Factoring humongous Cunningham numbers - Page 165

jyb · 2020-05-27, 17:39

If anybody knows who found a p56 factor from 11-8,283 on May 5, apparently by ECM, please let me know.

charybdis · 2020-07-18, 18:19

What's going on with 7-3_361? It is still unfactored in factordb, and it hasn't been removed from the ECM server, but it doesn't appear on Tom Womack's reservation page. Was a factor reported there and nowhere else?

EdH · 2020-07-18, 22:33

Quote:

Originally Posted by charybdis

What's going on with 7-3_361? It is still unfactored in factordb, and it hasn't been removed from the ECM server, but it doesn't appear on Tom Womack's reservation page. Was a factor reported there and nowhere else?

There's a possibility that a factor was found with a composite cofactor and the cofactor was what was reported on the reservations page. I have had this happen.

swellman · 2020-07-19, 02:56

Quote:

Originally Posted by charybdis

What's going on with 7-3_361? It is still unfactored in factordb, and it hasn't been removed from the ECM server, but it doesn't appear on Tom Womack's reservation page. Was a factor reported there and nowhere else?

As far as I can tell, it was inadvertently removed from the reservation page and has never been restored. ECMnet is still working on the remaining C213 composite but only 7399 curves have been completed in the march towards a full t55 (i.e. 17884 curves @B1=110M on ECMnet). With a SNFS difficulty of 305, we need a(nother) lucky ECM hit!

charybdis · 2020-07-19, 13:56

Quote:

Originally Posted by swellman

As far as I can tell, it was inadvertently removed from the reservation page and has never been restored. ECMnet is still working on the remaining C213 composite but only 7399 curves have been completed in the march towards a full t55 (i.e. 17884 curves @B1=110M on ECMnet). With a SNFS difficulty of 305, we need a(nother) lucky ECM hit!

Aha thanks, should have checked further back in the thread. Has anyone informed Tom about this?

swellman · 2020-07-19, 14:34

I sent him a PM.

jyb · 2020-07-27, 02:22

The tables and ECMnet server have been updated to reflect all factors reported to me through the end of July 26 (GMT). There were 44 new factors found since the last update, of which 35 completed the factorization of their respective numbers. A factor of 11-8,283 was found anonymously; it appears below and in the update file with a discoverer of "Unknown". If anybody wishes to claim it, please let me know and you will be rewarded with all of the fame and fortune which such a discovery deserves.

There are now 900 composites remaining in the tables. The minimum digit count is now 179. With the usual polynomial degrees, SNFS difficulties range from 229 to 310, with all difficulties below 255 requiring a quartic polynomial. However, there is one composite which has an SNFS difficulty of 211 with an octic polynomial.

Here are the factors found since the last update:

Code:

