## Residual Factorization Extension

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• Happy New Year to All: Based on my Residual Factorization Method described in www.csulb.edu/~mbrown10 I can computer the first digits of RSA factors. I would
Message 1 of 11 , Jan 4, 2004
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Happy New Year to All:

Based on my Residual Factorization Method described in

www.csulb.edu/~mbrown10

I can computer the first digits of RSA factors.

I would like to obtain a program like ECM which will use these
digits to complete the factorization.

Does anyone have such a program?

Thanks,

Milton L. Brown
miltbrown@...

[Non-text portions of this message have been removed]
• ... Hash: SHA1 Hello, Mr. Brown As you seen to keep blabbering about this delusion of yours, I ll present an ultimatum to you. It s pretty simple, put up or
Message 2 of 11 , Jan 4, 2004
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Hello, Mr. Brown

ultimatum to you. It's pretty simple, put up or shut up.

I'll offer you the following composite, a product of 2 prime factors that I
have generated. The composite is 633 bits long and should present no problems
to your method, which has already been applied on RSA-640, an even longer
composite.

3480925125583380047292768064672259783013463317972525411009349562\
8521164954867065730095925178008432834642985375018937463225024858\
713014016242755166317438515243696252992513883624198267118378431

If you can provide the first 5 digits of each prime factor of this integer, as
you did for RSA-640, I will code everything needed to render this a practical
and useful factorization algorithm. I ask for nothing in return, for if your
algorithm works indeed, then the delight in the mathematics of such a
groundbreaking algorithm would be enough. Although I hold no hope for that;
in fact I expect with this challenge to publicly humiliate you and put an end
to this nonsense.

Failure to respond to this message will indicate, to me and certainly to the
remainder of the list, that all your claims are bogus.

Décio

On Sunday 04 January 2004 21:07, Milton Brown wrote:
> Happy New Year to All:
>
> Based on my Residual Factorization Method described in
>
> www.csulb.edu/~mbrown10
>
> I can computer the first digits of RSA factors.
>
> I would like to obtain a program like ECM which will use these
> digits to complete the factorization.
>
> Does anyone have such a program?
>
> Thanks,
>
> Milton L. Brown
> miltbrown@...
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iD8DBQE/+NceFXvAfvngkOIRArm5AJsF8ILOAA66F6YiSaLCQGcnLQEunwCfUb1j
UKn9bX4OQdj0BkK1QRAKEB8=
=Tt0M
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• ... This has been done before (by me and others, I think). He never put up .
Message 3 of 11 , Jan 4, 2004
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At 10:16 PM 1/4/2004, Décio Luiz Gazzoni Filho wrote:
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>Hash: SHA1
>
>Hello, Mr. Brown
>
>ultimatum to you. It's pretty simple, put up or shut up.

This has been done before (by me and others, I think). He never "put up".
• ... Hash: SHA1 ... Let this be a hint to the moderators that this guy needs to be excluded from the list in that case. Décio ... Version: GnuPG v1.2.3
Message 4 of 11 , Jan 4, 2004
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On Monday 05 January 2004 01:22, Jud McCranie wrote:
> At 10:16 PM 1/4/2004, Décio Luiz Gazzoni Filho wrote:
> >-----BEGIN PGP SIGNED MESSAGE-----
> >Hash: SHA1
> >
> >Hello, Mr. Brown
> >
> > an ultimatum to you. It's pretty simple, put up or shut up.
>
> This has been done before (by me and others, I think). He never "put up".
>

Let this be a hint to the moderators that this guy needs to be excluded from
the list in that case.

Décio
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• Mr. Filho: I am sorry that you consider my method a delusion. Perhaps you are not able to reproduce the mathematics Described in www.csulb.edu/~mbrown10. If
Message 5 of 11 , Jan 4, 2004
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Mr. Filho:

I am sorry that you consider my method a delusion.

Perhaps you are not able to reproduce the mathematics
Described in www.csulb.edu/~mbrown10.

If you have indeed read it and are having trouble,
I will be glad to help. These numbers are reproducible
And not a delusion.

