.com> wrote:>
>>>>>>>>>> I don't like barbed criticism irrelevant to the math
>
>>>>>>>>> Then stop writing it.
>
>>>>>>>> I'm facing a society of people who lie.
>
>>>>>>>> So I've gone to the factoring problem and I'm putting out data to help
>>>>>>>> people see one thing--that today's math society is corrupt.
>
>>>>>>>> That's it!
>
>>>>>>>> I have HUGE mathematical accomplishments and while the factoring
>>>>>>>> problem is interesting, working at solving it is an effort meant
>>>>>>>> primarily to end the lying.
>
>>>>>>>> Math is a hard discipline.
>
>>>>>>>> There are a lot of academics who beat that by just never being right,
>>>>>>>> but if I am wrong, then could I slowly work out a solution to the
>>>>>>>> factoring problem on Usenet without anyone noticing?
>
>>>>>>>> Could I?
>
>>>>>>>> Yes, or no.
>
>>>>>>>> If mathematicians are brilliant and love mathematics could I slowly
>>>>>>>> work out a solution to the factoring problem on Usenet without it
>>>>>>>> being noticed?
>
>>>>>>>> If I do, then what does that mean about current math society?
>
>>>>>>>> I say, it means they ARE fakes. So that means that afterwards, they
>>>>>>>> lose their jobs as mathematicians.
>
>>>>>>>> James Harris
>
>>>>>>> Keep pounding your chest - because the truth is that you have nothing.
>
>>>>>>> Real accomplishment needs no chest pounding!
>
>>>>>> More program output of a test factorization using a "dumb" search for
>>>>>> k:
>
>>>>>> k=2224738
>
>>>>>> k = 1 mod 3, 9 mod 13, 40 mod 47, 25 mod 59, 2589 mod 2687
>>>>>> al
>>>>>> pha=1
>>>>>> Total all combinations: 4406
>>>>>> Time: 62
>>>>>> Time/combination: 0.01407172038129823
>
>>>>>> Surrogate:
>>>>>> ( 3^2 )( 13 )( 47 )( 59 )( 2687 )
>>>>>> Product: 871772967
>
>>>>>> Surrogate combinations checked: 184
>>>>>> Initial Factorization:
>
>>>>>> f_1=4801
>>>>>> f_2=2061663521
>>>>>> Now checking its factors...
>>>>>> Success!
>>>>>> Factors:
>>>>>> ( 4801 )( 2061663521 )
>>>>>> Product: 9898046564321
>
>>>>>> In coming is 9898046564321
>
>>>>>> Surrogate factorization data for target:
>
>>>>>> Surrogates factored : 34
>>>>>> Surrogates not factored : 0
>>>>>> Factored fuel percentage: 100%%
>
>>>>>> The program had to check 34 possible k's before it found the right one
>>>>>> as it was put in the neighborhood by the basic theory.
>
>>>>>> What are the odds that is a random find?
>
>>>>> Your target in this case, as in most others you have
>>>>> used as examples, is of the form
>
>>>>> T = (3x - y)(3x + y),
>
>>>>> which reduces the possibilities somewhat. You might
>>>>> try something like
>
>>>>> T = 41 * 53
>
>>>>> and see what your method produces.
>
>>>>> Citing a few examples, which presumably you have
>>>>> selected, does not prove much of anything. If your
>>>>> only criterion is better-than-random, this example does
>>>>> not show much. You need to carry out an objective
>>>>> test with randomly chosen, unselected examples. And
>>>>> you need to note ALL of the selections involved: those
>>>>> for n, p, a, and k. You may be searching a somewhat
>>>>> larger space than you realize.
>
>>>>> Marcus.
>
>>>> I just sit and type in numbers at random. A lot of them end up being
>>>> small primes with big primes so I just keep going, or they are all
>>>> small primes, or are primes themselves. It's weird how often you come
>>>> up with primes just typing in some numbers. Kind of bugs me.
>
>>>> If I see something that looks interesting where I see two big primes I
>>>> re-do with just those primes so that I don't have dinky primes in
>>>> there as well as they give no information.
>
>>>> Like for this example, originally 3 was a factor of what I randomly
>>>> typed in. Oh yeah, I do need to give n though, as you're right about
>>>> that as it's n=11.
