Factoring humongous Cunningham numbers - Page 170

VBCurtis · 2022-05-24, 15:33

I am mostly an observer to this project, but any changes that make the underlying math easier to understand / do on one's own seems a clear win for the project.

jyb · 2022-06-28, 17:29

Hi all,

The tables have been updated with all factors known to me by the end of June 27 (GMT). Additionally, they are now using the new format, as described a couple of posts above. Please let me know if you see any errors or omissions. There were 29 new factors found since the last update, of which 25 completed the factorization of their respective numbers. There are now 600 composites remaining in the tables. Digit counts range from 190 to 307. SNFS difficulties start at 242, with non-quartic polynomials starting at 264. 12 composites are currently reserved.

Most factors were found with NFS this time around, but ECM still has a healthy showing, with about one-third of the factors. Again, anyone using ECM should use B1 values of at least 260M.

Here are the factors found since the last update, showing appropriate credit:

Code:

8+5	850L	C224	329599299593581388834972260507612812028261767119965014859405901.	P161					R Propper		ECM	2022-05-09
9+8	299	C209	355702705244681331790601351256046337594016030549655709587598181519460919886241583794633397914667.	P113	R Propper		SNFS	2022-05-09
6-5	337	C205	50104787644609136623580894908972162419827861965844030960100487021747476809044299691.	P122			R Propper		SNFS	2022-05-10
4+3	1509L	C296	43762356175308046660646944020630193575737725449849393360671569.	C234						R Propper		ECM	2022-05-11
9+5	299	C253	13950848658574601856089264408716681144886348572842676627101170829130658485147598822557941952876211032632367.	P146	R Propper	SNFS	2022-05-11
9+8	614L	C289	4792112953435246180033897337789336744209777298618769882524823617.	C225					R Propper		ECM	2022-05-11
10+7	263	C226	3414099019906449885352961418094022234341079521756606698494375778389494075712154143323573.	P139		R Propper		SNFS	2022-05-12
3+2	589	C175	555789143030530142573673993707086124030978266160752243337744518019.	P109					NFS@Home & S Wellman	GNFS	2022-05-12
12+11	244	C236	6275789516968650441725552092506673781371360009522372287601342838186556465483877286820313124455243289.	P137	R Propper		SNFS	2022-05-13
4-3	487	C169	50946330712300824601152529187399316033302540918654677895622017872501.	P101					NFS@Home & S Wellman	GNFS	2022-05-13
7+5	875M	C194	1321750131471604665369371959385888919188109748858608197647353037056986858245501.	P116			NFS@Home & G Childers	GNFS	2022-05-14
5+3	389	C226	64682128365923161295715632462297188619519937924246325372943.	P167						R Propper		ECM	2022-05-14
4+3	1419M	C193	12355755579835943879787506328209710648639252011238264225398892279371238909.	P120				NFS@Home & G Childers	GNFS	2022-05-22
11+4	263	C225	368002869734693411807466759650071230238476568476694519009.	P168						R Propper		ECM	2022-06-04
4+3	1317M	C246	9660173080563518560302860800664949356082211662196978544155518739.	P182					R Propper		ECM	2022-06-05
10+7	308	C190	121779641446166343541376569451177980699081219317964953509785686074880760278524300170241659169.	P97		NFS@Home & S Wellman	SNFS	2022-06-06
11-2	281	C217	211104441916673844232588483487792243499111924423441832164727.	P158						R Propper		ECM	2022-06-08
9+7	322	C206	12164008544028330784930478789748320356220491390622581952822162078706057758651478388959817.	P118		R Propper		SNFS	2022-06-09
11+10	257	C267	8137321954005555790464111108691562365883638462410731020222298093725196561480812571100235927334141.	P170	R Propper		SNFS	2022-06-10
8+7	292	C198	106211316554164128394197503246941468295190747630652675430425897.	P136					NFS@Home & S Wellman	SNFS	2022-06-11
11+5	257	C244	16675002869710078308901966284982727724213817268281490922078644896339522332882338983094955450066041535150812024108950949.	P126	R Propper	SNFS	2022-06-12
11-8	257	C248	13073786367991597717665146109989433532084488919908131911899247659804122826998019182082385335851620187869158059300911.	P133	R Propper	SNFS	2022-06-14
10+3	262	C195	32772340053626272520481875966482174904318218019930167539938033832071623268957.	P119				NFS@Home & S Wellman	SNFS	2022-06-14
11+9	257	C206	12993237712575408728763551090300891005260702526261562291548203285229.	P139					R Propper		SNFS	2022-06-17
9-8	277	C215	23442328584325430176134126544990245223815726751936317768097.	P157						Yoyo@home		ECM	2022-06-17
7+4	338	C224	3257692639540513774976804174583784882036362654882898879561.	C167						NFS@Home & S Wellman	SNFS	2022-06-20
7+4	338	C167	108434590569397715268251596421252099121636176190588677930418757884629.	P99					NFS@Home & S Wellman	SNFS	2022-06-20
11-5	293	C268	30225541504489475185023309033081142359044642637183914163359411789.	C203					R Propper		ECM	2022-06-20
11-3	957M	C291	367685098098853274179810266890594407772505282306619624339.	P234						R Propper		ECM	2022-06-27

