f取值7，13，17，19，23，有可能都是正确

太阳

f取值7，13，17，19，23，有可能都是正确

yangchuanju

太阳先生的说法无道理
太阳先生认为：只要满足1楼所给条件，m-k必定是素数。
须知，9*10^a+1=900…01型正整数既有素数，又有合数，且大量的是合数。
若900…01是素数，题目所给代数式无意义。
若900…01是一个双因子合数，则第一代数式成立，900…01可分解成两个双因子m和f的乘积，第二代数式仍是无意义的。
只有900…01是三因子素数时，两代数式才有一定的数学价值，此时900…01=m*(m-k)*v，m-v必定是素数。然而此工况又不满足m取最小值的要求。
须知，更多的900…01型正整数的素因子个数多于3，此时若f是一个最小素因子，则m的素因子个数多于2；在k尽量大，m-k最小时，m-k会是一个次小素数，这时y仍是合数；或者y是一个次小素数，那么m-k就不是素数了。
还有，900…01中不一定含素因子7,13,17,19,23。
总起来说，这种命题无数学价值，题目中的各种关系无道理。

太阳

9000...01，你给出140位数据值，没有找到反例存在

太阳

yangchuanju：给出数据值
数字        分解式
91        91=P1 * P2
        P1 = 7
        P2 = 13
901        901=P2 * P2
        P2 = 17
        P2 = 53
9001        9001 is prime
90001        90001 is prime
900001        900001 is prime
9000001        9000001=P2 * P6
        P2 = 61
        P6 = 147541
90000001        90000001=P1 * P2 * P6
        P1 = 7
        P2 = 13
        P6 = 989011
900000001        900000001=P3 * P7
        P3 = 409
        P7 = 2200489
9000000001        9000000001 is prime
90000000001        90000000001=P3 * P9
        P3 = 113
        P9 = 796460177
9E+11        900000000001=P6 * P7
        P6 = 634939
        P7 = 1417459
9E+12        9000000000001=P7 * P7
        P7 = 1072157
        P7 = 8394293
9E+13        90000000000001=P1 * P2 * P3 * P10
        P1 = 7
        P2 = 13
        P3 = 103
        P10 = 9602048437
9E+14        900000000000001=P4 * P12
        P4 = 1097
        P12 = 820419325433
9E+15        9000000000000001=P2 * P2 * P13
        P2 = 23
        P2 = 53
        P13 = 7383100902379
9E+16        90000000000000001=P2 * P5 * P6 * P6
        P2 = 29
        P5 = 12553
        P6 = 286469
        P6 = 863017
9E+17        900000000000000001=P2 * P17
        P2 = 19
        P17 = 47368421052631579
9E+18        9000000000000000001=P2 * P3 * P6 * P11
        P2 = 17
        P3 = 173
        P6 = 264601
        P11 = 11565276061
9E+19        90000000000000000001=P1 * P2 * P7 * P12
        P1 = 7
        P2 = 13
        P7 = 9642641
        P12 = 102566401571
9E+20        900000000000000000001=P10 * P12
        P10 = 1669850621
        P12 = 538970365781
9E+21        9000000000000000000001=P6 * P17
        P6 = 101477
        P17 = 88690047991170413
9E+22        90000000000000000000001 is prime
9E+23        900000000000000000000001=P2 * P2 * P3 * P18
        P2 = 59
        P2 = 89
        P3 = 419
        P18 = 409059485884947929
9E+24        9000000000000000000000001=P4 * P5 * P18
        P4 = 1277
        P5 = 34781
        P18 = 202632707706349273
9E+25        90000000000000000000000001=P1 * P2 * P24
        P1 = 7
        P2 = 13
        P24 = 989010989010989010989011
9E+26        900000000000000000000000001=P6 * P10 * P12
        P6 = 876653
        P10 = 2462224309
        P12 = 416953065713
9E+27        9000000000000000000000000001 is prime
9E+28        90000000000000000000000000001=P2 * C28
        P2 = 53
        C28 = 1698113207547169811320754717
9E+29        900000000000000000000000000001 is not prime
9E+30        9000000000000000000000000000001=P3 * P7 * P22
        P3 = 661
        P7 = 9338569
        P22 = 1458010722709494472789
9E+31        90000000000000000000000000000001=P1 * P2 * P3 * P4 * P8 * P17
        P1 = 7
        P2 = 13
        P3 = 487
        P4 = 1493
        P8 = 28195807
        P17 = 48242279334679103
9E+32        900000000000000000000000000000001=P5 * P5 * P25
        P5 = 16901
        P5 = 48817
        P25 = 1090834891658648232287453
9E+33        9000000000000000000000000000000001=P2 * P9 * P10 * P15
        P2 = 47
        P9 = 909983219
        P10 = 1065587651
        P15 = 197479531885607
9E+34        90000000000000000000000000000000001=P2 * P8 * P27
        P2 = 17
        P8 = 41043601
        P27 = 128987650159127692753171553
9E+35        900000000000000000000000000000000001=P2 * P4 * P14 * P19
        P2 = 19
        P4 = 1289
        P14 = 36477404545339
        P19 = 1007423463151225049
9E+36        9000000000000000000000000000000000001 is prime
