

We can do better for RSA and bigger number. Feel free to comment - bosons
http://www.slideshare.net/SubhendraBasu2/thesis-cover-51186885

======
ColinWright

        We take the number to be factorized,
        N, and its base 4 representation, N4,
        expand them in powers of (2 pi) weighted
        by the sum of adjacent and errant digits.
    

Well, that really doesn't seem to mean anything at all. You don't actually
describe the process, and I'm not going to spend the time trying to reverse-
engineer what you've done.

    
    
        Then we take the ratio of N4/N10 or N4/N
    

But they are the same number, so the ratio is 1. I assume you mean something
else, but I don't know what.

Then trying to follow through the next part of the example you seem to have
apparently arbitrary correction factors, so I have no idea what you mean by
"errant digits", nor how you get these weird expansions in powers of (2.pi).
I'm sure you must have some process for doing this, but it's not clear from
what you have here.

And despite what I said earlier[0] you _still_ haven't just taken an existing,
difficult example and given us the factorisation. You say you can do one of
the RSA numbers, and yet you haven't.

In an earlier comment[1] you said:

    
    
        Now factorising Ras 1536.  Will
        post the results when done.
    

Do that and I'll listen.

Let me say that people in the past have made amazing advances that have then
been ignored by everyone, only later to be found to be exactly right. You may
be right, and you may have made an amazing discovery. But you might not, and
it's up to you to communicate clearly what you've done. That is, to
communicate _exactly_ what you've done.

Demonstrate _all_ of the process, in detail, written clearly, for two small
examples. Factor 10^4+1 for me using your method, then factor (10^7-1)/9\.
Then show your working in parallel for a _large_ example, perhaps 40 digits.
Finally, factor a large number such as RSA 1536 and present your answer.

I have to say that I'll also listen more if you spell my name correctly.

[0]
[https://news.ycombinator.com/item?id=9549682](https://news.ycombinator.com/item?id=9549682)

[1]
[https://news.ycombinator.com/item?id=9499462](https://news.ycombinator.com/item?id=9499462)

~~~
ColinWright
OK, I've followed your process, and now I'll attempt to use it to factor some
of my usual examples.

EDIT:

I've now done that. I've implemented your process, restricted to cases where
there are no zeros in either the base 10 or the base 4 representations, to
simplify the process.

I ran it with N=125 - I got this result:

    
    
        N10 = 125
        N4 = 1331
        K4 = 81.8746688941
        K10 = 15.4445545759
        K4/K10 = 5.30119975244
    

This matches your example exactly.

Then I ran it on 11111:

    
    
        N10 = 11111
        N4 = 2231213
        K4 = 34404.4992922
        K10 = 877.71000039
        K4/K10 = 39.1980258592
    

39 is not a factor of 11111.

Let's try 11129:

    
    
        N10 = 11129
        N4 = 2231321
        K4 = 34399.2238656
        K10 = 873.691116523
        K4/K10 = 39.3722944128
    

Nope, 39 isn't a factor of 11129.

Let's try some more:

    
    
        N     : factors   : N4        : K4            : K10         : Eta
        112311: 3 3 12479 : 123122313 : 971666.060082 : 5390.130571 : 180.26762...
        112313: 31 3623   : 123122321 : 971664.020326 : 5390.021531 : 180.27089...
        112315: 5 7 3209  : 123122323 : 971663.763393 : 5389.905399 : 180.27473...
        112317: 3 29 1291 : 123122331 : 971662.420476 : 5389.820132 : 180.27733...
        112319: 17 6607   : 123122333 : 971662.072077 : 5389.757255 : 180.27937...
        112341: 3 37447   : 123123111 : 971604.413941 : 5385.135790 : 180.42338...
    

As you can see, the factors vary wildly, as expected, the values of K4 and K10
vary slowly, as expected, and Eta varies very little, as expected. Given that
the factors vary so wildly, and Eta varies very little, why should we expect
this to work?

Well, in these cases it simply doesn't work.