R.D. Silverman · 2022-09-04, 22:35

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

chalsall · 2022-09-04, 23:08

Quote:

Originally Posted by R.D. Silverman

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

We care why?

Seriously... What are you doing next? And how might those interested help?

Hint... Some might care...

xilman · 2022-09-05, 08:35

Quote:

Originally Posted by R.D. Silverman

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

Well done.

LaurV · 2022-09-05, 09:20

Quote:

Originally Posted by R.D. Silverman

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

Wow, few of those are ~195-200 digits. How long did it take?

Dr Sardonicus · 2022-09-06, 12:56

Quote:

Originally Posted by R.D. Silverman

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

I note that your most recent contribution to the UPDATE file at the Homogeneous Cunningham Numbers site was in December 2019, completing the factorization of 3-2,321.

I infer from this that your recent efforts with n < 150 were for a > 12.

So - where may one find tables of HCN factors with 12 < a ≤ 20?

R.D. Silverman · 2022-09-06, 13:48

Quote:

Originally Posted by Dr Sardonicus

I note that your most recent contribution to the UPDATE file at the Homogeneous Cunningham Numbers site was in December 2019, completing the factorization of 3-2,321.

I infer from this that your recent efforts with n < 150 were for a > 12.

So - where may one find tables of HCN factors with 12 < a ≤ 20?

The factor database. http://www.factordb.com/

jyb · 2022-09-06, 22:53

Quote:

Originally Posted by R.D. Silverman

I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

Nice job, Bob. I trust that you were able to make use of the Aurifeuillian factorizations for these numbers when a > 12. The polynomials involved can be quite hideous, but they can save a lot of work.

Quote:

Originally Posted by Dr Sardonicus

I note that your most recent contribution to the UPDATE file at the Homogeneous Cunningham Numbers site was in December 2019, completing the factorization of 3-2,321.

I infer from this that your recent efforts with n < 150 were for a > 12.

Indeed, the last real HCN (*) composite with an exponent less than 150 was factored over 13 years ago.

* I note that numbers of this form with a >= 13 are not technically Homogeneous Cunningham Numbers, any more than a number of the form 13^n - 1 would be considered a Cunningham number. However, I think we all know what Bob meant here.

jyb · 2022-09-28, 06:48

The tables have been updated with all factors known to me by the end of September 27 (GMT). Please let me know if you see any errors or omissions. There were 27 new factors found since the last update, of which 25 completed the factorization of their respective numbers. There are now 575 composites remaining in the tables. Digit count and SNFS difficulty ranges remain the same.

Nearly all factors were found with NFS. ECM is still finding the occasional factor, but all of the small factors appear to have been cleared, so anyone using ECM should use B1 values of at least 260M.

Here are the factors found since the last update, showing appropriate credit:

Code:

