求证：y＝p

太阳

太阳

\(例1：\frac{\left( 10^{2a}-10^a+1\right)\div9999900001}{m}＝y，a＝1435\)
\(\frac{\left( 10^{2870}-10^{1435}+1\right)\div9999900001}{m}＝y\)
(10^2870-10^1435+1)/9999900001/9100182910928181890625077960716190275840421378458842541488529621046347492279388136563435920702863436564079297136563435920693763253653151115245938357959986673160723657918677720894432173242390216587017748425962466491067754938452710043355253457198127535464541891872464535458108127535464541891872464535458108127535464541891872464535458108127535464541891872464535458108127535464541891872464535458108127535464541891963466364567389946441715321499034367293862321912123889956777168674998933030921416839276433990421351714373998467546366526919823546453482180176453546517819823546453482180176453546517819823546453482180176453546517819823546453482180176453546517819823546453482180176453546517819823546453482179266435255425001634483945686108557425962475681977662199333327214348911768591884732706136758996885383955161114225635235829702863436564079297136563435920702863436564088397319474364102593488514524795487412403857299161705978052608918182910928200091=1098890000110999988901100000000000010988889012209998779011110988999999999999890111109877900012209888890108901109999890098901099010999988901089011110987790001220988889011000000000000109888890122099987790111219780098901100108791208900989000012197799890110012087899890110010988999999989011012087799880231000987910780219901099119669098924298997680208912090109889987911001220988768011122098899890087912200119779987912090329779987911880330901075701002319791087909890110012088998779011231988877901101208802087910880208913187909670220023077008681308923078008791197912090109889878022111098888780221010989008791197912090218679988033090207681088021891318691076911002319789877911111099010988888901111219888877901113308789878020891210011966909791220021977997681320021988997680210122088888900989011111098888780111122098886691210121978998900988021990209889868022002318678879121002208789889010011099010988888901111219877889001112198789989010001099011977899901110120877998791211120878997791210110989987802099011000098899879022110998887790221110988888901099011100098889879122001208788769232002197689890119902197900988998802210120866889012211109778889011111098900988888912210119767998902200230767997802200220880086702100120891197789879133110987788890221110988888901099011111087789880232001086810869230892197910768119913297899769219912088020879098901101219778889011112197789890109912088020879097813189130769096813200219670087923089119791087911979121010987788902321098778998912100109890087910880232000965810991329792087899780329912087899780210022087909889989012211097678901221001087899890109912089119767999034189008670209010990219781087901001319789977912101098899999998901100109889987912100109889978022099998900989120879110010989009780221109877900012209888890110000000000001098888901220999877901111098910988900001099010989009890000110989109888890122099987790111109889999999999998901111098779000122098888901100000000000010988900001109999889011
m位数940，y位数1921，m最前七位数9100182，m最后七位数820091，y最前七位数1098890
y最后七位数9889011，5＞(2870-9)/940＞3，(2870-9)/1921＞1.25
判断素数1098890000110999988901100000000000010988889012209998779011110988999999999999890111109877900012209888890108901109999890098901099010999988901089011110987790001220988889011000000000000109888890122099987790111219780098901100108791208900989000012197799890110012087899890110010988999999989011012087799880231000987910780219901099119669098924298997680208912090109889987911001220988768011122098899890087912200119779987912090329779987911880330901075701002319791087909890110012088998779011231988877901101208802087910880208913187909670220023077008681308923078008791197912090109889878022111098888780221010989008791197912090218679988033090207681088021891318691076911002319789877911111099010988888901111219888877901113308789878020891210011966909791220021977997681320021988997680210122088888900989011111098888780111122098886691210121978998900988021990209889868022002318678879121002208789889010011099010988888901111219877889001112198789989010001099011977899901110120877998791211120878997791210110989987802099011000098899879022110998887790221110988888901099011100098889879122001208788769232002197689890119902197900988998802210120866889012211109778889011111098900988888912210119767998902200230767997802200220880086702100120891197789879133110987788890221110988888901099011111087789880232001086810869230892197910768119913297899769219912088020879098901101219778889011112197789890109912088020879097813189130769096813200219670087923089119791087911979121010987788902321098778998912100109890087910880232000965810991329792087899780329912087899780210022087909889989012211097678901221001087899890109912089119767999034189008670209010990219781087901001319789977912101098899999998901100109889987912100109889978022099998900989120879110010989009780221109877900012209888890110000000000001098888901220999877901111098910988900001099010989009890000110989109888890122099987790111109889999999999998901111098779000122098888901100000000000010988900001109999889011

