Odd perfect related road blocks II - Page 48

warut · 2011-02-16, 07:26

C141 from Pascal's t1000.txt, by SNFS:

Code:

Φ₃(Φ₅(93815349051618588433552823))
= σ(77463228772770524004787917041260332031647497475185281171729201632503641470605202939306864648997862198161^2)
P38: 45931822205577863456160354972638439523
P44: 79436285734661950417729942820545398222610243
P59: 48486085092528803867556785299299387550402292051061506681527

warut · 2011-02-16, 13:36

William pointed out to me that for small a, Φ₃(Φ₃(n)/a) could be factored by SNFS in a way similar to Φ₃(Φ₃(n)) I mentioned before. He also gave me a list of numbers of this form in Pascal's tXXX.txt files. The first number I tried was a C122 from t600.txt:

Code:

Φ₃(Φ₃(31784737314210171707627237048461)/3)
= σ(336756508711114813210525750593533959832184338890841231366505661^2)
P52: 1685695688027899058359288651656545073520833499999297
P71: 13834024843642871505122620832960037296938067210331338197944632114092153

I'll factor larger numbers of this form later.

yoyo · 2011-03-03, 05:16

Did you saw this odd perfect factor: http://www.rechenkraft.net/yoyo/y_factors_ecm.php
yoyo

2 posts up, but I forgot to mention the yoyo connection - now fixed

wblipp · 2011-03-08, 05:19

From t600.txt

Code:

1036950426156829^11-1
P42: 1664337575670997812179266202740798055190637
P90: 626427088344571646338492998497791642682081665056615163958936593891710567300276469667757871

17 additional p^11-1 composites were just added to the composites page. These have completed ECM to t40. They range in size from SNFS 156 to 178. Degree Halving transforms these into x^5 + x^4 - 4x^3 - 3x^2 + 3x + 1 with x=p+1/p mod n

akruppa · 2011-03-10, 12:09

Did 5000 curves at B1=260M on 7,379- c320. No factor.

warut · 2011-03-12, 21:19

I think a Brent composite in William's sense is a composite cofactor of a number of the form: a^n +/- 1 with a, n < 10000.

wblipp · 2011-03-12, 23:49

Quote:

Originally Posted by warut

I think a Brent composite in William's sense is a composite cofactor of a number of the form: a^n +/- 1 with a, n < 10000.

Yes - these are the numbers for which Richard Brent collects and publishes factors. The recently added p^11-1 numbers have p too large for Richard Brent's publications; these numbers were pulled from Pascal Ochem's txxx.txt files of "first composites." First composites are desirable factorizations because they will always appear in the factor chains of the proofs, regardless of what other numbers are later factored. Other factorizations have a less certain long term utility.

wblipp · 2011-03-29, 03:31

The first was found by b-squared, the rest by Rich Dickerson. All were found doing ECM Prep work. b-squared is preparing large numbers that will eventually be factored by RSALS. Rich is preparing small numbers from Pascal's First Composites list that will soon show up on the Odd Perfect Composites page.

Code:

193^109-1
P49: 6219640968899872261766470666042342725279758337133

591844849257724269807300757620403665626236644845899786773573341602936225453^3-1
P38: 11094598615732439322349585157717573209
P65: 39587373439086136781585222889065566763380454233257382444861344133

4445920625921894859485886279431937154995365646144138427860902102965778617367847477907^3-1
P40: 9177504688899582795203360640936976465063
P63: 257000855858445375312045491671264776756953814743862450809873707

17039118605046803898613358569^7-1
P44: 30272272459128947250893376580097235948432241
P60: 456483850720981724823444379604314281049217115442740833148941

1169723339615428834795022674668346507972637072026989132703299973^3-1
P40: 1322232993342573900585508365218054774533
P66: 920905298436616394253055588442686820987267440408571357597366147527
 
10195753178238318213316021^7-1
P39: 969788281583095795641852052899977555611
P60: 13308217637211621155312651575922455975967706158852130666564998179991