I fail to see how you could produce better numbers than RSA's.
Please inform me and others if you can.

Perhaps the moderator should already be operating here.

Thanks.

Milton L. Brown
miltbrown@...

-----Original Message-----
From: Décio Luiz Gazzoni Filho [mailto:decio@...]
Sent: Sunday, January 04, 2004 7:17 PM
Subject: Re: [PrimeNumbers] Residual Factorization Extension

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Hello, Mr. Brown

present an
ultimatum to you. It's pretty simple, put up or shut up.

I'll offer you the following composite, a product of 2 prime factors
that I
have generated. The composite is 633 bits long and should present no
problems
to your method, which has already been applied on RSA-640, an even
longer
composite.

3480925125583380047292768064672259783013463317972525411009349562\
8521164954867065730095925178008432834642985375018937463225024858\
713014016242755166317438515243696252992513883624198267118378431

If you can provide the first 5 digits of each prime factor of this
integer, as
you did for RSA-640, I will code everything needed to render this a
practical
and useful factorization algorithm. I ask for nothing in return, for if
your
algorithm works indeed, then the delight in the mathematics of such a
groundbreaking algorithm would be enough. Although I hold no hope for
that;
in fact I expect with this challenge to publicly humiliate you and put
an end
to this nonsense.

Failure to respond to this message will indicate, to me and certainly to
the
remainder of the list, that all your claims are bogus.

Décio

On Sunday 04 January 2004 21:07, Milton Brown wrote:
> Happy New Year to All:
>
> Based on my Residual Factorization Method described in
>
> www.csulb.edu/~mbrown10
>
> I can computer the first digits of RSA factors.
>
> I would like to obtain a program like ECM which will use these
> digits to complete the factorization.
>
> Does anyone have such a program?
>
> Thanks,
>
> Milton L. Brown
> miltbrown@...
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Version: GnuPG v1.2.3 (GNU/Linux)

iD8DBQE/+NceFXvAfvngkOIRArm5AJsF8ILOAA66F6YiSaLCQGcnLQEunwCfUb1j
UKn9bX4OQdj0BkK1QRAKEB8=
=Tt0M
-----END PGP SIGNATURE-----

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• Hi All, As one of the moderators I approved this post as Milton s right of reply . However, and I am stating this publically for other members benefit, I,
Message 6 of 11 , Jan 4, 2004
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Hi All,
As one of the "moderators" I approved this post as Milton's "right of
However, and I am stating this publically for other members' benefit,
I, personally (being unable to speak for the other moderators), will
not approve another post to this list from Milton on his Residual
factorization method unless it contains an answer to the challenge he
has been issued (again).
Cheers
Ken
--- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
wrote:
> Mr. Filho:
>
> I am sorry that you consider my method a delusion.
>
> Perhaps you are not able to reproduce the mathematics
> Described in www.csulb.edu/~mbrown10.
>
> If you have indeed read it and are having trouble,
> I will be glad to help. These numbers are reproducible
> And not a delusion.
>
> I fail to see how you could produce better numbers than RSA's.
> Please inform me and others if you can.
>
> Perhaps the moderator should already be operating here.
>
> Thanks.
>
> Milton L. Brown
> miltbrown@e...
>
>
>
> -----Original Message-----
> From: Décio Luiz Gazzoni Filho [mailto:decio@r...]
> Sent: Sunday, January 04, 2004 7:17 PM
> Subject: Re: [PrimeNumbers] Residual Factorization Extension
>
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Hello, Mr. Brown
>
> present an
> ultimatum to you. It's pretty simple, put up or shut up.
>
> I'll offer you the following composite, a product of 2 prime factors
> that I
> have generated. The composite is 633 bits long and should present no
> problems
> to your method, which has already been applied on RSA-640, an even
> longer
> composite.
>
> 3480925125583380047292768064672259783013463317972525411009349562\
> 8521164954867065730095925178008432834642985375018937463225024858\
> 713014016242755166317438515243696252992513883624198267118378431
>
> If you can provide the first 5 digits of each prime factor of this
> integer, as
> you did for RSA-640, I will code everything needed to render this a
> practical
> and useful factorization algorithm. I ask for nothing in return,
for if
> your
> algorithm works indeed, then the delight in the mathematics of such
a
> groundbreaking algorithm would be enough. Although I hold no hope
for
> that;
> in fact I expect with this challenge to publicly humiliate you and
put
> an end
> to this nonsense.
>
> Failure to respond to this message will indicate, to me and
certainly to
> the
> remainder of the list, that all your claims are bogus.
>
>
> Décio
>
> On Sunday 04 January 2004 21:07, Milton Brown wrote:
> > Happy New Year to All:
> >
> > Based on my Residual Factorization Method described in
> >
> > www.csulb.edu/~mbrown10
> >
> > I can computer the first digits of RSA factors.
> >
> > I would like to obtain a program like ECM which will use these
> > digits to complete the factorization.
> >
> > Does anyone have such a program?
> >
> > Thanks,
> >
> > Milton L. Brown
> > miltbrown@e...
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.2.3 (GNU/Linux)
>
> iD8DBQE/+NceFXvAfvngkOIRArm5AJsF8ILOAA66F6YiSaLCQGcnLQEunwCfUb1j
> UKn9bX4OQdj0BkK1QRAKEB8=
> =Tt0M
> -----END PGP SIGNATURE-----
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
> To visit your group on the web, go to:
>
> To unsubscribe from this group, send an email to:
>
> Your use of Yahoo! Groups is subject to:
> http://docs.yahoo.com/info/terms/
• ... As far as I know, you have never shown that you method works on large numbers in which you don t know the prime factors. Show how it works on the examples
Message 7 of 11 , Jan 4, 2004
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At 11:31 PM 1/4/2004, Milton Brown wrote:

>I fail to see how you could produce better numbers than RSA's.
>Please inform me and others if you can.

As far as I know, you have never shown that you method works on large
numbers in which you don't know the prime factors. Show how it works on
the examples given here.
• ... Hash: SHA1 ... If you mean a PowerPoint presentation that s linked on that site, the same one you mentioned a few months ago, I indeed went to the trouble
Message 8 of 11 , Jan 4, 2004
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On Monday 05 January 2004 02:31, Milton Brown wrote:
> Mr. Filho:
>
> I am sorry that you consider my method a delusion.
>
> Perhaps you are not able to reproduce the mathematics
> Described in www.csulb.edu/~mbrown10.

If you mean a PowerPoint presentation that's linked on that site, the same one
you mentioned a few months ago, I indeed went to the trouble of opening it in
another computer (since I refuse to install software on my machine which
interoperates with Microsoft Office), only to see that I had indeed wasted my
time. But I may check back in case there's anything new. Not holding my
breath though.

> If you have indeed read it and are having trouble,
> I will be glad to help. These numbers are reproducible
> And not a delusion.
>
> I fail to see how you could produce better numbers than RSA's.
> Please inform me and others if you can.

I do not claim to produce better numbers than RSA, as you can check by reading
my post again. I just want to see your method applied on:
1. a number which you don't know the factors (which you did when you published
the results for RSA-576)
2. a number which I can readily verify the result, since in the few years
it'll take to factor RSA-640, I'll have already lost track of your email
containing the purported beginning digits of the factors.

I don't see what's so hard about it. I mean, your method sounds so simple you
could have just applied it to my composite instead of crafting this reply
debating the need to do so. Not to mention that you'd have someone to code
this algorithm for you in retribution, as I promised. So your reluctance here
makes it pretty clear that you were bluffing.

> Perhaps the moderator should already be operating here.

I agree. One of them has already manifested himself.

Décio
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• I ll have to admit that I even tried to implement Mr. Brown s algorithm, to torture-test the primality-checking routines in my programming language Frink ,
Message 9 of 11 , Jan 4, 2004
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I'll have to admit that I even tried to implement Mr. Brown's
algorithm, to torture-test the primality-checking routines in my
programming language "Frink", http://futureboy.homeip.net/frinkdocs/
(although I'll certainly admit that the description given in his
PowerPoint presentation does not give enough information to be usable to
anyone. The mention of the "Nyquist Criterion" is, I believe,
intentionally vague. I understand both the Nyquist stability criteria,
and the Nyquist sampling criteria, and those who understand them will
see, readily, that this mention is insufficient and inappropriate.)