12-11	759L	C177	8451455608858758494957315746588263289024944020415999960979482611554430048347642927.	P95			R Balfour		GNFS	2020-04-23
4+3	1347L	C238	18624291034971849251576454644774742818438952470539.	P189							J Becker		ECM	2020-04-24
8+5	710L	C255	25051177713319166401182155863001376685969498304893541.	C202							J Becker		ECM	2020-04-26
5+2	415	C177	438665378697522193365057469582331205965230446062763731911425993601951844291.	P103				R Balfour		GNFS	2020-04-27
12+11	257	C175	16960566022460643783228831321129508319345946082698358762541066045057.	P108					NFS@Home & S Wellman	GNFS	2020-04-28
9+8	626L	C293	528753116084755370498883106823610392871940162352989.	C242							J Becker		ECM	2020-05-03
4+3	1329M	C226	3833551108907650658505933916802309781485613870397.	P177							J Becker		ECM	2020-05-04
7-5	313	C178	269407097806950669149152219293401194920867800908211986142978450945831.	P109					R Balfour		GNFS	2020-05-04
5+3	1635L	C304	10648931168243962198791730892365788674854192807861.	P255							J Becker		ECM	2020-05-04
11-8	283	C240	54848727178062205909394461754596568992678948734608679439.	C184						Unknown			ECM	2020-05-05
12-7	945L	C178	1653799462409461818395727266432933603089015344075936334829143243080213865721898704701.	P93			E Hall			GNFS	2020-05-05
3+2	1842L	C233	79035920733994071075361205057719643436633311562514753.	P180							J Becker		ECM	2020-05-06
5+3	1215L	C223	6127974776513009158453033357708902494731083292859712481.	C168						Yoyo@home		ECM	2020-05-08
10+7	770L	C178	7073648670961932693667863719387939285051426287965759752238188083325621.	P108					R Balfour		GNFS	2020-05-09
8+3	302	C178	133311748530091743524560795336138237369108539697558563776017.	P119						R Balfour		GNFS	2020-05-15
5+3	1215L	C168	371665478433375483365507720510689568627189737113624731816387950552273231.	P96				R Balfour		GNFS	2020-05-16
3+2	1434L	C197	4546425166820486650780956694376937664856667163447201.	P146							Yoyo@home		ECM	2020-05-17
6+5	1290M	C257	113772073411890057775349148317422444096953153914202173488981.	P198						J Becker		ECM	2020-05-24
9+8	626L	C242	56386851282285329715435013081476766866289922483759135418161.	P183						J Becker		ECM	2020-05-29
5+3	1515M	C185	1145160499027770957049592541821231411252039070546091.	P134							J Becker		ECM	2020-06-01
4+3	1467M	C240	431957395880421967783872911630144562791628918790603117.	C186							R Balfour		ECM	2020-06-02
11+9	605M	C176	17309593935582209385143176176934906172519005742547921965234995421.	P112					NFS@Home & S Wellman	GNFS	2020-06-02
11-5	281	C176	904196169909093174550641943796051270601676264089481347142064950991357526967384477.	P95			NFS@Home & J Becker	GNFS	2020-06-03
9-2	295	C190	11951543426207449891620332909097282080692114803598920363090166685881.	P123					NFS@Home & R Dickerson	SNFS	2020-06-11
3+2	1842M	C238	1881941120468249708169539576246651193369513480043229827729929343069.	P172					R Balfour		ECM	2020-06-11
3+2	1422M	C218	83630060150279663947389753163959796956650566366042360084978177561.	P153					NFS@Home & R Dickerson	SNFS	2020-06-12
7+5	335	C184	425466479691783746114628980421043893875824760127740231089890102220497151.	P112				NFS@Home & J Becker	SNFS	2020-06-15
7+4	763M	C273	30143478415831559092449402609124657684579115087254157.	P221							J Becker		ECM	2020-06-15
8+7	310	C204	977265025563775563980229684688093484719263716876423624226721.	P144						NFS@Home & S Wellman	SNFS	2020-06-20
11+7	289	C239	805392889782945991074264789794130598559495177691453697.	P185							R Balfour		ECM	2020-06-21
4+3	1527L	C306	723522541625013357342147531518531968024054475727052327.	C252							S Wellman		ECM	2020-06-22
9+8	638M	C230	10922277035314040930762566688040232928970035455315985333139293.	C169						R Balfour		ECM	2020-06-25
3+2	613	C233	2442241384972785488087476599266777934279356654862568917769.	P176						J Becker		ECM	2020-06-26
9+8	638M	C169	6140347413441497506720969703057532359060433813219323469747168621172282661.	P97				R Balfour		GNFS	2020-06-29
3+2	1422L	C206	48540317716429836775702938668864881280828332435361561179963893824107234882969727533.	P123			NFS@Home & C Pinho	SNFS	2020-07-07
4-3	475	C195	942038437133362671627826181166337982140139760103761713051.	P138						NFS@Home & S Wellman	SNFS	2020-07-07
10+9	610L	C232	1242333559446076673023012296756916769822431138873834930275901.	C172						J Becker		ECM	2020-07-11
10+9	610L	C172	47876749787640439357126501820124811284504605168141.	C122							R Balfour		GNFS	2020-07-15
10+9	610L	C122	2086011135973449635483630725009450270868137672437486517089221.	P62						R Balfour		GNFS	2020-07-15
9+8	590M	C185	1012876283502116042584524486810616239051280235871445205816302602024260153243125921021.	P101			NFS@Home & J Becker	SNFS	2020-07-18
4+3	1485L	C181	3039683959425171664966674859289365376303218197726625801.	P127						J Becker		ECM	2020-07-19
5+3	1215M	C193	20619125064130241087652505809857595651770821621200591924712321.	P132						NFS@Home & C Pinho	SNFS	2020-07-20
7+3	304	C178	5818143916182057309683139546152516532774060186340026495952487531834236260064672686209.	P93			NFS@Home & S Wellman	GNFS	2020-07-22
5-4	815L	C196	60739707042844466179541796194412486421848074358866482480174347363807352866798442170755299171.	P104		NFS@Home & S Wellman	SNFS	2020-07-26

jyb · 2020-12-09, 05:57

Once again, everything has been updated to reflect all factors reported to me through the end of December 8 (GMT). There were 57 new factors found since the last update, of which 50 completed the factorization of their respective numbers.