9E+37        90000000000000000000000000000000000001=P1 * P1 * P2 * P2 * P5 * P6 * P24
        P1 = 7
        P1 = 7
        P2 = 13
        P2 = 23
        P5 = 87407
        P6 = 197339
        P24 = 356136186044107373212487
9E+38        900000000000000000000000000000000000001 is not prime
9E+39        9000000000000000000000000000000000000001=P5 * P36
        P5 = 38201
        P36 = 235595926808198738252925316091201801
9E+40        90000000000000000000000000000000000000001=P4 * C38
        P4 = 4129
        C38 = 21797045289416323565027851780092031969
9E+41        900000000000000000000000000000000000000001=P2 * P5 * P36
        P2 = 53
        P5 = 31081
        P36 = 546350892039242563405538662520875157
9E+42        9000000000000000000000000000000000000000001=P7 * C37
        P7 = 1032841
        C37 = 8713829137301869309990598746564088761
9E+43        90000000000000000000000000000000000000000001=P1 * P2 * C42
        P1 = 7
        P2 = 13
        C42 = 989010989010989010989010989010989010989011
9E+44        900000000000000000000000000000000000000000001=P2 * P2 * P3 * P4 * P5 * P8 * P24
        P2 = 29
        P2 = 97
        P3 = 313
        P4 = 8641
        P5 = 11813
        P8 = 16493429
        P24 = 607146191816885557369397
9E+45        9000000000000000000000000000000000000000000001=P4 * P10 * P11 * P24
        P4 = 1303
        P10 = 5532177317
        P11 = 10909587209
        P24 = 114444172630926939804739
9E+46        90000000000000000000000000000000000000000000001=P5 * P43
        P5 = 40697
        P43 = 2211465218566479101653684546772489372681033
9E+47        900000000000000000000000000000000000000000000001=P3 * P46
        P3 = 103
        P46 = 8737864077669902912621359223300970873786407767
9E+48        9000000000000000000000000000000000000000000000001 is not prime
9E+49        90000000000000000000000000000000000000000000000001=P1 * P2 * C48
        P1 = 7
        P2 = 13
        C48 = 989010989010989010989010989010989010989010989011
9E+50        900000000000000000000000000000000000000000000000001=P2 * P6 * P45
        P2 = 17
        P6 = 185177
        P45 = 285894989499712357874453344955494091662380889
9E+51        9000000000000000000000000000000000000000000000000001=P4 * P49
        P4 = 5303
        P49 = 1697152555157458042617386385065057514614369224967
9E+52        90000000000000000000000000000000000000000000000000001=P6 * C48
        P6 = 535637
        C48 = 168024240297066856845214202902338710731334840573
9E+53        900000000000000000000000000000000000000000000000000001=P2 * P3 * P3 * P9 * P39
        P2 = 19
        P3 = 317
        P3 = 373
        P9 = 621654619
        P39 = 644423915856720982631763433468126261601
9E+54        9000000000000000000000000000000000000000000000000000001=P2 * C54
        P2 = 53
        C54 = 169811320754716981132075471698113207547169811320754717
9E+55        90000000000000000000000000000000000000000000000000000001=P1 * P2 * C54
        P1 = 7
        P2 = 13
        C54 = 989010989010989010989010989010989010989010989010989011
9E+56        900000000000000000000000000000000000000000000000000000001=P5 * P53
        P5 = 22349
        P53 = 40270258177099646516622667680880576312139245603830149
9E+57        9000000000000000000000000000000000000000000000000000000001 is prime
9E+58        90000000000000000000000000000000000000000000000000000000001=P7 * C53
        P7 = 2836549
        C53 = 31728695679150968306910968222301113077898530926135949
9E+59        900000000000000000000000000000000000000000000000000000000001=P2 * P2 * P3 * P6 * P50
        P2 = 23
        P2 = 23
        P3 = 223
        P6 = 433241
        P50 = 17609718952061731403087007685427467197151800957383
9E+60        9000000000000000000000000000000000000000000000000000000000001=P8 * P12 * P13 * P30
        P8 = 52069729
        P12 = 165220125649
        P13 = 2903138521729
        P30 = 360351625548496622538364964689
9E+61        90000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P2 * P3 * C57
        P1 = 7
