TopCoder Statistics - Problem Statement

Problem Statement

In this problem a number is called an antiprime if it does not have any subsequence of digits which is a prime.

For example, 446, 18, and 844 are antiprimes, but 346, 181, and 222 are not. In particular, note that 181 is not an antiprime because its digits contain the subsequence 11 which is a prime.

You are given a String N representing a big integer N. You are also given an int D that is at most 8.

Let X be the number of antiprimes that have exactly N digits and each of those digits is between 1 and D, inclusive. Since X can be very large, compute and return the value (X modulo 1,000,000,007).

Definition

Class:: AntiprimeNumbers
Method:: countAntiPrimes
Parameters:: String, int
Returns:: int
Method signature:: int countAntiPrimes(String N, int D)
(be sure your method is public)

Notes

A positive integer is a prime if it has exactly two positive integer divisors. The smallest few primes are 2, 3, 5, 7, 11, 13, 17, 19, and so on. Notably, the number 1 is not a prime.

Constraints

N will have between 1 and 1,000 characters, inclusive.
Each character of N will be a digit.
The character N[0] will not be '0'.
D will be between 1 and 8, inclusive.

Examples

"608478"

8

Returns: 397463353
"183"

8

Returns: 573571367
"220"

2

Returns: 0
"1"

1

Returns: 1
"50114"

7

Returns: 823979831
"1"

3

Returns: 1
"32"

3

Returns: 0
"1"

4

Returns: 2
"120030"

3

Returns: 0
"10"

1

Returns: 0
"1"

1

Returns: 1
"3034"

6

Returns: 219316322
"1"

1

Returns: 1
"4313227"

7

Returns: 573342780
"10"

1

Returns: 0
"112325"

5

Returns: 2
"73"

7

Returns: 240195015
"1111"

1

Returns: 0
"824"

8

Returns: 509500532
"1111"

2

Returns: 0
"4145151034304051222355504123532555424043555140100"

5

Returns: 2
"223202213103313101023010110132001310013020321330"

3

Returns: 0
"31330232232313212101121201113113110012232223200013333102003303211021020320132021333003232003000303011010022111120100130210300031210303001301233211103000101230012332"

3

Returns: 0
"110011001110001010110011110111111100011100"

1

Returns: 0
"3603563261420522310610422106120111424141106112404662054200032230564312262016501422603223201441010243222043356134555631525006605410246600564"

6

Returns: 893076515
"3300120203101232212012130201111013121011101033000320133111"

3

Returns: 0
"1110010"

1

Returns: 0
"10"

2

Returns: 0
"26"

8

Returns: 583948556
"5"

8

Returns: 351
"3233132444441140401321221420440141"

4

Returns: 2
"1000000100011101111111011100011001111000000100010011001111"

1

Returns: 0
"211132333121010011111222111202311"

3

Returns: 0
"10222310"

3

Returns: 0
"2103020203312330112221100220320231220323310220331"

3

Returns: 0
"3011"

3

Returns: 0
"5"

6

Returns: 48
"61123267513306360174020743456044273516135735444701261601503752371313010271730723143"

7

Returns: 932810584
"777644165102706716006573271337716"

7

Returns: 689913692
"16532121343261"

6

Returns: 779788895
"100222200"

2

Returns: 0
"4135255430341153217222632757214773240104056467266722726612430235265"

7

Returns: 56169720
"101011010111100100000010010100011000011001100010111110001100110100100000111111101110100010010100001000000000000000000011000000001"

1

Returns: 0
"1000010011001000101100100101101111111011000010001111"

1

Returns: 0
"3303231320210103301300202233230220211010013123210032"

3

Returns: 0
"2132051032436600"

6

Returns: 738149540
"51050200330646322646445020340552426340410360624562052663636411226001625226335245316121234205316021"

6

Returns: 783647476
"162314032505160544566605551201"

6

Returns: 333723606
"61214027451155456631310754220433707056704675307344311"

