The "Hey YOU" Thread

[henryzz]

I was thinking about running a script to ecm them. I realised though that it is quite possible that they are rsa 1024 bits.

[xilman]

Originally Posted by henryzz

I was thinking about running a script to ecm them. I realised though that it is quite possible that they are rsa 1024 bits.

If you would like to run ECM on 309-digit composites I could provide you with 21 of them. You are rather more likely to find factors than you would from RSA public moduli.

The numbers in question come from the generalized Cullen and Woodall tables. Smaller numbers, limited to C300, are presently loaded into the ECMNET server running at 109.109.168.71:8194.

What the heck, let's give you the 21 anyway.

103470031948673683726339153635683761355208833883657645585291989182981257252649992837738889820481690730558328044057946777181625252059928887075198340634642911898819920316220350235918973603306193944462407306778805013773731515357328368757721664020635520451987268791346772235139542239218885510965618180177168514733	5,527+
112439027058982259448198339440684216479510805766824786571985491793754422997056749891823281162674298688712989151920065356046839443889902367695374009760260735708625469346380054413549327471867488061999768287287185867910364805129176555875171719889376866945040542540997050499184858355770633680348955543589845367641	5,448+
115283834567776362686345744079330876125293905679336558147617600751900232066224922899951236401847880809790011659669447270637338978342511327616114106433101156281158937262901096904690232165205015710141153276152369661126263383765093388572697014889699733512706231767066508993211207880661151315263265739455751563767	4,565-
135395490349784497062818724348012462291096633246013652309362185664748791284784985006594471945991068390844712045493588559548646992073404473081235517984587066762674991137394088284013669814133337774337486737166421459085601556748584443292562450569555939175092911625644370634614688335065459236300463404001360407799	5,457+
140361837935479012014035852315526836713697080019768662353315665698687167331653288598856609507127660739067333002630153320959000654493644775503591622490518098195467710656115915816126243856333451889762284255250029853553389605591356225186431228604750522700054833027867878453389676257654568357819690565173208196497	3,674+
151468222415814222700612217619957934230825690568155580584592928365041736265707380897679640368373501894315654055774808081810727347374866943552165509935946860791421676980395744790421042364952040641719599337776406728759896146661048544482697639928639714777092013402340885592623354996346797138377842016498047782307	4,528+
152522830371920606522352438505320861163774363385490062278377778978294927474913376804513924673770368420592400380128833509033105188972689907156462607747721188798662042314942281713587781040133297183553597622071545739235196021109241110008406460910018235038842462104441542351539362122090793479483384650748473079837	9,398-
165795513931263859634567602833791285118168685499493897986216885946349832084674918895914628856625995220994554417897071615817602640018448143805959348641491696780475436492519245847707725087023964285234453801968763194387547030138699897340604390381248573379758186350042431898905203776025359557803949453273601678419	8,478-
170758864163926210793183064135373197726594966841743239322728261953270728913458174324300292298182180511442943122438649028023240455137533366867277138518228190689482653314091447099070591523900383494543565466326812185076149765422487107788724617573393728074479306389986158080505344939505205180867785280842659604387	10,342+
188886749735226183734462067805190212341100216656067568341187225283417608270723825711117251342918184514887287992837641151137163829461522221758481566068180676336452311354485671728847298259506933331456186513661349591790555108326208161865922127168983380860240666751139351182370201697086531525451499396340686218727	6,529-
190084158149182512903136458852062078689263536151744222893556587461145039833523388190106830057587540019234363270984927936576645483674422978022312506488779843872436999347756288817875554538226300399079550477583949203599994270587651709445584544448372500962505386064266141533376562109597559925836118346829850016387	12,333-
210866986195445849309766031517613588168732866453268372278751559226495928144110806246430133650038874857498494028196169479680928560899082455229849230873853622864381090203792122790370843896638307507731384778937061158329594906048778898708481525611161239124336410683440097256160233485389129205560361699508227954029	4,628-
235167021203180136128930665365565587697663141213239856915940872580479451759415170772675760987933240962309958946820569966913967305303208735406559694157502321822570545900874862905958374432567106589288851338088148007469445200505887673840079078327698407698811028046230322593715863115847520812998189911761707362233	3,655+
273288534482794703722375633839212395471585220681762333159396542548640728234335281856311267741185278029238955668700216346794444041143078276845750186652020867064750345773474004591761314795381408202462039227860995552609200284198625318968577885439738285211937068434321926149426111206509589736271126031592823757521	12,286-
285862863481756588966592636682786722857879894320565482314228526861595535082684813415220060786808732243241490905888923357388400914723663663755359913805603804238888316476396379237492865039085248082351397090039781901664803035658853111641119261134260438308558379861873943832465810610186887443853905563325020712563	4,534+
296435877645613589680150041812075427512143260847087095144896189511124289148999635691238009236033495486914820916380780697351099699743984640586600346297258327478959679479871325498094865477641017232901730520117801759072724030724214107778304267296809231045907001605057474967716217574113399394233362086109798139451	12,328+
325417296785683148553178401802141633620405064895730636410133635356142642498063953344777304915534266290223222218270658999459835170123233154127305257144268056238792413814659071006354963025475483334950458845666407552154607264456935293437221971620605867680597203865485316780409903679801594932805018737507867978021	5,487+
404434959731225169183255219101488383700528847831095567702997328824030780958072461909392760482196079447307366146219440318897885706567077301754615658534421500161004494769388566238055797125114651394105779644883362808472648275785783535177598003703925300895419865829300035
103470031948673683726339153635683761355208833883657645585291989182981257252649992837738889820481690730558328044057946777181625252059928887075198340634642911898819920316220350235918973603306193944462407306778805013773731515357328368757721664020635520451987268791346772235139542239218885510965618180177168514733	5,527+
112439027058982259448198339440684216479510805766824786571985491793754422997056749891823281162674298688712989151920065356046839443889902367695374009760260735708625469346380054413549327471867488061999768287287185867910364805129176555875171719889376866945040542540997050499184858355770633680348955543589845367641	5,448+