太阳

a＝1265，1761位素数
109889010998901109890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989022087801209779121989000989001099001098890109990109879122076902307779230978021087910098911208789109899120888021986812218680131877912098901009890010989900000999990999979011199889110988001109000009988900109999010997801219778032997801999891009991009881009981109980021067802409778210988001109098999010008900109900108799121886813217681140768822090910978812189691310779210779122976904296571441857012088011097902107781229869030978921078822297480332778012987892000002088881209879110990100878102197881218969120188908100020088809209799110799110888012007802219669022000000890001987992108991008981008981130068810200898091020088810199800110899000890012087791210889001000090899101987993207870120179909079021287700309788211997999999110986912317679120899110888011996903217770030089908991029967822298700209789110899120876823208690110899999800211788012996793119880908982020968812289790200899091000099889112087791209989099899110998002007891020090799102007871031079910079910089911189790199989100000219867022197810209789110898110898011907891020000808892020869922078802200779100990110879012078891200000188790309778332974803217881118880129869032077811198801109791209659244065703398680320878111878113086992207880109091217868141076822307689220897910999010998910009899900911099790111778014197771119980011080010079010090010089000197800329778022097800109900010998890009999911099790110889002109880000090000099998990109989010098901208779230976922207690219789120899010887912108901008791119780131877813198681220879010990010988901099901099890099890220878012097791219890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989011098900109889011
a＝1295，1729位素数
1098890000110999988901100000000000010879011001098899890120889999999999998912098899890110010987910999999998901219888889011111097790109999999989120988998901100109879110000000000001087901111098789990122088889011001098780111219778998913198888901208910879011001088130768119802200108769218912098888903396800978132000966912090219888780220892296691100109792187912088998911869242869097801001230670098901111096603199021867999033087909780111219779107703309998780207923087899902188130757130913078009770428800989009793396800978130913065811980329899768131892296690001328582186923089096713078142869086921979350560197912090316482309021869086935275920770210121857119792309998671417703187910892186922967020913078020649439802087909683517690978130913064724079218800978141770207800990328582296811979218813065932980196811979350560197911980427482297921870196825275920781197922968229681199020770317703188020781185835177019692188031748339802088019561528802077019803285713079218802077031759329900978119682407800979218814164713091307800868252770087911980438471197813091196703186921891087922968240669000131880206592210119681185835286908692199131747229912088019561528802186908693407813067008913186921759330999867031892307679990329802075713091307800977042880098900979339680097813091306581307921989987913188119779000132968108780221109780087913298997692199022957011110989009671321000978008693418692088998912087921880110010867031891219778890219912086701002307800977042988889012089218679110021980207681307911001098791089120988889023088998780221109779011001098888912209899879011110987911000000000000108790110010988998901208900000000109878011111098888890220989000000001087901100109889989012088999999999999891209889989011001098791100000000000010988900001109999889011