7

Returns: 328754822
"11002213201320003202321332202033332022202000313130213320101111202232202321022030333303220211020200223030112021"

3

Returns: 0
"5463350602653456413074212475145177051473427744552503675745340271013042"

7

Returns: 558536978
"3"

3

Returns: 0
"3185840334357162051740425736246138686214221352507842"

8

Returns: 146778914
"222404233421"

4

Returns: 2
"3513133212001455434454053002"

5

Returns: 2
"10011101100111001011011000111110111010111111000000001111100100001100001111011011000100010110101110101010001101101111101101111111101110110001110111"

1

Returns: 0
"35151330242545000434333403404243042242402241013010401255341252531313140025124405540225544254541305200112141534"

5

Returns: 2
"12211333020200222132023011330112313331013321323012203121011101002332002221230101121321"

3

Returns: 0
"181417805780804177182128778527876608288614314"

8

Returns: 152609035
"234163404500114056146155614510255515116566634461165125440"

6

Returns: 951045182
"30741144415346"

7

Returns: 784731528
"522300301030141"

5

Returns: 2
"101010101010111111101010000010001100111000110111110100110110010100110100111100001100101011010110110010110101111110001001110111101101"

1

Returns: 0
"6310"

6

Returns: 469480361
"52605231031530430"

6

Returns: 518829237
"33231122131023321321300311130301111112100012300123330322222203322022303122021002222303303311333100210002001213023211013000231122030"

3

Returns: 0
"103232230100322102103113303101023011221000012131111310100111330123021032313213302003200310"

3

Returns: 0
"1111102120121110201121020110101000122112112200010011210021010120220121101102200020211012122000010111100112021200221100212022022121122"

2

Returns: 0
"32111004"

4

Returns: 2
"2621667048144301780573102853268614378552360603180773807"

8

Returns: 385159320
"612"

8

Returns: 419447101
"56602462140165702065464600511451360115763324"

7

Returns: 416559718
"5141354115040343052024014522105150002"

5

Returns: 2
"13862484112621302562340731083457640260241240150253158205163182365865817662475340047750858336634051265682618153671323235"

8

Returns: 684451992
"2103031021020311031112130322000331132122332303101021121030132133300032102003231222"

3

Returns: 0
"101110000000100101000011011000100001010111100010100110101011010011111100010111001010100101101110011100101001000111"

1

Returns: 0
"2011002122011101201022101001101020002021211021102010"

2

Returns: 0
"7046388143877408122670643410203822068448151825076050"

8

Returns: 635718124
"140525511402231522350054"

5

Returns: 2
"10000100001011110110110111001100110011101010000010110101101000101011000111100010011100011111111011011101"

1

Returns: 0
"1211054160473733575170016174430323756571337421561341520010560347706301720604177247625477365645604362630335117521450002451247010767631600673365631562733233443066677547632753457513040524745433745651146232414161011510734131633651317206746737072320566240063030161715164110137127526174540275362100355450472645160763107250327563176532636160446735467601317512074424211045671100441142317257475133626532765331222271577306664571011525502265603045233645036177141461745461656012751112114643314326"

7

Returns: 488766478
"1201122120102121100010022221111220011020020012112222"

2

Returns: 0
"127444166042516653627406525722030037310506014526610756056621426652542030237051161003251714036316424753"

7

Returns: 834288374
"425421332414150032312104433030555424232032431040550302542430210530112024023120531540334000345215212551335552501132224552503251024052445043032450531044024353131311304530014525441311520254012214134142324050112552100000531034412133325241532514510540511125343003302500534551223125040413213225254401524510502533334222202215315035520313121551344300554543045050512015305440"

5

Returns: 2
"11110100202010012220021020000020220122002000212112200022101202212102110021010011120100120220111120110201220001010121220101000121120020021101010212021210002200210220022222000001011211110100021012022211212220221102022211201221000121112101012100110110221111001221101110000010000121012011202101022200200121210002011211110211122122201212100222212222102202010210122100010012020100002002220111222110011210100000112021011012110221022100020012002210002212101102002012001221020101001221100012220020220120110"