115283834567776362686345744079330876125293905679336558147617600751900232066224922899951236401847880809790011659669447270637338978342511327616114106433101156281158937262901096904690232165205015710141153276152369661126263383765093388572697014889699733512706231767066508993211207880661151315263265739455751563767	4,565-
135395490349784497062818724348012462291096633246013652309362185664748791284784985006594471945991068390844712045493588559548646992073404473081235517984587066762674991137394088284013669814133337774337486737166421459085601556748584443292562450569555939175092911625644370634614688335065459236300463404001360407799	5,457+
140361837935479012014035852315526836713697080019768662353315665698687167331653288598856609507127660739067333002630153320959000654493644775503591622490518098195467710656115915816126243856333451889762284255250029853553389605591356225186431228604750522700054833027867878453389676257654568357819690565173208196497	3,674+
151468222415814222700612217619957934230825690568155580584592928365041736265707380897679640368373501894315654055774808081810727347374866943552165509935946860791421676980395744790421042364952040641719599337776406728759896146661048544482697639928639714777092013402340885592623354996346797138377842016498047782307	4,528+
152522830371920606522352438505320861163774363385490062278377778978294927474913376804513924673770368420592400380128833509033105188972689907156462607747721188798662042314942281713587781040133297183553597622071545739235196021109241110008406460910018235038842462104441542351539362122090793479483384650748473079837	9,398-
165795513931263859634567602833791285118168685499493897986216885946349832084674918895914628856625995220994554417897071615817602640018448143805959348641491696780475436492519245847707725087023964285234453801968763194387547030138699897340604390381248573379758186350042431898905203776025359557803949453273601678419	8,478-
170758864163926210793183064135373197726594966841743239322728261953270728913458174324300292298182180511442943122438649028023240455137533366867277138518228190689482653314091447099070591523900383494543565466326812185076149765422487107788724617573393728074479306389986158080505344939505205180867785280842659604387	10,342+
188886749735226183734462067805190212341100216656067568341187225283417608270723825711117251342918184514887287992837641151137163829461522221758481566068180676336452311354485671728847298259506933331456186513661349591790555108326208161865922127168983380860240666751139351182370201697086531525451499396340686218727	6,529-
190084158149182512903136458852062078689263536151744222893556587461145039833523388190106830057587540019234363270984927936576645483674422978022312506488779843872436999347756288817875554538226300399079550477583949203599994270587651709445584544448372500962505386064266141533376562109597559925836118346829850016387	12,333-
210866986195445849309766031517613588168732866453268372278751559226495928144110806246430133650038874857498494028196169479680928560899082455229849230873853622864381090203792122790370843896638307507731384778937061158329594906048778898708481525611161239124336410683440097256160233485389129205560361699508227954029	4,628-
235167021203180136128930665365565587697663141213239856915940872580479451759415170772675760987933240962309958946820569966913967305303208735406559694157502321822570545900874862905958374432567106589288851338088148007469445200505887673840079078327698407698811028046230322593715863115847520812998189911761707362233	3,655+
273288534482794703722375633839212395471585220681762333159396542548640728234335281856311267741185278029238955668700216346794444041143078276845750186652020867064750345773474004591761314795381408202462039227860995552609200284198625318968577885439738285211937068434321926149426111206509589736271126031592823757521	12,286-
285862863481756588966592636682786722857879894320565482314228526861595535082684813415220060786808732243241490905888923357388400914723663663755359913805603804238888316476396379237492865039085248082351397090039781901664803035658853111641119261134260438308558379861873943832465810610186887443853905563325020712563	4,534+
296435877645613589680150041812075427512143260847087095144896189511124289148999635691238009236033495486914820916380780697351099699743984640586600346297258327478959679479871325498094865477641017232901730520117801759072724030724214107778304267296809231045907001605057474967716217574113399394233362086109798139451	12,328+
325417296785683148553178401802141633620405064895730636410133635356142642498063953344777304915534266290223222218270658999459835170123233154127305257144268056238792413814659071006354963025475483334950458845666407552154607264456935293437221971620605867680597203865485316780409903679801594932805018737507867978021	5,487+
404434959731225169183255219101488383700528847831095567702997328824030780958072461909392760482196079447307366146219440318897885706567077301754615658534421500161004494769388566238055797125114651394105779644883362808472648275785783535177598003703925300895419865829300035536955197246008577584578137493263004400927	9,383-
540195828306582103041280926363297795691142234135668730975868223910186519801905337483536078338721686095435163652349058397513775279424986809273443722498370347256536394389656284524353092111679679139141134444088463611938395961060701291387280050773850991494112033171731468738055022837393324964663920122481400091971	9,322-
778726014664867897808070109721278291185074321957306409008924589724372894933114047245431658665835642230681458221535131606577452635463144484184931703277425591376870979232022933171190985291546004865041053565360091738043965556400138117580190807971901193932758780258880676115694951164288692850834717730294768964531	4,581+
838272631636288649111119861337957638437421603929354576946835575879345327283575961081440278845017656795112814755971237751923101050627975876298888052565848413237589538258045262617522739761155964816438470813369964302127421939826143701445172856603882799741865940631699427961409409072081859484711833618444653397471	4,592-
536955197246008577584578137493263004400927	9,383-
540195828306582103041280926363297795691142234135668730975868223910186519801905337483536078338721686095435163652349058397513775279424986809273443722498370347256536394389656284524353092111679679139141134444088463611938395961060701291387280050773850991494112033171731468738055022837393324964663920122481400091971	9,322-
778726014664867897808070109721278291185074321957306409008924589724372894933114047245431658665835642230681458221535131606577452635463144484184931703277425591376870979232022933171190985291546004865041053565360091738043965556400138117580190807971901193932758780258880676115694951164288692850834717730294768964531	4,581+
838272631636288649111119861337957638437421603929354576946835575879345327283575961081440278845017656795112814755971237751923101050627975876298888052565848413237589538258045262617522739761155964816438470813369964302127421939826143701445172856603882799741865940631699427961409409072081859484711833618444653397471	4,592-

