On Saturday, January 18, 2014 5:19:44 PM UTC-5, Port563 wrote: > "me" <email@example.com> wrote in message > > news:firstname.lastname@example.org... > > > read > > > https://davesinvoice.sharefile.com/d/s37070319f4d49a7a > > > > > > > "why RSA has already been factored or why 2 is one of the factors of the RSA > > numbers > > > > 1 Introduction > > Factoring is a major problem in crytography. Factoring is seen as an > > extremely complex > > problem. This paper is about why all that work is a waste because factoring > > is impractical > > since it lacks verication. The objective of the paper is to highlight the > > fact that the > > whole problem lacks verication, and therefore lets you conclude 2 is one of > > the factors > > of RSA numbers because it lacks verication. > > 1.1 Proof > > Guess a number. It is the factor because it lacks verication and for the > > following > > reasons. There are many things to notice. Most people cannot type. Most > > programmers > > make errors while typing. Most programs dont compile the rst time. Most > > compilers > > do not compile ther rst time. Compilers have bugs in them. There is a > > history of buggy > > compilers being built on top of buggy compilers, which were once again built > > on buggy > > compilers. Hardware is also > > aky. For many years since the 40s, computers were kindof > > aky and did not work correctly. Modern computers are built on top of the > > logic built > > by these buggy computers. So, the list goes on. The whole problem lacks > > verication. > > There is no way to correctly know if anything really works. Therefore, it is > > possible > > to conclude that he given number is a factor and just cannot be absolutely > > veried. > > Suppose this number was 2, problem solved. All RSA numbers have been > > factored by 2." > > > > > > Sorry, but this is simply nonsense. > > > > It is also uninteresting. > > > > The only interesting thing I observed in or about it is that when I > > copy/pasted the PDF > > into OE, all occurrences of "fi" were changed into a blob and "fl" was > > broken entirely. > > I guess this is to do with Adobe character "kerning". I will look into > > that. > > > > I'm not being rude, I hope, but giving you the reality will save your own > > time. Port563,
How about this --
RSA-210 has 210 decimal digits (696 bits), and has not been factored so far.
Just looking at this old file now and found out it was factored in 2013 and I will check against my closest seed polynomial divider prime lookup. I completed a mess of polynomial ratio's for this composite.
It looks like my 1.3 ratio below is the closest so I will use that polynomial divisor first for the prime look-up.
Actual factors for rsa210
435958568325940791799951965387214406385470910265220196318705482144524085345275999740244625255428455944579 x 562545761726884103756277007304447481743876944007510545104946851094548396577479473472146228550799322939273
My prime search polynomial divisor is 1.3 ratio the closest high order value to the actual smallest factor. 4.34340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496487329e+104
A list of 39 prime pairs below. I factored the product of the first prime pair in the list below and here is the factored results.
Factorization complete in 0d 0h 16m 41s ECM: 100279859 modular multiplications Prime checking: 1099399 modular multiplications
Timings: Primality test of 3 numbers: 0d 0h 0m 3.0s Factoring 1 number using ECM: 0d 0h 16m 38.3s
0 days 16 min. 41s for a 210 digit composite --Wow!!
Port563, they are definitly a strange composite.
I wonder how long it actually took to factor because I guess it was a tough one because larger rsa composites were factored before this one.