There are now 850 composites remaining in the tables. The minimum digit count is now 180, with one such composite currently unreserved (it may be easier by SNFS than GNFS). With the usual polynomial degrees, SNFS difficulties range from 232 to 310, with all difficulties below 255 requiring a quartic polynomial. There is one composite which has an SNFS difficulty of 226 with an octic polynomial.

Here are the factors found since the last update:

Code:

12-7	819L	C183	63679918074845200457251757329985681533274978434088912447993793100278487.	P112				NFS@Home & J Becker	SNFS	2020-07-27
5-4	835L	C179	12619875490369093335356775567635732306476333267232436651047915618216082338389464702995621.	P91		R Balfour		GNFS	2020-08-02
4+3	475	C202	506032995406068462232861183129512506423127070479405590186142092526291906018531372038824549348731451.	P103	NFS@Home & J Becker	SNFS	2020-08-03
9+2	614M	C293	1678244368765933698107575862790096510755011793521192073.	C239						Yoyo@home		ECM	2020-08-08
9+8	586L	C179	521005436533667334642990339766532464501627901833462750307712687543279036692516305193.	P96			R Balfour		GNFS	2020-08-08
6+5	1290L	C232	17640764379486005557935172179790445162733229199560801.	P180							J Becker		ECM	2020-08-10
7-2	313	C180	81254131154771066751556487801525789283022802566200772732418082099945884873849.	P103				R Balfour		GNFS	2020-08-13
8-7	311	C277	5314057157377032758863869566122097423681511895219387667.	P222						J Becker		ECM	2020-08-15
12+7	272	C180	38371440502563236186604147781238619222925214249105559750275974321522240919555680150557281.	P91		R Balfour		GNFS	2020-08-19
7+6	340	C205	19031680868498272284731172984102702769724256779313011171523839601389687907351464964521.	P119			NFS@Home & J Becker	SNFS	2020-08-20
12-7	819M	C188	161660383184039289810887443459053824632444713855315416606277184732909071140440241480616239467.	P96		NFS@Home & S Wellman	SNFS	2020-08-21
8+3	283	C184	16611186508636708372061518009440469654003953659508949067779797947.	P120					NFS@Home & M Vang	SNFS	2020-08-28
7+4	707L	C253	1726181340046329480016109671482020294033494699791243031855229704788098216003017069884595330561541.	P157	NFS@Home & S Wellman	SNFS	2020-08-29
8+5	314	C182	20208825584095730991962953420367456372385446555702870761.	P127						R Balfour		GNFS	2020-08-29
7+5	332	C278	3197593226567524579830470570581187369737392912479387195161.	P220						J Becker		ECM	2020-09-02
5+3	410	C213	30352594418462909734662880580659648066477065201395350377415441.	C151						NFS@Home & S Wellman	SNFS	2020-09-05
5+3	410	C151	113185632973382962509787548559204569234601229367339789989076697661.	P86					NFS@Home & S Wellman	SNFS	2020-09-05
5+2	1070M	C296	11691812304428162034345642186038162009012788415920834109067481.	P235						Yoyo@home		ECM	2020-09-07
10+7	302	C183	12709581398099528695930639710267412717117433728451188264091224457426783532083563501.	P101			R Balfour		GNFS	2020-09-07
12+5	795M	C192	47730115056948316442832129138944871628372532585609978885781312650080888124571046007612818081.	P101		NFS@Home & M Vang	SNFS	2020-09-15
11+9	539M	C215	469894765546570531499635429464037590208235071786259150588735209.	C152					NFS@Home & J Becker	SNFS	2020-09-15
11+9	539M	C152	703677101652371300856775781012547718297696195174006325065439479327.	P86					NFS@Home & J Becker	SNFS	2020-09-15
11+8	287	C240	130091682754289606420997877917754023568291319545556392747387974055144379886101799761783967740891.	P145	NFS@Home & J McClintock	SNFS	2020-09-16
11+9	272	C236	30682057513755904521000153057008355891586378372633981697.	P180						R Propper		ECM	2020-09-19
5-3	401	C271	872571438444547379078309462482781304418891949228200321.	P217							R Propper		ECM	2020-09-19
5+4	368	C180	1491554589693399130177226629083882148805780945574429485625819504523180801.	P108				R Propper		GNFS	2020-09-19
4+3	466	C184	29308415948418948025489498450711137087492897209305599721.	P128						R Balfour		GNFS	2020-09-20