太阳

a＝2485，3361位素数
1098890000110999988901100000000000010988900001109999889010999999999999989011099998890000110988999999999998791220999877900012208789999999999989120988998901100109879110000000000012087790001220999877912100000000001208779000122099987791210000000000010879011001098899890120889999999999987912209998779000122087899999999998791220999877900012208789999999999989121098887901111209878000110000000012088888891221110877901001100000001208777901232099876791221098900000010878890123198887680122110878999999987911133086578891342098776921999998791222318545900145408776681319999989121109766912112308777890230890000012088865814531108546901234176900001208777682552989854702223307581100010878890244076787692332109658120999987911134185468891453098765823099998791222317447010145297776692418899989121109755923212307667890341879000012088865814531108546901234176900001208777682554088744702334307570001110878890244087776592333219658010010987911134185457902553097655823210987791222317445801366297654592431108779121109755912333296666791441988879122088865814543196336902455176777913308777682554197534812345296568902319778890244087655714433207448011231866911134185456814651997545933221975702222317445802575076654714531096570331109755912344175677792540888769242978865814543184249112453955778035396677682554197424923345285468903429668890244087655824322207459111230757021134185456815750887546044221964603322317445802575076654714531096570331109755912344175567903540877669244088755814543184248013563955667035407776582554197424923345285468903429668890244087655824432096459122330755911244185456815751975447144331854592334406445802575076544825531085470332219645912344175567903540877669244088755814543184248024552855668145407665593554197424923454075578914418667791452987655824432085470222329645911355174456815751975447144331854592334406445802575076545924421085581332208547012344175567914419888670342988645935433184248024551756778145296665604653097424923454075578914418667791452987655824432085580111329657011354064566815751975448232232954702224395457891575076545924311196581321108548122234175567914419888670342988645935433184248024551767767045297775604542108424923454075688803418678891451877765824432085580111329657011354064566815751975448232221965802223285458002564076545924311086692321097448123344065567914419888780231988657035432074358024551767779133087776825541986337023454075688912208788902440876667033332085580111208779111341854568036630975448232220877901123175568013551987545924311087901100097570223331856777914419888791110999658134331964478914551767779120999986824320986459111354075688912099998792429887668132123185580111208899989241866778035410096448232220879000013175679013540888645924311087900001207570112331867876814419888791100010758133221964589903551767779120999986824320986459111354075688912099999891319887779132112086680111208900000230766779145409985459232220879000002186779012430888756913311087899999998791112209767889023209888791099999989011220876790012320987779121000000011000987791111220888888912100000000109997790121110987889011208899999999999879122099987790001220878999999999987912209998779000122087899999999999891209889989011001098791100000000000120877900012209998779121000000000012087790001220999877912100000000000108790110010988998901208899999999999879122099987790001220878999999999998901109999889000011098900000000000001098890000110999988901100000000000010988900001109999889011