You should use B1 at least 43M and preferably 110M or 260M as they have all been completed well into a t50 test.

Have fun!

[EdH]

xilman,

Just curious, but are your 21 in the db presently? I would query it to see, but then they would be, whether or not they had been.

[xilman]

Originally Posted by EdH

xilman,

Just curious, but are your 21 in the db presently? I would query it to see, but then they would be, whether or not they had been.

I don't know for certain but it seems very likely that they will be.

[EdH]

Originally Posted by xilman

I don't know for certain but it seems very likely that they will be.

A non-committal test appears to show the first one is, anyway:

http://www.factordb.com/index.php?id...00000593028069

[chris2be8]

Originally Posted by EdH

Chris,

Depending on how bad you want those "invisible" 309s, this might allow you to find them.

I don't want them that badly. All my script is doing is looking for numbers that have algebraic factors and telling factordb about any factors it didn't know of. So I'm happy enough to check just the numbers I can easily find.

Your script goes through them by index. Which isn't guaranteed to find them all unless I check every index higher than the last 309 digit one I can see. Which would also find a lot of partly or fully factored numbers.

Chris

[chris2be8]

Originally Posted by xilman

Writing from a position of profound ignorance here: is it possible to ask for all 309-digit numbers which begin with (or end with) a specific string of digits?

I don't know of any way to do it. I'm screen-scraping http://factordb.com/listtype.php?t=3 and that doesn't offer any option to do that.

Chris

[EdH]

Originally Posted by chris2be8

...
Your script goes through them by index. Which isn't guaranteed to find them all unless I check every index higher than the last 309 digit one I can see. Which would also find a lot of partly or fully factored numbers.

Chris

True! I hadn't considered the "other than composite" returns. I suppose I could build that check in also, but as you point out, all indexes above the highest known would be quite a load.

[henryzz]

I was thinking of ecm to remove small primes and bring it under 50000 composites. An initial test on the first 5000 makes it look like 5% can be removed fairly easily. How many do we need to remove?

[schickel]

Originally Posted by EdH

xilman,

Just curious, but are your 21 in the db presently? I would query it to see, but then they would be, whether or not they had been.

The way to check that is go ahead and query. If it's new, you get the * indicator that it was freshly added. If there's no star, check the "More information" field to see approximately when the record was created.

Originally Posted by EdH

A non-committal test appears to show the first one is, anyway:

http://www.factordb.com/index.php?id...00000593028069

For example, this shows:

Create time

Between March 17, 2013, 5:05 pm and March 17, 2013, 5:20 pm

I don't know if you can pick that up programmatically though.

[EdH]

Originally Posted by henryzz

I was thinking of ecm to remove small primes and bring it under 50000 composites. An initial test on the first 5000 makes it look like 5% can be removed fairly easily. How many do we need to remove?

From the distribution graph, I had estimated ~2000, but someone else might want to check that.