7-3	1071L	C231	32259627287265089267855311069399608930082347651491058747619.	P173						NFS@Home & C Pinho	SNFS	2020-09-20
7+6	328	C240	434572645155561217873472328163084062849954466629714241.	C186							R Propper		ECM	2020-09-21
4+3	1467M	C186	53547739097404257269613756910163391128699406878304513109.	P130						R Propper		ECM	2020-09-21
3-2	605	C189	238334164069340332169737677005213007518601028607576390714036146884389147022529791451.	P105			NFS@Home & S Wellman	SNFS	2020-09-25
8+7	320	C222	718444299676339976046358538151903759225888478618505665128659138778217042280231477753550658872045234531411841.	P114	NFS@Home & C Pinho	SNFS	2020-09-26
10-3	301	C179	128084378089378914585133764224324012987239437147051688430186359531.	P114					NFS@Home & S Wellman	SNFS	2020-09-30
4+3	1461L	C261	103952437629676548491190499977971053176403160086161650623.	P205						J Becker		ECM	2020-10-01
8+3	870M	C192	1113395195181441232897635316868625150150474892498911434248545375214552261.	P120				NFS@Home & D Delgado	SNFS	2020-10-03
4-3	443	C183	237095928832273884620719905077575223536214414407957207692132422006147.	P115					R Balfour		GNFS	2020-10-03
7+3	344	C182	940178235247332289120926771690327661238990851387961713089990970947156178623557951982496321.	P92		NFS@Home & C Pinho	GNFS	2020-10-08
3+2	1686L	C179	7733961215190182800111443172129093940119104012591035433912855778239413875374875085001.	P94			NFS@Home & S Wellman	GNFS	2020-10-13
3+2	1446M	C189	2525863113019784866485159026033476058673368058897447200161.	C131						NFS@Home & C Pinho	SNFS	2020-10-14
3+2	1446M	C131	4092548937881641137005120020566114770332136530455541914336089917.	P68					NFS@Home & C Pinho	SNFS	2020-10-14
3+2	1770L	C184	142619007046258448105972293381467496947975175023493578902832121842910107683161.	P107				R Balfour		GNFS	2020-10-16
3+2	1446L	C187	8216950503934210834225885598887128532598250771152129072532752177866627797484873.	P109			NFS@Home & R Dickerson	SNFS	2020-10-26
11+8	263	C184	5097782188596955772497836508749456765536703440917818469704842939403053303553424697477.	P99			R Balfour		GNFS	2020-10-27
5-2	415	C212	1881521115835592636704229207284490834976445908718569894604726391.	P149					NFS@Home & J Becker	SNFS	2020-10-27
9+2	646M	C235	121182958696027507233052264449832303064712766854569633.	C182							J Becker		ECM	2020-10-28
9+8	305	C186	19652183625441417364455036701749227215746653115421156493850613911841785292330548132931.	P100			NFS@Home & R Dickerson	SNFS	2020-11-01
3+2	1578M	C198	314389616949051947856531832346566233331973715733290450537058841292768618820674371082757.	P112		NFS@Home & J Becker	SNFS	2020-11-10
7+4	302	C224	2557396306858622536833198950269232920231851223586758960283894639279364999101.	P149				NFS@Home & J Becker	SNFS	2020-11-10
7+3	317	C184	28204976801726893770940946548136769733219938920169790226922594128506831.	P113				R Balfour		GNFS	2020-11-11
11+6	251	C180	3957405750386562094847466159178975554292764438278704429144425199966447655485189.	P102			NFS@Home & J Becker	GNFS	2020-11-24
9-2	277	C181	2591985522785094027728418963176410108368253613313707193012892374986507260879.	P106				NFS@Home & R Dickerson	GNFS	2020-11-24
7+6	352	C199	88193898208640357904516928196833112372685168071347452417793.	P140						J Becker		ECM	2020-11-28
7+4	344	C184	22254644140889631672211468778719718932739271230514716517775169.	P123						R Balfour		GNFS	2020-11-29
7+5	302	C202	2662904328553964805743785730951982862253245773503902750041322049968738541001702673.	P121			NFS@Home & J Becker	SNFS	2020-12-04
9+2	646M	C182	3186379591602880389032186942173786149037918331087026157.	C128						R Balfour		GNFS	2020-12-07
9+2	646M	C128	436091713557115168388752974629117370750691279476078650276049841.	P65					R Balfour		GNFS	2020-12-07
11+2	292	C262	511399645441902897222621352772341622984550677052429649873.	P206						Yoyo@home		ECM	2020-12-08