>
>>> Your printout raises several questions. For example,
>>> your printout makes no mention of n, yet obviously from what you
>>> say here, you had to try several choices of n to arrive at
>>> a factorization. See also below.
>
>> You're right, sorry about that as I am now using n=11.
>
> Your method has changed again???
No. The requirement is nT mod 3 = 2. I said that I was using 5
because I didn't think 2 would work, when T mod 3 = 1, but I haven't
checked into that thoroughly.
In response to a case you found where n=5 wasn't working, I went to
n=11, with my test program and forgot about that change until a
question was made about n.
I'm going to add output on what n is, which will help me keep up as
well.
But that turned out to be an interesting series of events as n=5
didn't factor one of my latest examples, so I'm wondering if that is
just chance or if it means something significant.
>> That is actually a relic of when I was debating with you about an
>> example you put forward.
>
>> So out of curiosity I changed back to n=5, and it couldn't find the
>> factors!
>
>> That may mean something.
>
> It must mean that what you claimed to have proven
> to work - easy math, etc. - was wrong. Again.
It's the difference between theory and implementation with any system
of some complexity, which is why having the theory doesn't mean that
it is possible to just immediately have the best implementation.
That is research math that ends up being a lot about experiments as
there are so many variables and ways for the full system to operate
that it is more effective to experiment.
>> In any event, it's a bit of luck that I'd changed to n=11 as otherwise
>> I wouldn't have that example.
>
> Maybe there are other cases where none of n = 1,
> 5, or 11 works ... or do you claim a proof that
> those will suffice? Where is that proof?
It's not that they don't work, it is that they do not work with the
test criteria my program is using now.
It is a complex system of equations.
Too complicated to be handled completely by theory, so experiments are
needed.
The test program is like running experiments.
>
>>>> New thing is it is keeping up with what alpha's worked to factor the
>>>> surrogates.
>
>>>> It is a 45 bitlength number:
>
>>>> Number factored.
>
>>>> k=910720
>
>>>> k = 1 mod 3, 23 mod 43, 3601 mod 3733, 105658 mod 134177
>
>>>> k^2 = 1 mod 3, 13 mod 43, 2492 mod 3733, 86564 mod 134177
>
>>>> alpha=20
>
>>> So you also had to try 20 different values of alpha before
>>> you obtained the factorization?
>
>>>> {1,608}, {2,74}, {3,0}, {4,48}, {5,34}, {6,0}, {7,16}, {8,12}, {9,0},
>>>> {10,13}, {
>>>> 11,10}, {12,0}, {13,7}, {14,15}, {15,0}, {16,4}, {17,3}, {18,0},
>>>> {19,4}, {20,3},
>>>> {21,0}, {22,1}, {23,1}, {24,0},
>
>>> What do all these pairs of numbers mean?
>
>> The first number is alpha. The second number is how many surrogates
>> were factored with that alpha or the one case where the target was
>> factored which is at {20,3} so of 3 cases one is the target.
>
>> So, 608 numbers--surrogates--factored with alpha=1.
>
Yup.
> Why so many? I thought all you needed was one fairly
> large prime such that (1 + a^2)^{-1}nT mod p is a
> quadratic residue. Do you really need any "surrogates"
> at all? Why?
The program recurses to factor the surrogate, which is being used to
try and factor the target.
It is currently moving in a non-optimal search space as I have yet to
implement everything that follows from theory.
I am following a methodical process which involves incremental
changes, gathering and observing experimental data.
It is the research process.
There is theory.
And there is experimentation.
Two different processes with two different strategies.
>>>> Total all combinations: 1147989
>
>>> Combinations of what?
>
>> Um, I think that's the combinations of prime factors of the
>> surrogates.
>
> You think??? Are you saying you don't know what your
> own program is doing?
>
I forget at times. It does have some complexities to it as I try to
figure out what data I need and what data I can throw away.
Complex systems are a lot of work.
It seems to me that your replies indicate you've never been involved
in any kind of experimental process.
Like, did you have to take any science courses?
Do any experimental labs? And write lab papers?
>> The program counts how many ways it checks with factors of surrogates.
>
>>>> Time: 10719
>
>>> What are the time units?
