求证：y＝p

yangchuanju · 发表于 2022-3-14 04:57

本帖最后由 yangchuanju 于 2022-3-14 05:19 编辑

又查知
10^1435+1 = 1000000000...<1436> = 11 × 9091 × 909091 × 4147571 × 19214818177409<14> × 3479575598798881<16> × 265212793249617641<18> × 2670502781396266997<19> × 3404193829806058997303<22> × 436026711667335044426416921<27> × 2522755993328297304992975667536987368752-4422119109873612963516263168625757367193-4071328913935425167793515435649973267232-99457284056291<134> × 5724747847...<227> × [2612675210...<945>](34.19%)

yangchuanju · 发表于 2022-3-14 04:58

本帖最后由 yangchuanju 于 2022-3-14 05:22 编辑

计算知
(10^4305+1) / (10^1435+1) = (10^2870-10^1435+1) = 7^2 × 13 × 127 × 211 × 241 × 739 × 2161 × 2689 × 3691 × 148339 × 459691 × 16344241 × 16419517 × 22873327 × 1309140169<10> × 29970369241<11> × 5317679142481<13> × 1661378260814161<16> × 18276168846821336356291<23> × 2227500794590370844147583<25> × 6331512614238234077508187988343438690524-7847<44> × 1102678522581138741425727962459101300689-046291<46> × 1109649393276867840472199951726880949173-205522051<49> × 1843455308146833369419577117401177102515-401880306453871619994561<64> × 6105179603552296927117127487655417850454-4683763248923853725596423<65> × 1257614379020165056772347240819559956723-1572995613590701680970702041170548930281-0599648062430084467242774758397202086029-812476912145657137081<141> × [2154768431...<396>] × [1098890000...<1921>](24.28%)

(10^2870-10^1435+1) ÷9999900001 = 7 × 127 × 739 × 2689 × 3691 × 148339 × 459691 × 16344241 × 16419517 × 22873327 × 1309140169<10> × 29970369241<11> × 5317679142481<13> × 1661378260814161<16> × 18276168846821336356291<23> × 2227500794590370844147583<25> × 6331512614238234077508187988343438690524-7847<44> × 1102678522581138741425727962459101300689-046291<46> × 1109649393276867840472199951726880949173-205522051<49> × 1843455308146833369419577117401177102515-401880306453871619994561<64> × 6105179603552296927117127487655417850454-4683763248923853725596423<65> × 1257614379020165056772347240819559956723-1572995613590701680970702041170548930281-0599648062430084467242774758397202086029-812476912145657137081<141> × [2154768431...<396>] × [1098890000...<1921>](24.28%)

yangchuanju · 发表于 2022-3-14 05:08

本帖最后由 yangchuanju 于 2022-3-14 05:24 编辑

又经计算知，你的940位的m等于
7 × 127 × 739 × 2689 × 3691 × 148339 × 459691 × 16344241 × 16419517 × 22873327 × 1309140169<10> × 29970369241<11> × 5317679142481<13> × 1661378260814161<16> × 18276168846821336356291<23> × 2227500794590370844147583<25> × 6331512614238234077508187988343438690524-7847<44> × 1102678522581138741425727962459101300689-046291<46> × 1109649393276867840472199951726880949173-205522051<49> × 1843455308146833369419577117401177102515-401880306453871619994561<64> × 6105179603552296927117127487655417850454-4683763248923853725596423<65> × 1257614379020165056772347240819559956723-1572995613590701680970702041170548930281-0599648062430084467242774758397202086029-812476912145657137081<141> × [2154768431...<396>]

相除后的y就是复合因子[1098890000...<1921>]啦。

yangchuanju · 发表于 2022-3-14 05:16

本帖最后由 yangchuanju 于 2022-3-14 09:00 编辑

尽管[1098890000...<1921>]没有被分解开，但网站已经确定它不是素数。

网站中的分解数据凡是放在方括号[]中的数据都是未完全分解开的复合因子。

[1098890000...<1921>]是10^8610-1的一个φ因子,
Φ8610(10) = 1098890000...<1921> = [1098890000...<1921>](0.00%)