        P2 = 13
        P2 = 13
        P3 = 173
        C57 = 439755886621160076028906620280564255664300128506442423739
9E+62        900000000000000000000000000000000000000000000000000000000000001 is prime
9E+63        9000000000000000000000000000000000000000000000000000000000000001=P7 * P7 * P51
        P7 = 1846367
        P7 = 6443011
        P51 = 756546466489705346851565812353711496009046424433973
9E+64        90000000000000000000000000000000000000000000000000000000000000001=P3 * C63
        P3 = 509
        C63 = 176817288801571709233791748526522593320235756385068762278978389
9E+65        900000000000000000000000000000000000000000000000000000000000000001=P4 * P4 * P59
        P4 = 4721
        P4 = 7459
        P59 = 25558060971253457331200579406921787420600688835179728118459
9E+66        9000000000000000000000000000000000000000000000000000000000000000001=P2 * P2 * C64
        P2 = 17
        P2 = 61
        C64 = 8678881388621022179363548698167791706846673095467695274831243973
9E+67        90000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P2 * P2 * P3 * P60
        P1 = 7
        P2 = 13
        P2 = 53
        P2 = 89
        P3 = 967
        P60 = 216824706300274768218062939196360764018857398893392710120649
9E+68        900000000000000000000000000000000000000000000000000000000000000000001=P10 * P60
        P10 = 1937018929
        P60 = 464631494574310378357691309892201884620818798410410371369169
9E+69        9000000000000000000000000000000000000000000000000000000000000000000001=P6 * P14 * C51
        P6 = 223849
        P14 = 56519161534037
        C51 = 711363602530245908762799315716791946722922712239477
9E+70        90000000000000000000000000000000000000000000000000000000000000000000001=P6 * P66
        P6 = 177481
        P66 = 507096534276908514150810509293952592108451045464021500893053340921
9E+71        900000000000000000000000000000000000000000000000000000000000000000000001=P2 * P10 * C62
        P2 = 19
        P10 = 1021624687
        C62 = 46365775666334870926399629037773613381142209078813674896413717
9E+72        9000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P7 * P15 * C51
        P2 = 29
        P7 = 1193737
        P15 = 369568350763637
        C51 = 703462716197286561893566473716153635964886210257401
9E+73        90000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P3 * P3 * P10 * P20 * P39
        P1 = 7
        P2 = 13
        P3 = 131
        P3 = 157
        P10 = 3434714219
        P20 = 40505281728310780921
        P39 = 345643109794933143493746424616869980967
9E+74        900000000000000000000000000000000000000000000000000000000000000000000000001=P5 * P71
        P5 = 26513
        P71 = 33945611586768754950401689737110096933579753328555802813714027081054577
9E+75        9000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P5 * C69
        P3 = 761
        P5 = 27259
        C69 = 433858322793388134138773633889811266326872042020239105106469073445899
9E+76        90000000000000000000000000000000000000000000000000000000000000000000000000001=P8 * P70
        P8 = 39191309
        P70 = 2296427506414751290904827904574455525330883946744417238015703940891589
9E+77        900000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P3 * P10 * P63
        P3 = 797
        P3 = 997
        P10 = 1347545921
        P63 = 840514975997107693570604695977849746413871622498980856073069009
9E+78        9000000000000000000000000000000000000000000000000000000000000000000000000000001 is prime
9E+79        90000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P1 * P2 * P2 * P4 * P6 * P9 * P58
        P1 = 7
        P1 = 7
        P2 = 13
        P2 = 47
        P4 = 1361
        P6 = 939179
        P9 = 362132527
        P58 = 6494282636470574357798239086613389616047164558265238476143
9E+80        900000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P7 * C73
        P2 = 53
        P7 = 7228517
        C73 = 2349186157474859381697178988416478892519306675501416362182340796482848601