太阳

a=4255，6337位素数
1098890109999999999999989011098899999890110989109889011000001098890110000010988901089011098899999890110989000000000109890109890109999999998901109889999989011098910988901100000109889011010989999990108901109889890100000098898901109891098999999011010988901100000109889010890110988999998901109890000000001098901098901099999999989011098899999890110988010998901000001098890120988912088901198900109790110879110987901109889999990109989020988901100000109889010999999999890109890109890000000001098890110000010988901089011098899999890110988989010000009891098890110108801109791101098890108911988902088989120987910890001099989108790120890001087901208910988900001099010987911000000010879010990109999889011990099989109998912098780100099009998800990001198878130889021989989000110119790010880112197790108791110989988989011208790109780220989109887912109891098879121098921976703298901208789010901111977891207802329670000979111197909888912100978120975932999900989990208900119789902209880208900009901000979011089009999889011979110989099010000009891099001098119800010791090099000118800900990990188021097712111869101088119900010889882407769338788912099891186911207811010878913188011097801010891210868111097912108681099980221086810988913188890198888241887912977891318999018691021870111076910120801001869200099119898802110870210087899020900989880198999119887812099891209988019900021889891099990218790009791991188989207811010889881188111206810910880002287998008921010781198769330007812009672200100097898922978914167000099108910890000979210097789130790000990089109010019789902090111086920998812001869101087021009790890871408978228799911990980297998129810911869002286899129799801991090088010117603220661211078010108811989782299978219986921888903187990206910030789803178001307919909691003079198998019810901990859210098021009680992190188108019899913089978099108030799900781200098988030789912101968100109119810890891081308988018789913079990177009229798912869101198219017602021772298978119019712989672387989229897712990992178099107811131769992177000327799909792101078120095722010801990979209998031788804089970309097919800901970090298008019701001870300087119029800901980089209117919711891881189098008920801891970189088229898812001969200198007920910890882386889327819800901981188109117809822880892179208008920801782081178199216712009683179189208117721900892080188109008041680012969089219007820801891980090196910020801882080189198118909801012958211186018930800791970299098128808603101871397998128710923869871299098129799801772191277108117712011881079187120227612010671201188107908821900892078979219007832889683180200196908921890893179078208118919691990969309206907831800793179089206930920691882179199107919810791991959308987030910780992069309097019909803089980297008029810801879991297888140688813981080188109128602011761191287009117612990772389076130117711890881189198227808832780893276999217820811780882278099217809811892091068208998030910780992168209206929799803091078098117919821791881080307998040690802982168199206930810792970180407007929701892081178197019139591012859200208117819701902981189087020019713979772388099218908702001981289087118919921780981178209227808711891992277009216622022780871189209118920690783202157219096831901892069078319117820800782190189206908930802001969089219007941679804070200196908920802991970178208120018593100860409197017820811891970288097139819702881081287119017721802980871397998129810791882180188208007810912979980287119117721900781091297999117710911892080078219007831790782081178218996832890783279078318018920790892068210305808941680903058209096930920582101959309107919810804078871407888030899791981080298097029799912980090197009128711900781091296899128601901881080188109018821791871191287118908822880982278087119128700901870189208117808822890892189087020019822769893278099218798811890992179088107921020671102058320206918810792102068208106830921681979980308009030689694191069307998040692012959079308009029701880981289195921117603100980089208018919811791981200087019909801891981178099218908703099772398099107919811890992168208118918822770102067219017820811781981189098118821890793180078209107920801990980178328886941790891091188098020018702002078990317908919701891981189098008920791892070188209118909801990980299206910029692000970198098029909701990980188009129699913978882298000118800901981102166010207811011880089978329996821899682311078109007821900903067990318897941669903070199207799031682201958199218021008693088980319096819899813089879197899130810890891080209110007702012089881297899010020780989981298109007799913089990198107919921900770101198010118590901991080197999018813000870090188130997822979881300087119897922988892186900217800031779902079110097811120571222958210097909910901979980308986931998692091080307998029800902089979317799140690890880101196911008692002079001186911109911989880200099108909900999881308878010118800999891089109009996724088803188988010010021670102078100328679020781101189097997931999791091077121107920789891101078118898920901880099879219900010889892199990197900120890012077890208999019789900991198987910119691111978990209010018692000981210086811109692200869198999230887803087892417889019888923088901076911219800010769112088011107691120891100978011097923088791101078121086920890012088879428678141789891099990207911008692112068011197919900900990979209999009910881099980208010999010890100000099008901108802098890000098911098801000990099989119790121989880209989119899900990003285801207801012088890088021108800999670331978120887802110991098879120989032966802189011208789010890112087890108901219780109879121098898899901110879109878022109791099880210109998899902198891307789020999900979000099010009779012089000108900009902098890000109901098791100000001087901099010999988901089120987910999891209879108900010999891087901208898911988902089109889011010880110979110109889010890100000098898901109889999989011098910988901100000109889010999999999890109890109890000000001098890110000010988901198900109899999890110987901108791109880109989020988912088901209889011000000989001097901109889999989011098900000000010989010989010999999999890110988999998901109891098890110000010988901101098999999010890110988989010000009889890110989109899999901101098890110000010988901089011098899999890110989000000000109890109890109999999998901109889999989011098910988901100000109889011000001098890108901109889999989011098900000000000000109889011

