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Re: Factorization theory wrong? Or algorithmic error?
Posted:
Apr 8, 2012 9:17 AM
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On Apr 8, 9:13 am, Pubkeybreaker <pubkeybrea...@aol.com> wrote:
> On Apr 8, 7:22 am, barker
>
>
>
>
>
> <name.temporarily.withh...@antispamming.harvard.edu> wrote:
> > hagman <goo...@von-eitzen.de> wrote innews:21567801.642.1333835088537.JavaMail.geo-discussion-forums@vbtv42...
>
> > > Am Samstag, 7. April 2012 17:50:35 UTC+2 schrieb William Hughes:
> > > > On Apr 7, 10:46=A0am, hagman <goo...@von-eitzen.de> wrote:
> > > > > Am Freitag, 6. April 2012 22:46:50 UTC+2 schrieb William Hughes:
>
> > > > > > On Apr 5, 7:19=A0pm, barker
> > > > > > <name.temporarily.withh...@antispamming.harvard.edu> wrote:
> > > > > > > -----BEGIN PGP SIGNED MESSAGE-----
> > > > > > > Hash: SHA512
>
> > > > > > > We (mathematicians) have grown to accept the primality checkers as
> > > > > > > gospel. So did I, until recently.
>
> > > > > > > This could be big, or it could be I've overlooked something, though=
> > > I
> > > > > > > have hunted for 3 days for a flaw. I'd appreciate if you could chec=
> > > k
> > > > > > > this over for me. This post is digitally signed in case I need to p=
> > > rove
> > > > > > > ownership, should my discovery (if it is a discovery) be stolen.
>
> > > > > > > As part of my research into improving factorization algorithms, I
> > > > > > > encountered this composite number, 347 decimal digits long (>1150 b=
> > > its),
> > > > > > > which I'll call A:
>
> > > > > > > 3634908448770161716619462884730373820150226880205007030541419827683=
> > > 585
> > > > > > > 7931761274740311086713549497603607279611408949613526779622187756741=
> > > 117
> > > > > > > 9048935484829402996681944342388178421558785023331981868685440034884=
> > > 277
> > > > > > > 9396792124395994336764804183754455993340622344242614470170379064513=
> > > 230
> > > > > > > 0552661368276733695867117608484513671228954258971153834928109857741
>
> > > > > > > I won't tell you how I generated A, because if there's no flaw in w=
> > > hat
> > > > > > > I've done (I intend to make real money out of this, if it is possib=
> > > le),
> > > > > > > the way I came up with A is a giveaway to the whole process.
>
> > > > > > > I won't ask you to factorize A, because you may not be able to. Her=
> > > e is
> > > > > > > its "smaller prime factor"** ("B"), which is 156 decimal digits lon=
> > > g:
>
> > > > > > > 3246726736489147307461784686107468324672673648914730746178468610746=
> > > 834
> > > > > > > 6821883878114173728372983219193183717113173468218838781141737283729=
> > > 832
> > > > > > > 1919318371711317
>
> > > > > > > ** that is, smaller as identified by all the factorization algorith=
> > > ms
> > > > > > > that I have encountered. If you are not professional mathematicians
> > > > > > > and do not have access to factorization tools, I recommend you use:
> > > > > > > =A0http://www.alpertron.com.ar/ECM.HTM
> > > > > > > which will work on any modern web browser, to confirm what I have
> > > > > > > just stated (i.e., that A is composite, B is prime and that A/B is =
> > > an
> > > > > > > integer; whether A/B is prime is moot).
>
> > > > > > > ECM's author Dario Alpern has diligently implemented factorization
> > > > > > > algorithms. His implementations are not in question (I assume they =
> > > are
> > > > > > > accurate, as do my colleagues) - it is the theory itself that is no=
> > > w
> > > > > > > in question.
>
> > > > > > > Divide A by B to get the 192 decimal digit number C. =A0Since 192/2=
> > > < 156,
> > > > > > > it follows that if B was the smaller prime factor of A, then C must=
> > > be
> > > > > > > prime.
>
> > > > > > > {Lemma: Assume C was non-prime. Then it must have at least one prim=
> > > e
> > > > > > > factor that is less than 97 (=3D 192/2 + 1) decimal digits long. Th=
> > > is
> > > > > > > would falsify the algorithmic result that B, at 156 decimal digits,=
> > > is
> > > > > > > the smallest prime factor of A. Therefore C must be prime.}
>
> > > > > > > I didn't want to give you C (=3D A/B) as I want you to (trivially) =
> > > compute
> > > > > > > it yourself (but for the lazy, it appears at the end of this post).
>
> > > > > > > Now check C's primality. C should be prime, per the lemma above. Ri=
> > > ght?
>
> > > > > > > Indeed, all the primality checkers I have tested show that C is pri=
> > > me.
> > > > > > > Including the java one at:
> > > > > > > =A0http://www.alpertron.com.ar/ECM.HTM
>
> > > > > > > Well, I can tell you that I have factorized C... and hand-checked i=
> > > t, as
> > > > > > > at first I could not believe the fluke finding.