2

Returns: 0
"62652426244641202513112051415560164502562625504460453666362503400602016133233314504030212013632235513206242553245500330534651014166100561022266126511521316361163136146125042104502603544461311541235406321615024415002263251600403265463635605306653643325413652601325464253665145000600465650043656045551516324244343222356632242665465161544320023354012604510520605131353623341636305052433012522136364150646524500010403660363360306042651443143541255402533664556641443223423002060360346456326356155362664351532645406623365163643651142122065413540460033245454462336541351235560635463224062104400661333121361160403323112523314323031403611152163112105460601223013603662136412000316160605334552625202445432014321001561403441011606110666405320310626030650265632436131341654410205236660636012356145044434353341220161425525330545501"

6

Returns: 480417111
"1111100001001010111110100101111100010011000100111111001110111110111100101111100111000011010010101010110010111011111011010010110010110010011001011001101100100100010110101011001001101010101110011101010000010111101010110010100110001100010101100101011000010100101000100010010001010011111111011101"

1

Returns: 0
"314124022233302331000223304223333443411101423040000414033341012432202142243443231430322321323200221324334022241220311344410230214430043121203432302004113200212414210123241332234440332243131011003421101214102211000000444102412012013334034421303300410443340311213310344202444302"

4

Returns: 2
"11000000010100001110010110110011100000110111110000001001011001011101110111010010100100000101010100000011011101001000010101110001111011100010001011001010001011101000010010000001100010000010000100110001000010000110110011111111111110111100000110111010001011100101100001100010001010011111000011110011010011101100011000011010000001001001001000011111001110010100101011111001110011010000010111101101001110110001011001000100101010011111001101110111100110000000111101010111101111111111000010001011100100001001000001001010101000111010011001110000110000100000010110100101111111110101010110110100010000100000101001101110001110111010100011111100110100111001001000111011000111111111100000101101000110101011101001001110000010110101110000100101111110011000001110100110011100110111100110011111001101010110"

1

Returns: 0
"1002232232020112123132322111130331130013311313130221131221310301022001301310203031033121320030120133000322003001211220313200202020103000310112000320013111323030123230221231203123020323202311313100221002012013221220301020013320120003030230021101213222031023030202303020213311310120210021331031012000021023301200221010222030132000031221111221021203020301232301102121102001233012"

3

Returns: 0
"22000221200012000002200122111010220200201012000101212221200200222101201120102001200102001102010022210211102210112220002120000101111002011122000120110211000201112211101112221212002202021012010122111212201221111012212210100210200202021012022201000212100010020200101210010110101211212021121020020002212101102120021222110111010110010022122222012210101110101001202211202122102010022101210211101221101110100121110021120221011201211212220120122120200201222222220111121210122002001002202012021021121201202112202021220010121012102220221112011212021120112201212220100202001022211010200110201020010221010212122120202110100222201100010020220020112012102212211022212000220101020221021122100"

2

Returns: 0
"220111110102100222000200112101202201002222112201000110100110222012021111212211001011000120121020000120200010201111121121001012120111021210021000010210121120201212221111210011220100121001212021021111222002201000200211110221111010200121120121222120121221200020112102020202201002022011221221211122202210121211120221202120211020111200022"

2

Returns: 0
"26332500707028117710344410301"

8

Returns: 335502914
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

3

Returns: 0
"52530101054024425353401155551115205500102445235310022101045044150425540254203440021230342202341251222120504122204031244504555412005035042204304320133143414020431010005140242225"

5

Returns: 2
"11100111010001111110101110111110011110101110110111"