太阳

a=2015，2881位素数
1098890109999890110989000010988791210989000010988901099998901120889890001098900010999890109998898912109890000109889010999989011208789010999989011098900001109879011099998901109890000109887912109888901219779011109878022208887911219778011109987912198888990219978010111097791209988890221977891211087780220988890121977901110988791210989000010988901099998890120988900001098890109999890112087890111098780220989000010988791101099879121989988891208900011010878912099888792319780109999888021998899901219790109790100011087911099009890108780219999998901099999989010990110990098890109999889012098899900999781210989000011098899999020889020890009891098890099011088011098009900109780220989989012077901090098890220888890012087802100010880120879998902208790000120876921998899901219779011110976912198999000218789010999988901100000979110979109990108901109900988911988901990099890219779009901098911098920890010879110011108791098999988020989010001207680219900989013078110989109780209890208801098811978911980109891219780109999997921998910890119779009901098901198009998020889110000218790109890089011078011089109879109990108902098902089010879011990099890208790108910878033087909901109780210000088022186909989119879119891098892188000978123078001100208680220790979024176801000999770220989009912087801099020889021989998891207791099012077011098009790220780209902187802188901079120978020891097681219900890013077901100108681330889988021986811999999780330779098802297801199020978031979008781329780000002076902197899891330769110010987813099890990220768010891197801208810988921977921990119781219880098011096812099010878120888999902198891199010977912090098901219680001000976824198800881219769120010997813207800997921889010890208790208900086922197910000119780110990087913297791089109879119890009902098791098911989011989109900108790108911097811098909890109879220000108891198000098020989010990098780209891089002188000000109780220890109802088802079010979119890119780108901107813098900990219768121000098901197899999010879111100108791099891189011089010990098780219890009901988902088900990110989109900108801108801000010988900001098879219998999022086801111098780220989989002186791209999879121988999791209791100011977912099888891219889009910987812098899901219780109990098011097911099009889010890099891198891198999989011099998901120780000989989012098890000109889009901109901098900000010989000000219779109890099011087911100009880109880220989989002197890000109780231878890012088791101099989120888899902208790011010878901099998901219779011109887912109890000109889010999988901209889000010988901099998901120878901110987802209888901219777911120887802219888900120878011110097800219898889022087900111097780221087889122197790111098780220988890112087890109999890110989000011098790110999989011098900001098879121098900001098890109999890112088989000109890001099989010999889891210989000010988901099998901120878901099998901109890000109889011

yangchuanju

太阳 发表于 2022-3-12 18:00
\(例1：\frac{\left( 10^{2a}-10^a+1\right)\div9999900001}{m}＝y，a＝1435\)
\(\frac{\left( 10^{2870}- ...

例1：(10^2a-10^a+1)÷9999900001/m＝y，a＝1435
令(10^2870-10^1435+1)÷9999900001/m＝y
暂且不管太阳的940位m如何得来的，姑且做除法求得1921位的y；
经查对1921的y是一个没有分解开的复合因子，太阳先生怎么把这个十分明显的复合因子当成素数呢？

素数公式是不存在的，不要再盲目发布那些假新闻啦！
太阳先生的第一个例子就是错的，其它几个例子不再一一复核！

太阳

a＝1265，1761位素数
109889010998901109890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989022087801209779121989000989001099001098890109990109879122076902307779230978021087910098911208789109899120888021986812218680131877912098901009890010989900000999990999979011199889110988001109000009988900109999010997801219778032997801999891009991009881009981109980021067802409778210988001109098999010008900109900108799121886813217681140768822090910978812189691310779210779122976904296571441857012088011097902107781229869030978921078822297480332778012987892000002088881209879110990100878102197881218969120188908100020088809209799110799110888012007802219669022000000890001987992108991008981008981130068810200898091020088810199800110899000890012087791210889001000090899101987993207870120179909079021287700309788211997999999110986912317679120899110888011996903217770030089908991029967822298700209789110899120876823208690110899999800211788012996793119880908982020968812289790200899091000099889112087791209989099899110998002007891020090799102007871031079910079910089911189790199989100000219867022197810209789110898110898011907891020000808892020869922078802200779100990110879012078891200000188790309778332974803217881118880129869032077811198801109791209659244065703398680320878111878113086992207880109091217868141076822307689220897910999010998910009899900911099790111778014197771119980011080010079010090010089000197800329778022097800109900010998890009999911099790110889002109880000090000099998990109989010098901208779230976922207690219789120899010887912108901008791119780131877813198681220879010990010988901099901099890099890220878012097791219890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989011098900109889011
a＝1295，1729位素数
1098890000110999988901100000000000010879011001098899890120889999999999998912098899890110010987910999999998901219888889011111097790109999999989120988998901100109879110000000000001087901111098789990122088889011001098780111219778998913198888901208910879011001088130768119802200108769218912098888903396800978132000966912090219888780220892296691100109792187912088998911869242869097801001230670098901111096603199021867999033087909780111219779107703309998780207923087899902188130757130913078009770428800989009793396800978130913065811980329899768131892296690001328582186923089096713078142869086921979350560197912090316482309021869086935275920770210121857119792309998671417703187910892186922967020913078020649439802087909683517690978130913064724079218800978141770207800990328582296811979218813065932980196811979350560197911980427482297921870196825275920781197922968229681199020770317703188020781185835177019692188031748339802088019561528802077019803285713079218802077031759329900978119682407800979218814164713091307800868252770087911980438471197813091196703186921891087922968240669000131880206592210119681185835286908692199131747229912088019561528802186908693407813067008913186921759330999867031892307679990329802075713091307800977042880098900979339680097813091306581307921989987913188119779000132968108780221109780087913298997692199022957011110989009671321000978008693418692088998912087921880110010867031891219778890219912086701002307800977042988889012089218679110021980207681307911001098791089120988889023088998780221109779011001098888912209899879011110987911000000000000108790110010988998901208900000000109878011111098888890220989000000001087901100109889989012088999999999999891209889989011001098791100000000000010988900001109999889011
如何确定两个数是合数？找到其它素数因子吗？