太阳

900...01分解式（含81-140个0）：
9E+80        900000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P7 * C73
        P2 = 53
        P7 = 7228517
        C73 = 2349186157474859381697178988416478892519306675501416362182340796482848601
9E+81        9000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P2 * P3 * P4 * P5 * P69
        P2 = 23
        P2 = 59
        P3 = 103
        P4 = 9539
        P5 = 15569
        P69 = 433572640799482999983753283405797953951283348120523679061716819187841
9E+82        90000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P3 * P7 * P15 * C59
        P2 = 17
        P3 = 197
        P7 = 4373989
        P15 = 444342046542949
        C59 = 13827136953803135915227779562819305309247744855725029151109
9E+83        900000000000000000000000000000000000000000000000000000000000000000000000000000000001=P8 * P8 * P11 * P58
        P8 = 73235077
        P8 = 82599773
        P11 = 43082588561
        P58 = 3453366913153286556653523424034883035479542624501723609121
9E+84        9000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P6 * C77
        P4 = 1229
        P6 = 166349
        C77 = 44022067166610283366084365425399101982112650405733539680740523170278906355481
9E+85        90000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * C84
        P1 = 7
        P2 = 13
        C84 = 989010989010989010989010989010989010989010989010989010989010989010989010989010989011
9E+86        900000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P7 * P8 * C74
        P7 = 2684897
        P8 = 16342553
        C74 = 20511384588721237948664065474561600385631983983167661345986948771736735561
9E+87        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P9 * C77
        P3 = 887
        P9 = 386371357
        C77 = 26261163668678774102910222964726950487592747255637280662376555551200627554739
9E+88        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * C87
        P3 = 769
        C87 = 117035110533159947984395318595578673602080624187256176853055916775032509752925877763329
9E+89        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P4 * P4 * P83
        P2 = 19
        P4 = 1013
        P4 = 1637
        P83 = 28564773432627871239776865954944655910167469236294439209861550034422138918173953059
9E+90        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P4 * C84
        P4 = 1913
        P4 = 6353
        C84 = 740540276792562079285697888036728164696815816689622043876353141935487586940457023609
9E+91        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P3 * P6 * C82
        P1 = 7
        P2 = 13
        P3 = 823
        P6 = 288931
        C82 = 4159174494750921523372414780632662165069892884998547063789420925456629331456173047
9E+92        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P10 * C84
        P10 = 1645448113
        C84 = 546963464170930074171229731143761687245619029738435757044135976349683899148268068177
9E+93        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P4 * C89
        P2 = 53
        P4 = 3253
        C89 = 52201451200343369545673369719678207054156105539734004605328028119181713251628395269388489
9E+94        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P11 * C82
        P4 = 6113
        P11 = 13693948969
        C82 = 1075126108696142426199572830688768662376780750405651587919247117002743359677355833
9E+95        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 is not prime
9E+96        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * C95
        P3 = 821
        C95 = 10962241169305724725943970767356881851400730816077953714981729598051157125456760048721071863581
9E+97        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P5 * C92
        P1 = 7
        P2 = 13
        P5 = 11251
        C92 = 87904274198825794239535240335169230378545106124876811926851923296683762420141408675761177761
9E+98        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P6 * P10 * P83
        P2 = 17
        P6 = 665117
        P10 = 1302994037
        P83 = 61087606833217334930936140025570390625015013586542691774287192644976828132114177457
9E+99        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P7 * P92
        P3 = 647
        P7 = 1159303
        P92 = 11998895445679379799918978391750473540741698203219135396897417073903734149720758838785348561
9E+100        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P5 * P6 * P7 * P83
        P2 = 29
        P5 = 44497
        P6 = 852673
        P7 = 6267889
        P83 = 13049983777688172742896635745449048831681908684773511663795549758829314812199285941
9E+101        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P4 * C96
        P3 = 929
        P4 = 1087
        C96 = 891245297443215296145958252089722654366161198546676001635930257084657410259025591613579805569887
9E+102        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P4 * P8 * P9 * P10 * P13 * P59
        P3 = 857
        P4 = 4729
        P8 = 27724157
        P9 = 146688169
        P10 = 7824928201
        P13 = 1082959301461
        P59 = 64438650881125819456903404728709964010133394499896709654209
9E+103        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P2 * C101
        P1 = 7
        P2 = 13
        P2 = 23
        C101 = 43000477783086478738652651696129956999522216913521261347348303870043000477783086478738652651696129957
9E+104        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P6 * P98
        P3 = 173
        P6 = 401017
        P98 = 12972797010421811792073566252600451214059928931270279995193146281071704670643674584536446143483661
9E+105        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P6 * C101
        P6 = 146173
        C101 = 61570878342785603360401715775143152292146976527812933989177207829079241720427165071524837008202609237
9E+106        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P3 * P3 * C101
        P2 = 53
        P3 = 109
        P3 = 601
        C101 = 25921830703371594915519313636006229303938361342831476130170217141415395320879141768508259127292605913
9E+107        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P12 * C96
        P2 = 19
        P12 = 140725352693
        C96 = 336601899701529703434021871004838007731653651820999518518992617044366642164251527562746976439503
9E+108        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P6 * P7 * C97
        P6 = 373777
        P7 = 4126417
        C97 = 5835214450292052431336126474646284560227499398302155339750431004300338522096120621448455426681889
9E+109        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P8 * P8 * P94
        P1 = 7
        P2 = 13
        P8 = 18480611
        P8 = 36737531
        P94 = 1456715783890529448958356929556268261049304839622936526296628689514369386951968743985378548771
9E+110        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P6 * C106
        P6 = 535741
        C106 = 1679916228177421552578578081572998893121862989765577023225775141346284865261385632236472474572601312947861
9E+111        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * C111
        P2 = 89
        C111 = 101123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550561797752809