He also sent me a spreadsheet that just had unexplained numbers in
it, all entered by hand; there was no equation in the entire thing, and
was thus useless.

In any case, even though the description was clearly insufficient, I
gave him the benefit of the doubt and tried many different
interpretations of the vague bits.

For example, it's unclear what "minimums of R" means, so I tried all
of the following:

* Minimum value of R found in a range
* Minimum absolute value of R
* Minimum sum of values of R
* Minimum sum of absolute values of R
* Minimum RMS sum of values of R

In addition, since this is obvious *incredibly* sensitive to the
exact numbers you sample, I tried lots of sampling rates and sampling
offsets, including very high sampling rates which should exceed any
interpretation of the Nyquist sampling criterion, if indeed that is what
was meant. I tried lots of "bin" sizes for the sums and averages. I
also tried scaling the minima along with their magnitudes (the values of
R tend to get larger as you sample larger numbers, of course.)

I worked with numbers of which I knew the factors, and, to make a
long story short, I see absolutely no evidence that the algorithm, as
presented, has any utility. Even if you know the exact factors, and try
really hard to make it fit, you can't even force the algorithm to point
to the right places, other than what would be expected by pure
probabilities. If you have 10 bins, 1/10 of the time you'll sample
numbers that drop it in the right bin. I don't see that as strong evidence.

Rather, it became quite clear that the minima found, even with the
smoothing produced by summing, has a lot of stochastic variation which
is directly due to the particular sample points that you chose.

It is easy to see, therefore, that _post facto_, one could choose a
set of sample points that "proved" this algorithm true if you already
knew the factors of a number. I will absolutely not accept any post
facto evidence as evidence that this algorithm works, especially when
work is not shown.

I agree that Décio's test is fair, acceptable, and should well be
within the reach of Mr. Brown's algorithm if it works as claimed. So,
please, either provide the digits, or go back to the drawing board, and
stop making further unsubstantiated claims. I would suggest that it is
not a worthwhile use of one's time to attempt to reproduce this
algorithm unless Mr. Brown provides the digits requested (unless you're
writing a programming language that you're torture-testing. :) )

If, indeed, he provides the factors, I will gladly help code the
algorithms. Seems like pretty safe money.

--
Alan Eliasen | "You cannot reason a person out of a
eliasen@... | position he did not reason himself
http://futureboy.homeip.net/ | into in the first place."
| --Jonathan Swift
• Oh, and the fact that if you happen to sample dead-on a factor, that it doesn t produce a minimum, is exceptionally telling. -- Alan Eliasen |
Message 10 of 11 , Jan 4, 2004
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Oh, and the fact that if you happen to sample dead-on a factor, that
it doesn't produce a minimum, is exceptionally telling.

--
Alan Eliasen | "You cannot reason a person out of a
eliasen@... | position he did not reason himself
http://futureboy.homeip.net/ | into in the first place."
| --Jonathan Swift
• Hi all and happy new year, I too have discovered an amazing algorithm that factorizes a composite integer N in O(log(log(Pmax))^1/2) where Pmax is the largest
Message 11 of 11 , Jan 5, 2004
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Hi all and happy new year,

I too have discovered an amazing algorithm that factorizes a
composite integer N in O(log(log(Pmax))^1/2) where Pmax is the
largest prime factor of N !!!

I have a truly marvelous demonstration of this proposition but this
margin is too narrow to contain it...

;-)

Jean-Louis.

--- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
wrote:
> Happy New Year to All:
>
> Based on my Residual Factorization Method described in
>
> www.csulb.edu/~mbrown10
>
> I can computer the first digits of RSA factors.
>
> I would like to obtain a program like ECM which will use these
> digits to complete the factorization.
>
> Does anyone have such a program?
>
> Thanks,
>
> Milton L. Brown
> miltbrown@e...
>
>
>
> [Non-text portions of this message have been removed]
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