>
> > > > > > > C's smaller factor is almost 2^300, so C's decomposition is non-tri=
> > > vial.
> > > > > > > In the time window before you can brute-force this, I will disclose=
> > > its
> > > > > > > factors, and the methods that:
> > > > > > > 1) got me to A (Hint: diagonalization, Cantor), and
> > > > > > > 2) factorized C.
>
> > > > > > > But at this point, I do not want to disclose C's factors, until I h=
> > > ave
> > > > > > > heard the more competent fellow mathematicians here confirm C's all=
> > > eged
> > > > > > > primality, according to the algorithms we all becomed conditioned t=
> > > o
> > > > > > > believing are true.
>
> > > > > > > I do hope I have not overlooked anything. Your assistance is apprec=
> > > iated.
>
> > > > > > > Thank you,
>
> > > > > > > "barker" (associate of the late falsified non-dullrich Dr Pertti Lo=
> > > unesto)
>
> > > > > > > Footnote: =A0For the lazy, here is the 192 decimal digit number C:
> > > > > > > 1119560943616947347400615409002575284369887465143010602130506309766=
> > > 179
> > > > > > > 0753006072671322304202892348769562317880539561982179986874385643005=
> > > 873
> > > > > > > 1438452818437316840959014392166803390411010978334873
> > > > > > > which tested algorithms suggest is prime, but which I have factoriz=
> > > ed.
>
> > > > > > > -----BEGIN PGP SIGNATURE-----
>
> > > > > > > VQEcBAEBCgAGBQJOe7YRAAoJEAjjY4weks8oA7QIAK3ELb/+NKP1vLPT8f7HQTaf
> > > > > > > Ym-qnG0TdO44RMJdbqpxsp6DoMx5JkMgluha8y6LIV3rBHHDKGQx3YwKzVTT5r81
> > > > > > > DOOQ-r3LQdLgmoemhdot2Dse16XQ7OoWzvJw-qvvYYBZ0S/J2SsrAFUAoQAe35/4
> > > > > > > 9NkVg3-JSzV+AFPQyv5hpS780v0cObSPl7yz32MypgvZkYZupC3xP/3Pdl8Fg205
> > > > > > > NkiDEaDl-JcIKM8ARJJtndd7cfNBKZ3Bh1OEQ1NwPFEMZ6uAR3S/DLdF0dY1MMxr
> > > > > > > RRcluph+ML-mTRZngA8NG9qRCBQT2IgTZNatjnZv2pcwgC0MddUnyS07bNypHg8=3D
> > > > > > > =3D87KU
> > > > > > > -----END PGP SIGNATURE-----
>
> > > > > > I predict that if and when you provide your putative factors, one of
> > > > > > them will have a prime factor less that 1,000,000
>
> > > > > > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 - William Hughes
>
> > > > > Since it is readily checked that C has no prime factors less than 1,000=
> > > ,000
> > > > > (or even less than 1,000,000,000), your prediction amounts to barker
> > > > > not revealing factors at all. =A0:)
>
> > > > > hagman
> > > >=20
> > > > Nope. The above is only valid if the putative factors are in fact
> > > > factors of C.
> > > > Since C does not have any proper factors they will not be.
> > > >=20
> > > > - William Hughes
>
> > > Well, at least I can write C as product of two integers such that neither
> > > of these integers has a prime factor < 1,000,000.
> > > Up to permutation of factors there's only one way to do so. ;)
>
> > At last, someone is at least a little bit on the right track?
>
> > Very poor reading and analytical skills shown in sci.math, no better than
> > in alt.politics.org.nsa. The original post contains no mistake(s),
> > error(s)
> > or wrong statement(s). Was it read carefully enough? Apparently, no.
> You wrote:
>
> "Well, I can tell you that I have factorized C... and hand-checked it,
> as
> at first I could not believe the fluke finding.
>
> C's smaller factor is almost 2^300, so C's decomposition is non-
> trivial.
> In the time window before you can brute-force this, I will disclose
> its
> factors, and the methods that:
> 1) got me to A (Hint: diagonalization, Cantor), and
> 2) factorized C. "
>
> Since C is prime, any intelligent reader is going to conclude that you
> are a spamming and lying piece of shit.
>
>
>
> > I will supply a further hint. If we add together the 2 factors of C, to
> > arrive at D, the largest prime factor of D is the 183 decimal digit
> > number:
> > 358050379911852746241673609972200391570944003061600841442151335677224869
> > 764099592907918958324761500403496107209279988661853710490640317981357174
> > 732801778565826180964783476648958068743
>
> IMPOSSIBLE by the statement you made before. You stated that the
> smallest
> factor of C was approximately 2^300. The sum of the two factors of C
> is
> therefore approximately S = 2^300 + C/2^300 and this number is
The rest got cut off. S is TOO SMALL to have a 183-digit factor.
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