求证：y＝p

太阳

太阳 发表于 2022-3-14 08:11
a＝1265，1761位素数
1098890109989011098900098900109900109889010999010998901108790120888912098791109 ...

日本的专业网站已确定它不是素数，但未能分解，没有找到其它素数因子，有可能它是素数

yangchuanju

太阳 发表于 2022-3-14 09:40
日本的专业网站已确定它不是素数，但未能分解，没有找到其它素数因子，有可能它是素数

当今时代，判定一个整数是不是素数已有多种专门的判断方法，准确度极高，可以判断数千万位整数；对于1761位整数不再话下。
但整数分解远远跟不上，相当多200多位的整数都不能完全分解。
你的那几个大数中没有素数，不用再盼望它们中还可能有素数存在！

yangchuanju

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？

从您提供的一些数据看，网页factordb.com您是能够打开的，
http://www.factordb.com/tables.php?open=6
依次点击网页中的Factor tables、Depression、Dwpression 1(0)w1右侧的Show
打开网页http://www.factordb.com/index.php?query=10%5Ex%2B1
也可以搜索到10^x+1的分解式。

yangchuanju

太阳 发表于 2022-3-14 09:40
日本的专业网站已确定它不是素数，但未能分解，没有找到其它素数因子，有可能它是素数

给太阳先生提供几个万位大素数，它们来自：       
10^246362-1        p122365_1099999999_583530053（位数_首10位数字_但最后的9-10位数字不是素因子的尾部数字，可能是存放该因子的地址）
10^217500-1        p28000_9999999999_849356182
10^246500-1        p44801_1000000000_810990544
10^231620-1        p44929_2796099999_3413207923
10^214398-1        p69552_9990010000_4001152018
10^237498-1        p75680_9100000000_1960547188
10^212014-1        p91960_9090909091_4014757097

太阳

a＝1265，1761位素数
109889010998901109890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989022087801209779121989000989001099001098890109990109879122076902307779230978021087910098911208789109899120888021986812218680131877912098901009890010989900000999990999979011199889110988001109000009988900109999010997801219778032997801999891009991009881009981109980021067802409778210988001109098999010008900109900108799121886813217681140768822090910978812189691310779210779122976904296571441857012088011097902107781229869030978921078822297480332778012987892000002088881209879110990100878102197881218969120188908100020088809209799110799110888012007802219669022000000890001987992108991008981008981130068810200898091020088810199800110899000890012087791210889001000090899101987993207870120179909079021287700309788211997999999110986912317679120899110888011996903217770030089908991029967822298700209789110899120876823208690110899999800211788012996793119880908982020968812289790200899091000099889112087791209989099899110998002007891020090799102007871031079910079910089911189790199989100000219867022197810209789110898110898011907891020000808892020869922078802200779100990110879012078891200000188790309778332974803217881118880129869032077811198801109791209659244065703398680320878111878113086992207880109091217868141076822307689220897910999010998910009899900911099790111778014197771119980011080010079010090010089000197800329778022097800109900010998890009999911099790110889002109880000090000099998990109989010098901208779230976922207690219789120899010887912108901008791119780131877813198681220879010990010988901099901099890099890220878012097791219890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989011098900109889011
这个数一定是素数，不可能是合数，找不到素数因子

yangchuanju

太阳 发表于 2022-3-14 15:10
a＝1265，1761位素数
1098890109989011098900098900109900109889010999010998901108790120888912098791109 ...

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

3个放在方括号内的数字都是合数！不要怀疑它啦。
它是7590（=1265*3*2）的复合φ因子，至今尚没有找到如何素因子：
Φ7590(10) = 1098890109...<1761> = [1098890109...<1761>] (0.00%)

太阳

11881位，它是合数，找到素数因子2501251
109889010998901109890009890010990010988901099901099890110879012088891209879110989001099001098890109990109989009989022087
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890099890110989001098890109999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999890110989001098890109990109989009989011098900
098900109889120987911108790120889010998900998901109890009890010990010977912198790220878010999010998900998901109890009890
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yangchuanju

太阳 发表于 2022-3-14 22:05
11881位，它是合数，找到素数因子2501251
109889010998901109890009890010990010988901099901099890110879 ...

经查证，2501251是φ3450（10）的一个φ因子，最早出现在R3450=(10^3450-1)/9中，在10^1725+1中也有它的身影。
但R3450只有3450位，10^1725+1只有1726位，11881位的大合数不会是它们。
由于2501251最早出现在R3450中，以后将分别出现在R（3450*k）之中，k是正整数；但10^3450+1中没有素因子2501251，10^5175+1中有素因子2501251，10^6900+1中又没有；更大一点，10^12075+1中也有素因子2501251，12075=1725*7。
按照太阳先生的“素数公式”体系，11881位的大合数应该是10^12075+1的某些素因子或复合因子的乘积，其中包含有素因子2501251。
请太阳先生提供您的11881位大数来自何处。

太阳

11881位
(10^12650-10^6325+1)