8+3	292	C246	1052978866100786783025717446683389141645216850859679864279830521030784425545763029752356216472416249402265353580312537.	P129	NFS@Home & S Wellman	SNFS	2022-06-28
11+8	257	C204	17075874565902409322444197094868958968470367281527468021955084000044685362628263.	P125			NFS@Home & S Wellman	SNFS	2022-07-04
6+5	1230L	C243	1989800570943488339928933561015964539542655988013406417531416242271774048314207462132810560347401.	P147	NFS@Home & G Childers	SNFS	2022-07-04
9+2	554L	C222	785405241763272827266539000271680547920091338929913866449945296789297329771233392812428833763295281.	P123	NFS@Home & J Becker	SNFS	2022-07-14
7+5	317	C196	39551807143587968689431661033886896020314449933187827579745593137725006467.	P123				NFS@Home & S Wellman	SNFS	2022-07-16
11+2	257	C196	12775545422106235965902970642137921047695187726991767763981292812067790719492439578936327974855107.	P99	NFS@Home & S Wellman	SNFS	2022-07-16
5+2	950M	C192	827973016668650713388064731991152830057402447576623382393481045697281201.	P120				NFS@Home & F Baur	GNFS	2022-07-19
3+2	554	C226	491957583434283203543710659321522765907925734494053878882261.	P167						NFS@Home & J Becker	SNFS	2022-07-22
7+4	352	C262	75571824253497297244265561377969228207427590275365249040536859841.	P198					R Propper		ECM	2022-07-23
7-6	323	C192	18790799179598956677809813233818970955254712169449836196099826918661598374937.	P116				NFS@Home & S Wellman	SNFS	2022-07-25
10+3	308	C196	21138257428341940342261700575370842035375710357751294329870507540918201.	P126				NFS@Home & S Wellman	SNFS	2022-07-25
11+9	254	C191	65336013292081495688672021029847039582049115912993429714485637.	P129						NFS@Home & G Childers	SNFS	2022-07-30
11+2	254	C205	101486362901140678261171708632867124284479727559218063558677.	C146						Yoyo@home		ECM	2022-07-31
9+8	277	C239	15049216317836517294600907995288190450795051840238103964985359740395657.	P169				NFS@Home & F Baur	SNFS	2022-08-04
3-2	563	C197	487954727601792310733889624676202540802213356569913262940345252835252947.	P125				NFS@Home & S Wellman	SNFS	2022-08-04
11-3	825M	C195	607719356537969445063090532178811350550204708372847673422478671508059765167436159622001495558301.	P99	NFS@Home & G Childers	GNFS	2022-08-05
11+2	254	C146	114160175726708146143903571642347497903131199348933676859210883980904797.	P75				T Singer		GNFS	2022-08-05
11+8	550M	C195	156633173306047512731921167253251662689806487953768876257292126301.	P129					NFS@Home & G Childers	GNFS	2022-08-12
11-10	263	C192	43772239261143980058605126681492516148852436751064240441463240476666791.	P121				NFS@Home & S Wellman	SNFS	2022-08-13
4+3	1329L	C196	165260950848037754239594315128137343845636834362504208249832742037106909819247.	P118				NFS@Home & S Wellman	SNFS	2022-08-22
12-11	251	C198	2035465913458804305820214862408486637224697117703085112756081.	C137						S Wellman		ECM	2022-08-19
12-11	251	C137	2061597151103823130093839594338244696855215839235642461598771612603.	P71					S Wellman		GNFS	2022-08-19
11+3	254	C251	318624065917983908126192389251257677611045545897205339174088395838964464123182491968328601126910194682524704093.	P141	NFS@Home & G Childers	SNFS	2022-09-02
11+8	254	C213	2963897012281681678709613115834105724195821421454260604345654902584241693501.	P137				NFS@Home & S Wellman	SNFS	2022-09-06
11+7	290	C193	28199492106618420118790918900294456520871384392799925501276860722361.	P125					NFS@Home & G Childers	SNFS	2022-09-13
6+5	374	C237	2519751942762294485397051765376313628460580899030932248700562905617.	P171					NFS@Home & G Childers	SNFS	2022-09-26
8-7	293	C250	45577986245992569622450804260695140424715070942005385893770859894797.	P182					NFS@Home & G Childers	SNFS	2022-09-27

R.D. Silverman · 2022-09-28, 21:25

Quote:

Originally Posted by jyb

The tables have been updated with all factors known to me by the end of September 27 (GMT). Please let me know if you see any errors or omissions. There were 27 new factors found since the last update, of which 25 completed the factorization of their respective numbers. There are now 575 composites remaining in the tables. Digit count and SNFS difficulty ranges remain the same.

Nearly all factors were found with NFS. ECM is still finding the occasional factor, but all of the small factors appear to have been cleared, so anyone using ECM should use B1 values of at least 260M.