9E+112        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 is not prime
9E+113        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P5 * P7 * C104
        P5 = 22699
        P7 = 1184459
        C104 = 33474627453340210450558941161791675296296994782280919086160013356355525225661891419848286880377772846761
9E+114        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * C114
        P2 = 17
        C114 = 529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353
9E+115        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P3 * P7 * C106
        P1 = 7
        P2 = 13
        P3 = 103
        P7 = 3391343
        C106 = 2831340987036667571098801337230607550125181781769048544470896338148836442399891898973267857546594570354459
9E+116        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P6 * C108
        P4 = 3917
        P6 = 719189
        C108 = 319481637436666301862417530975811618189214620608706212631721564718698248156838639004348142600655848305387377
9E+117        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P5 * C114
        P5 = 12527
        C114 = 718448151991697932465873712780394348207870998642931268460126127564460764748144008940688113674463159575317314600463
9E+118        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P6 * C114
        P6 = 196073
        C114 = 459012714652195865825483365889235131813151224288912802884639904525355352343259908299459895039092582864545347906137
9E+119        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P6 * C114
        P2 = 53
        P6 = 141413
        C114 = 120081831765620544880651334529437327223925531118606292901736103096390086631036163444181761731227774020402436914009
9E+120        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 is not prime
9E+121        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P1 * P2 * P4 * P5 * P5 * P6 * C101
        P1 = 7
        P1 = 7
        P2 = 13
        P4 = 8329
        P5 = 13099
        P5 = 45779
        P6 = 398459
        C101 = 70994079165901357774302508596374222973187651738164763773225091228534809576347428381458718947064150183
9E+122        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P3 * P7 * C113
        P3 = 113
        P3 = 229
        P7 = 2618281
        C113 = 13283494167595707594701695021323613648294145264418189068744715504356629299697769452353777609855703091779894048373
9E+123        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P4 * P5 * P8 * P105
        P4 = 2383
        P4 = 5569
        P5 = 35081
        P8 = 28502281
        P105 = 678249788730965343155876794263068283826182488644313608841077587266701477227270380314651873177483730318783
9E+124        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P12 * P12 * P103
        P12 = 168745086793
        P12 = 360847422557
        P103 = 1478045369332241890902656097128029833077561869578361464994129936119444146965960462980286762223022100301
9E+125        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P2 * P2 * P4 * P7 * P113
        P2 = 19
        P2 = 23
        P2 = 47
        P4 = 1091
        P7 = 2340179
        P113 = 17162849181227637954686586305558908249546272559153601351238220969425254370779811594520448516673293863019660069131
9E+126        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P4 * P7 * C116
        P2 = 61
        P4 = 1609
        P7 = 4480517
        C116 = 20465789404222357840404381875745801274688927352651621232555433527637138892346348967984191087403221105854908526202697
9E+127        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P3 * P3 * P4 * P9 * P111
        P1 = 7
        P2 = 13
        P3 = 167
        P3 = 401
        P4 = 1289
        P9 = 112974047
        P111 = 101416511916384986434377207218778382110001626648805153438789813840049798877618436058332277078236972412647025251
9E+128        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P4 * P4 * P8 * P113
        P2 = 29
        P4 = 2833
        P4 = 6121
        P8 = 19705421
        P113 = 90821744521678073858476364997021996717514800118315880931365217585390573943501211754500252286470470063005559638673
9E+129        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P5 * P7 * C120
        P5 = 32801
        P7 = 2379277
        C120 = 115321536164667735888492935425573063879167720081542955638813507247273800701381449317112867250303185722672231194163915813
9E+130        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P5 * C126
        P2 = 17
        P5 = 24593
        C126 = 215269289922287786338054109131962466603361549556186480610216680499711778339604048019402938664995539141936610369760883656516321
9E+131        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 is not prime
9E+132        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P3 * C129
        P2 = 53
        P3 = 317
        C129 = 535682399857151360038092970656508541158264389024462829593476578775072912326647223379560740432117135884768763764061662996250223201
9E+133        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * C132
        P1 = 7
        P2 = 13
        C132 = 989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011
9E+134        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P3 * P4 * P11 * P120
        P3 = 181
        P4 = 2753
        P11 = 16531089961
        P120 = 109258751591334591151303372851647591688655864712545289987012012810113495421933518921235388716934090390154756359979711637
9E+135        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P7 * P10 * C117
        P4 = 5927
        P7 = 3426823
        P10 = 4329778969
        C117 = 102341124002116886890802769572431620180185546879491021271962594087713193270517160649114163216150099920249933560241049
9E+136        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P5 * P5 * C129
        P5 = 10037
        P5 = 17333
        C129 = 517326646039550392331618841935447509765129621565614254317238874101553784258498560231085444249745048495665558577899169944223163081
9E+137        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P5 * C134
        P5 = 12487
        C134 = 72074957956274525506526787859373748698646592456154400576599663650196204052214302874989989589172739649235204612797309201569632417714423
9E+138        9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P4 * P5 * P5 * C127
        P4 = 2477
        P5 = 16193
        P5 = 95401
        C127 = 2351994273131163932011470571366592962213409754392142945080247744180276601507505786882653964394865333813159089372234186818386141
9E+139        90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P1 * P2 * P2 * P2 * P10 * C126
        P1 = 7
        P2 = 13
        P2 = 13
        P2 = 59
        P10 = 4424608127
        C126 = 291427774943488532047152968430812186544474227918461927420354897872451236915447049045959903935550375259390389351446759644503379
9E+140        900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=P2 * P3 * P3 * P4 * C131
        P2 = 97
        P3 = 149
        P3 = 293
        P4 = 4733
        C131 = 44903519496482035685920893374806943061833411079228781276315961742360447241922023072917417784572160800690565957656776306254923604493