>
>> Milliseconds, as is standard.
>
> 11 seconds to factor a 14 digit number???
>
Actually a little less than 11 seconds to be more precise.
>>>> Time/combination: 0.009337197481857405
>
>>> Are you saying you had to evaluate
>>> 1147989 different combinations?
>
>> Not sure. I'd have to look at the program, but that should be how
>> long it took to evaluate the 10719.
>
> Indeed, you don't know what your own program is doing!
It's giving a lot of data. I'm in the process of figuring out what
data is actually important.
Experimentation is a whole other world from theory.
Don't math people do any experimental work?
> Above you said that 10719 was the milliseconds required.
> Now you seem to think it is a count of things that were
> "evaluated".
>
> You don't know what you're doing. But of course
> you want credit for doing it .
>
Well, I wrote the program.
>> So it was taking an unimaginable small amount of time or roughly
>> 1/100th of a millisecond per.
>
>> These modern laptops are fast.
>
>> I'm working now with my dual core AMD Turion 64 X2.
>
> Ooooh. Impressive.
Not really. It's ok for this task though.
>
>> I may switch later to my other pc but for now it will do.
>
>>>> Surrogate:
>>>> ( 3 )( 43 )( 3733 )( 134177 )
>
>>> Once again: how do you arrive at the
>>> surrogate? The only factor of the surrogate
>>> that you seem to use is 134177. Does your
>>> program do anything with the other factors?
>
>> It loops through combinations of the factors to solve for x and y
>> where
>
>> x^2 = y^2 + S
>
>> where S is the surrogate and S = nT - (1+a^2)k^2.
>
>>>> Product: 64613873589
>
> What is this number ?
The surrogate.
The program factors the target through the factorization of the
surrogate.
So first thing it had to do was factor 64613873589, so it calls itself
recursively to factor that surrogate.
That factorization was given earlier:
( 3 )( 43 )( 3733 )( 134177 )
>
>>>> Surrogate combinations checked: 11874
>
>>> What do you mean when you say "checked" ?
>>> Did you have to try 11874 candidates to find
>>> k, or what? How does this relate to the
>>> 1147989 combinations previously noted?
>
>> The program is non-optimally finding k by starting with k =
>> floor(sqrt(nT/(a^2+1)), and then incrementing up, that is, adding 2,
>> for 100 iterations. And then it's incrementing alpha and doing that
>> again.
>
>> In this case it ended up checking 11874 combinations of factors of
>> surrogates that way.
>
>>>> Initial Factorization:
>
>>>> f_1=123503
>>>> f_2=244770767
>>>> Now checking its factors...
>>>> Success!
>>>> Factors:
>>>> ( 123503 )( 244770767 )
>>>> Product: 30229924036801
>
>>>> In coming is 30229924036801
>
>>>> Surrogate factorization data for target:
>
>>>> Surrogates factored : 1298
>
>>> This needs clarification too. How does it
>>> relate to the 11874 surrogate combinations
>>> that were "checked" ?
>
>> It tried 1298 surrogates before it factored.
>
> But 11874 "surrogate combinations ..."
Like 2(3)(5) has combinations of factors by two's, so one factor 6 and
the other 5 is one combination and one factor 2 and the other 15 is
another.
The program looped through 11874 combinations of the factors of the
1298 surrogates.
>> Of those 1298 it looped through 11874 combinations of their factors
>> trying each to get x and y.
>
>>>> Surrogates not factored : 33
>>>> Factored fuel percentage: 97%%
>
>>> What is "fuel" ?
>
>> The surrogates. I call them fuel for the factoring engine. LOL.
>
> Yeah, cute.
>
Experimental work can get tedious.
It's best to have a sense of humor about the process.
Experimentation is an entirely different animal from theoretical work,
which is why I do my best to get all the theoretical work done before
I completely shift gears.
Now that I have a complete surrogate factoring theory, I can proceed
with the experimental work.
Same thing happens in physics, so for instance, a theoretician will
write a paper or theoreticians will write a series of papers and then
experimentalists start doing work to test the theory, like building
giant colliders and stuff or other things more mundane.
It's what's necessary when studying complex systems, mathematical or
in the real world.
James Harris