Here are the factors found since the last update, showing appropriate credit:

Code:

8+3	292	C246	1052978866100786783025717446683389141645216850859679864279830521030784425545763029752356216472416249402265353580312537.	P129	NFS@Home & S Wellman	SNFS	2022-06-28
11+8	257	C204	17075874565902409322444197094868958968470367281527468021955084000044685362628263.	P125			NFS@Home & S Wellman	SNFS	2022-07-04
6+5	1230L	C243	1989800570943488339928933561015964539542655988013406417531416242271774048314207462132810560347401.	P147	NFS@Home & G Childers	SNFS	2022-07-04
9+2	554L	C222	785405241763272827266539000271680547920091338929913866449945296789297329771233392812428833763295281.	P123	NFS@Home & J Becker	SNFS	2022-07-14
7+5	317	C196	39551807143587968689431661033886896020314449933187827579745593137725006467.	P123				NFS@Home & S Wellman	SNFS	2022-07-16
11+2	257	C196	12775545422106235965902970642137921047695187726991767763981292812067790719492439578936327974855107.	P99	NFS@Home & S Wellman	SNFS	2022-07-16
5+2	950M	C192	827973016668650713388064731991152830057402447576623382393481045697281201.	P120				NFS@Home & F Baur	GNFS	2022-07-19
3+2	554	C226	491957583434283203543710659321522765907925734494053878882261.	P167						NFS@Home & J Becker	SNFS	2022-07-22
7+4	352	C262	75571824253497297244265561377969228207427590275365249040536859841.	P198					R Propper		ECM	2022-07-23
7-6	323	C192	18790799179598956677809813233818970955254712169449836196099826918661598374937.	P116				NFS@Home & S Wellman	SNFS	2022-07-25
10+3	308	C196	21138257428341940342261700575370842035375710357751294329870507540918201.	P126				NFS@Home & S Wellman	SNFS	2022-07-25
11+9	254	C191	65336013292081495688672021029847039582049115912993429714485637.	P129						NFS@Home & G Childers	SNFS	2022-07-30
11+2	254	C205	101486362901140678261171708632867124284479727559218063558677.	C146						Yoyo@home		ECM	2022-07-31
9+8	277	C239	15049216317836517294600907995288190450795051840238103964985359740395657.	P169				NFS@Home & F Baur	SNFS	2022-08-04
3-2	563	C197	487954727601792310733889624676202540802213356569913262940345252835252947.	P125				NFS@Home & S Wellman	SNFS	2022-08-04
11-3	825M	C195	607719356537969445063090532178811350550204708372847673422478671508059765167436159622001495558301.	P99	NFS@Home & G Childers	GNFS	2022-08-05
11+2	254	C146	114160175726708146143903571642347497903131199348933676859210883980904797.	P75				T Singer		GNFS	2022-08-05
11+8	550M	C195	156633173306047512731921167253251662689806487953768876257292126301.	P129					NFS@Home & G Childers	GNFS	2022-08-12
11-10	263	C192	43772239261143980058605126681492516148852436751064240441463240476666791.	P121				NFS@Home & S Wellman	SNFS	2022-08-13
4+3	1329L	C196	165260950848037754239594315128137343845636834362504208249832742037106909819247.	P118				NFS@Home & S Wellman	SNFS	2022-08-22
12-11	251	C198	2035465913458804305820214862408486637224697117703085112756081.	C137						S Wellman		ECM	2022-08-19
12-11	251	C137	2061597151103823130093839594338244696855215839235642461598771612603.	P71					S Wellman		GNFS	2022-08-19
11+3	254	C251	318624065917983908126192389251257677611045545897205339174088395838964464123182491968328601126910194682524704093.	P141	NFS@Home & G Childers	SNFS	2022-09-02
11+8	254	C213	2963897012281681678709613115834105724195821421454260604345654902584241693501.	P137				NFS@Home & S Wellman	SNFS	2022-09-06
11+7	290	C193	28199492106618420118790918900294456520871384392799925501276860722361.	P125					NFS@Home & G Childers	SNFS	2022-09-13
6+5	374	C237	2519751942762294485397051765376313628460580899030932248700562905617.	P171					NFS@Home & G Childers	SNFS	2022-09-26
8-7	293	C250	45577986245992569622450804260695140424715070942005385893770859894797.	P182					NFS@Home & G Childers	SNFS	2002-09-27

Ryan has had two numbers reserved for over four months. Did he forget about them?

2022-09-04, 22:35	#1862
R.D. Silverman "Bob Silverman" Nov 2003 North of Boston 2²×1,877 Posts	Minor Milestone I have finished factoring all HCN composites a^n +/- b^n for a > b, (a,b) = 1, a <= 20 and n <= 150

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2022-05-24, 15:33	#1860
VBCurtis "Curtis" Feb 2005 Riverside, CA 1011000001100₂ Posts	I am mostly an observer to this project, but any changes that make the underlying math easier to understand / do on one's own seems a clear win for the project.