太阳

yangchuanju 发表于 2021-3-6 16:03
太阳先生的说法无道理
太阳先生认为：只要满足1楼所给条件，m-k必定是素数。
须知，9*10^a+1=900…01型正 ...

900…01必定含素因子7,13,17,19,23，命题是正确，条件是必定含7，13，17，19，23
你给出140位数据900...01，我已经查看过了，没有反例存在

太阳

试除法找素数，(9*10a+1)/f=m，取7为例，(9*10a+1)/7=m，m取整数，这里使用试除法
9E+31为例
9E+31        90000000000000000000000000000001=P1 * P2 * P3 * P4 * P8 * P17
P1 = 7
P2 = 13  
P3 = 487
P4 = 1493
P8 = 28195807
P17 = 48242279334679103
试除法确定：含有7素数因子，
例：90000000000000000000000000000001/7=m=13*487*1493*28195807*48242279334679103
m/(m-k)=y，y取正整数，k取最小值，验证：m-k是不是素数？
P2 *P3* P4 * P8<P17，m-k必定是素数
如果m-k是合数，必定有P3 * P4 * P8>P17
通过检验可知：P2* P3 * P4 * P8<P17，m-k必定是素数
网友：给出900...01，140位数据中，验证：m-k都是素数

太阳

900...01，140位数据，没有找到一个反例

太阳

给出例子：m-k必定是合数
100000000001/11=m=11*23*4093*8779
m/(m-k)=y，y取正整数，k取最小值，验证：m-k是不是素数？
检验：11*23*4093>8779，m-k必定是合数

太阳