太阳

如何判断1921位数是合数？
1098890000110999988901100000000000010988889012209998779011110988999999999999890111109877900012209888890108901109999890098901099010999988901089011110987790001220988889011000000000000109888890122099987790111219780098901100108791208900989000012197799890110012087899890110010988999999989011012087799880231000987910780219901099119669098924298997680208912090109889987911001220988768011122098899890087912200119779987912090329779987911880330901075701002319791087909890110012088998779011231988877901101208802087910880208913187909670220023077008681308923078008791197912090109889878022111098888780221010989008791197912090218679988033090207681088021891318691076911002319789877911111099010988888901111219888877901113308789878020891210011966909791220021977997681320021988997680210122088888900989011111098888780111122098886691210121978998900988021990209889868022002318678879121002208789889010011099010988888901111219877889001112198789989010001099011977899901110120877998791211120878997791210110989987802099011000098899879022110998887790221110988888901099011100098889879122001208788769232002197689890119902197900988998802210120866889012211109778889011111098900988888912210119767998902200230767997802200220880086702100120891197789879133110987788890221110988888901099011111087789880232001086810869230892197910768119913297899769219912088020879098901101219778889011112197789890109912088020879097813189130769096813200219670087923089119791087911979121010987788902321098778998912100109890087910880232000965810991329792087899780329912087899780210022087909889989012211097678901221001087899890109912089119767999034189008670209010990219781087901001319789977912101098899999998901100109889987912100109889978022099998900989120879110010989009780221109877900012209888890110000000000001098888901220999877901111098910988900001099010989009890000110989109888890122099987790111109889999999999998901111098779000122098888901100000000000010988900001109999889011

yangchuanju

太阳 发表于 2022-3-13 20:45
如何判断1921位数是合数？
10988900001109999889011000000000000109888890122099987790111109889999999999 ...

已在日本网站https://stdkmd.net/nrr/repunit/phin10.cgi?p=87查知：
10^4305+1 = 1000000000...<4306> = 7^2 × 11 × 13 × 127 × 211 × 241 × 739 × 2161 × 2689 × 3691 × 9091 × 148339 × 459691 × 909091 × 4147571 × 16344241 × 16419517 × 22873327 × 1309140169<10> × 29970369241<11> × 5317679142481<13> × 19214818177409<14> × 1661378260814161<16> × 3479575598798881<16> × 265212793249617641<18> × 2670502781396266997<19> × 3404193829806058997303<22> × 18276168846821336356291<23> × 2227500794590370844147583<25> × 436026711667335044426416921<27> × 6331512614238234077508187988343438690524-7847<44> × 1102678522581138741425727962459101300689-046291<46> × 1109649393276867840472199951726880949173-205522051<49> × 1843455308146833369419577117401177102515-401880306453871619994561<64> × 6105179603552296927117127487655417850454-4683763248923853725596423<65> × 2522755993328297304992975667536987368752-4422119109873612963516263168625757367193-4071328913935425167793515435649973267232-99457284056291<134> × 1257614379020165056772347240819559956723-1572995613590701680970702041170548930281-0599648062430084467242774758397202086029-812476912145657137081<141> × 5724747847...<227> × [2154768431...<396>] × [2612675210...<945>] × [1098890000...<1921>](24.28%)
其中后3个大因子都是未完全分解开的复合因子。