
Re: Factorization theory wrong? Or algorithmic error?
Posted:
Apr 7, 2012 11:50 AM


On Apr 7, 10:46 am, hagman <goo...@voneitzen.de> wrote: > Am Freitag, 6. April 2012 22:46:50 UTC+2 schrieb William Hughes: > > > > > > > > > > > On Apr 5, 7:19 pm, 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 check > > > this over for me. This post is digitally signed in case I need to prove > > > 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 bits), > > > which I'll call A: > > > > 3634908448770161716619462884730373820150226880205007030541419827683585 > > > 7931761274740311086713549497603607279611408949613526779622187756741117 > > > 9048935484829402996681944342388178421558785023331981868685440034884277 > > > 9396792124395994336764804183754455993340622344242614470170379064513230 > > > 0552661368276733695867117608484513671228954258971153834928109857741 > > > > I won't tell you how I generated A, because if there's no flaw in what > > > I've done (I intend to make real money out of this, if it is possible), > > > 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. Here is > > > its "smaller prime factor"** ("B"), which is 156 decimal digits long: > > > > 3246726736489147307461784686107468324672673648914730746178468610746834 > > > 6821883878114173728372983219193183717113173468218838781141737283729832 > > > 1919318371711317 > > > > ** that is, smaller as identified by all the factorization algorithms > > > that I have encountered. If you are not professional mathematicians > > > and do not have access to factorization tools, I recommend you use: > > > http://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 now > > > in question. > > > > Divide A by B to get the 192 decimal digit number C. Since 192/2 < 156, > > > it follows that if B was the smaller prime factor of A, then C must be > > > prime. > > > > {Lemma: Assume C was nonprime. Then it must have at least one prime > > > factor that is less than 97 (= 192/2 + 1) decimal digits long. This > > > 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 (= 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. Right? > > > > Indeed, all the primality checkers I have tested show that C is prime. > > > Including the java one at: > > > http://www.alpertron.com.ar/ECM.HTM > > > > Well, I can tell you that I have factorized C... and handchecked it, as > > > at first I could not believe the fluke finding. > > > > C's smaller factor is almost 2^300, so C's decomposition is nontrivial. > > > In the time window before you can bruteforce 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 have > > > heard the more competent fellow mathematicians here confirm C's alleged > > > primality, according to the algorithms we all becomed conditioned to > > > believing are true. > > > > I do hope I have not overlooked anything. Your assistance is appreciated. > > > > Thank you, > > > > "barker" (associate of the late falsified nondullrich Dr Pertti Lounesto) > > > > Footnote: For the lazy, here is the 192 decimal digit number C: > > > 1119560943616947347400615409002575284369887465143010602130506309766179 > > > 0753006072671322304202892348769562317880539561982179986874385643005873 > > > 1438452818437316840959014392166803390411010978334873 > > > which tested algorithms suggest is prime, but which I have factorized. > > > > BEGIN PGP SIGNATURE > > > > VQEcBAEBCgAGBQJOe7YRAAoJEAjjY4weks8oA7QIAK3ELb/+NKP1vLPT8f7HQTaf > > > YmqnG0TdO44RMJdbqpxsp6DoMx5JkMgluha8y6LIV3rBHHDKGQx3YwKzVTT5r81 > > > DOOQr3LQdLgmoemhdot2Dse16XQ7OoWzvJwqvvYYBZ0S/J2SsrAFUAoQAe35/4 > > > 9NkVg3JSzV+AFPQyv5hpS780v0cObSPl7yz32MypgvZkYZupC3xP/3Pdl8Fg205 > > > NkiDEaDlJcIKM8ARJJtndd7cfNBKZ3Bh1OEQ1NwPFEMZ6uAR3S/DLdF0dY1MMxr > > > RRcluph+MLmTRZngA8NG9qRCBQT2IgTZNatjnZv2pcwgC0MddUnyS07bNypHg8= > > > =87KU > > > 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 > > >  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. :) > > hagman
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.
 William Hughes