以上各表中大于40位的素因子中都有1个或几个连字符“-”，在那里不是减号，用于计算时必须删除！

yangchuanju · 发表于 2022-3-14 05:29

又经计算知940位的m中有一个396位复合因子[2154768431...<396>]，它的展开式是：
215476843101610319550520023786563607467798392970033529187472677043962164134586204643191638038990671893872249418985947814522772479498861097561552618741871389773873011424181295373843417104379455110381335300775945300788132826422279147318170735511934890017003002488055533008936852550253197286470082906369200798643292375799040579148623970671273167060664600820704191805608369299193104439303773379423157——396位

太阳 · 发表于 2022-3-14 08:11

a＝1265，1761位素数
109889010998901109890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989022087801209779121989000989001099001098890109990109879122076902307779230978021087910098911208789109899120888021986812218680131877912098901009890010989900000999990999979011199889110988001109000009988900109999010997801219778032997801999891009991009881009981109980021067802409778210988001109098999010008900109900108799121886813217681140768822090910978812189691310779210779122976904296571441857012088011097902107781229869030978921078822297480332778012987892000002088881209879110990100878102197881218969120188908100020088809209799110799110888012007802219669022000000890001987992108991008981008981130068810200898091020088810199800110899000890012087791210889001000090899101987993207870120179909079021287700309788211997999999110986912317679120899110888011996903217770030089908991029967822298700209789110899120876823208690110899999800211788012996793119880908982020968812289790200899091000099889112087791209989099899110998002007891020090799102007871031079910079910089911189790199989100000219867022197810209789110898110898011907891020000808892020869922078802200779100990110879012078891200000188790309778332974803217881118880129869032077811198801109791209659244065703398680320878111878113086992207880109091217868141076822307689220897910999010998910009899900911099790111778014197771119980011080010079010090010089000197800329778022097800109900010998890009999911099790110889002109880000090000099998990109989010098901208779230976922207690219789120899010887912108901008791119780131877813198681220879010990010988901099901099890099890220878012097791219890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989011098900109889011
如果它是合数，是否能找到一个素数因子？

yangchuanju · 发表于 2022-3-14 08:19

10^3795+1 = 1000000000...<3796> = 7 × 11^2 × 13 × 23^2 × 47 × 139 × 211 × 241 × 331 × 691 × 2161 × 2531 × 4093 × 5171 × 8779 × 9091 × 31051 × 176089 × 6866927 × 11313931 × 599144041 × 4124507971<10> × 20163494891<11> × 127688571001<12> × 183411838171<12> × 194656286401<12> × 272168891611<12> × 143574021480139<15> × 549797184491917<15> × 776471438412978001<18> × 134411715692212607377411<24> × 318727841165674579776721<24> × 19835636682880495867311241<26> × 24649445347649059192745899<26> × 2832165561296805799533565929552471103<37> × 1112314101311286003379752617807870409611-285281<46> × 7386441591567953769105190285927615814299-177561<46> × 1591879884384947756889998393793196655587-7132981347465830696251648192619376266439-940521<86> × 4381032561373952229810899174127764174713-7547565878057174130075470872858289958280-148759277150273598401<101> × 5181616821054419379398089043147253841557-1334188381106616809835077169803782358320-2138442087113080605799348512678760456904-9916282420132402437223582964524090767945-91284845951908904139995059681<189> × [8634288537...<369>] × [9091000000...<880>] × [1098890109...<1761>](20.71%)

yangchuanju · 发表于 2022-3-14 08:29

Φ7590(10) = 1098890109...<1761> = [1098890109...<1761>](0.00%)

太阳 · 发表于 2022-3-14 08:32

yangchuanju 发表于 2022-3-14 08:19
10^3795+1 = 1000000000... = 7 × 11^2 × 13 × 23^2 × 47 × 139 × 211 × 241 × 331 × 691 × 2161 ...

日本网站https://stdkmd.net/nrr/repunit/phin10.cgi?p=87
网站怎么打不开？

yangchuanju · 发表于 2022-3-14 09:07

太阳发表于 2022-3-14 08:32
日本网站https://stdkmd.net/nrr/repunit/phin10.cgi?p=87
网站怎么打不开？

试试网页Factorization of near-repdigit-related numbers
https://stdkmd.net/nrr/
中的9.1 Repunit
Factorization of 11...11 (Repunit)
Factorization of 100...001
Factorization of cyclotomic number Φn(10)
怎么样？

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