charybdis · 2021-02-07, 14:10

Quote:

Originally Posted by jyb

With the usual polynomial degrees, SNFS difficulties range from 232 to 310, with all difficulties below 255 requiring a quartic polynomial.

Aren't there three easy sextics in the 230s, or am I mistaken?

Code:

8+3_774L
x^6-144*x^4-288*x^3+5184*x^2+20736*x+13824
96479729228174488169059713024*x-680564733841876927255006182258073500539 = 24^21*x-(8^43+3^43)

8+3_774M
x^6-144*x^4+288*x^3+5184*x^2-20736*x+13824
96479729228174488169059713024*x-680564733841876927255006182258073500539

3+2_1494L
x^6-36*x^4-36*x^3+324*x^2+648*x+216
80204967233062404407033075859456*x-3990838394187349600940803592605746684635 = 6^41*x-(3^83+2^83)

jyb · 2021-02-08, 07:12

Quote:

Originally Posted by charybdis

Aren't there three easy sextics in the 230s, or am I mistaken?

Code:

8+3_774L
x^6-144*x^4-288*x^3+5184*x^2+20736*x+13824
96479729228174488169059713024*x-680564733841876927255006182258073500539 = 24^21*x-(8^43+3^43)

8+3_774M
x^6-144*x^4+288*x^3+5184*x^2-20736*x+13824
96479729228174488169059713024*x-680564733841876927255006182258073500539

3+2_1494L
x^6-36*x^4-36*x^3+324*x^2+648*x+216
80204967233062404407033075859456*x-3990838394187349600940803592605746684635 = 6^41*x-(3^83+2^83)

Oh my goodness, yes! This is very useful line of attack, which I've overlooked. However, I would adjust the polynomials:

Code:

For 8+3,774L:
27x^6-108x^4-36x^3+108x^2+72x+8
6*24^21*x-(8^43+3^43)

And similarly for the other numbers. That will probably sieve much better.

charybdis · 2021-02-08, 12:22

Quote:

Originally Posted by jyb

Oh my goodness, yes! This is very useful line of attack, which I've overlooked. However, I would adjust the polynomials:

Code:

For 8+3,774L:
27x^6-108x^4-36x^3+108x^2+72x+8
6*24^21*x-(8^43+3^43)

And similarly for the other numbers. That will probably sieve much better.

Ah yes, of course. In fact it's the same algebraic poly for 3+2_1494L.

There's also 3+2_1566L at difficulty 250.

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New phi for homogeneous Cunningham numbers	wpolly	Factoring	26	2016-07-29 04:34
Mathematics of Cunningham Numbers (3rd ed., 2002, A.M.S.)	Xyzzy	Cunningham Tables	42	2014-04-02 18:31
Don't know how to work on Cunningham numbers.	jasong	GMP-ECM	6	2006-06-30 08:51
Doing Cunningham numbers but messed up.	jasong	Factoring	1	2006-04-03 17:18
Need help factoring Cunningham numbers	jasong	Factoring	27	2006-03-21 02:47

2020-05-27, 17:39	#1805
jyb Aug 2005 Seattle, WA 1,697 Posts	If anybody knows who found a p56 factor from 11-8,283 on May 5, apparently by ECM, please let me know.

2020-07-18, 18:19	#1806
charybdis Apr 2020 13·17 Posts	What's going on with 7-3_361? It is still unfactored in factordb, and it hasn't been removed from the ECM server, but it doesn't appear on Tom Womack's reservation page. Was a factor reported there and nowhere else?

2020-07-19, 14:34	#1810
swellman Jun 2012 5²·7·17 Posts	I sent him a PM.