682737496472109341658594748416032562780892160430974558396413220364357876150169^3-1
P37: 1226781262202102167563367062143371579
P72: 975060999284654305871688637001362238778610782755702588207377705424658991

69433502216552087300217330881104501292582167869851658609133^3-1
P47: 23231215585033517251941059490735317535356319283
P60: 597093957946325459607131163817678628648438810661741808558561

9228242750041962470319626992325126540970611860639873168266215645119^3-1
P24: 588899757585967787140033
P96: 337033580300397244899997585068673029865329234985496584131038392680498962778525327718618201478983

science_man_88 · 2011-03-29, 22:10

Quote:

Originally Posted by a chat I had on a chess site

corruptedRook: I proved that odd-perfect numbers don't exist

www.oddperfectnumbers.com

http://www.chess.com/members/view/corruptedRook. they say they have a degree in math.

wblipp · 2011-03-30, 07:07

A Brent composite from t600.txt factored by b-squared during ECM prep for RSALS

Code:

127^113-1
P51: 140181581203042574337271028133337517940041111878369
P103: 1807733474707303116072862670848657823684575250443103225022450118900897394639261687397621273863617965643

em99010pepe · 2011-03-31, 11:13

Code:

P57a^5-1
Factor found!  2 / (probable) 3443450951966387388568495383344024027071391  B1: 11000000 sigma: 1969753819 (found in step 2)
Co-factor:  2 / (Probable) 10170031742457729877293348308499200113607512723761224242961

P57a = 627385547625315727741052544625222814860038107817342738067

2011-02-16, 13:36	#519
warut Dec 2009 89 Posts	William pointed out to me that for small a, Φ₃(Φ₃(n)/a) could be factored by SNFS in a way similar to Φ₃(Φ₃(n)) I mentioned before. He also gave me a list of numbers of this form in Pascal's tXXX.txt files. The first number I tried was a C122 from t600.txt: Code: Φ₃(Φ₃(31784737314210171707627237048461)/3) = σ(336756508711114813210525750593533959832184338890841231366505661^2) P52: 1685695688027899058359288651656545073520833499999297 P71: 13834024843642871505122620832960037296938067210331338197944632114092153 I'll factor larger numbers of this form later.

2011-03-03, 05:16	#520
yoyo Oct 2006 Berlin, Germany 619 Posts	Did you saw this odd perfect factor: http://www.rechenkraft.net/yoyo/y_factors_ecm.php yoyo 2 posts up, but I forgot to mention the yoyo connection - now fixed Last fiddled with by wblipp on 2011-03-03 at 14:32

2011-03-08, 05:19	#521
wblipp "William" May 2003 New Haven 2366₁₀ Posts	From t600.txt Code: 1036950426156829^11-1 P42: 1664337575670997812179266202740798055190637 P90: 626427088344571646338492998497791642682081665056615163958936593891710567300276469667757871 17 additional p^11-1 composites were just added to the composites page. These have completed ECM to t40. They range in size from SNFS 156 to 178. Degree Halving transforms these into x^5 + x^4 - 4x^3 - 3x^2 + 3x + 1 with x=p+1/p mod n

2011-03-30, 07:07	#527
wblipp "William" May 2003 New Haven 2·7·13² Posts	A Brent composite from t600.txt factored by b-squared during ECM prep for RSALS Code: 127^113-1 P51: 140181581203042574337271028133337517940041111878369 P103: 1807733474707303116072862670848657823684575250443103225022450118900897394639261687397621273863617965643

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2011-03-10, 12:09	#522
akruppa "Nancy" Aug 2002 Alexandria 9A3₁₆ Posts	Did 5000 curves at B1=260M on 7,379- c320. No factor.

2011-03-12, 21:19	#523
warut Dec 2009 89 Posts	I think a Brent composite in William's sense is a composite cofactor of a number of the form: a^n +/- 1 with a, n < 10000.