1

Returns: 0
"403617403640133466151735403643416454124525233445551664421601176125313263445421312146152134570207236520610263752272065724114360604135276774267477357057477403021772733254601715575045640620610144310612731021556537777723064671347154572527616556275737524063175632000075404461660277306340104175514151640403160462537601474437262565206666207314243621461144365462744335640611236570607023242267733251460555300400666"

7

Returns: 459311972
"87140002414624368216060876108607026170483346522515"

8

Returns: 317514590
"10221121110200101121122112210200121111001212220121201101101022202121202110102121002220210010011201120212222"

2

Returns: 0
"3645204561544011266505244625331303601404222642405365445313612503503132512514453113432353003214016464464125342113301520435463531205526132343444601002424543310633235110430000131662666243611315164454632"

6

Returns: 909889387
"13123003130132313120102100223112002023333332320002200113022102112130101301130102132133"

3

Returns: 0
"22101101122222012021221102200110221021001122222221201112010202112112022111211112012220021002202111200111222012212120100002011210222200021001000100222202010102012121220021010201202022212122100022011202100222212112001020000111021000201211002121120101120100002200121221100000100210120021020120121200020110220200122001002012221010202102002010002210111201020022012001011200220111020102002112120011120202121011002"

2

Returns: 0
"11202222210001102000111222120100120011101202222101220112221201112012101112211202101202111012101200002202101221021000220012201111000012221010101110221010010121220001020100010221210212212001011110102221100102002200220210021200011000010110012100122021010100201020020022000212022221002120020202002201202022001222101100212200222102200022212222100012101221000221221011222212"

2

Returns: 0
"1011011011101011001110101110011001001000001000001010101001100110001000101011000011110011011011000101111101111011011011110000110100100110011000101101100010000010101011111001011100111111000111111000100100001001111010101111011001101011001001111000010101010001100111100011010111110110111110110010110101000011111001011010110101100001001111000101100101111110100111011111000111111001010001100100101111101001000010001000111100110100001010110011100100010100111110101000001011111110"

1

Returns: 0
"202122100111010101101112101020110101101100001202020022201110112100211210200001201110202020202122011012212202201201221210001222200020010111002121121201110110202120020200212012001212122110122200010000"

2

Returns: 0
"401133224000202112343412140441343232203322230102120344022244203142434241412324234203142402322300343"

4

Returns: 2
"301444200414343143322144120414401332442143341341444432043134013113423234231311002323110011122313411243402321424103130020342024043204444124312200123334043420324431431002431340343310302110410243001334413221132323411002444200103140143124214000231213410101113"

4

Returns: 2
"1011122110021220212002111202212002202102021120222001222220201210021021222200102120102002"

2

Returns: 0
"122112222002131121231031200321031231232323000120200030223201322113011020111211120032202233132233322221323330203320213203100322111213000111300010320102011220121020121130220033102033111111023102031300023002301231012322201020101033200203131021013310111"

3

Returns: 0
"3451220120360613311223304641413344544121514263"

6

Returns: 537211463
"101011101010111010000001001110010001100011110000010011001100011110101000101010101100010101010010000001100010110010010001101110111110010111100101100101000111001000101101111101011010010110111001110110111010110100001011010011001000000010011111000010111111000100111011111011100101011011001011010011011101110101111111010001101011000010101111000001010100111100100001101011010111100010010101001110101011100011111100110110000111111001001011010000101100101001011010001100101000111011110011001111001100101101000101110010010010010111000010011001111001110110110110100101010111000100000011001010010111101011000100110001010100"

1

Returns: 0
"144260058230868388104838388146748832477650705687513068"

8

Returns: 557908256
"10110110010101111111010110111111101010011"

1

Returns: 0
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

3

Returns: 0
"10010001100010101011000101010111100000111111000110110110100011001011111011100010010001010110110011100000000110110111011011000011001000011010001100110100000100000000010111101110000010011000011111100010110100100010011111100010100110000110110011001111110011"

1

Returns: 0
"4536140541415624263341062452453666462552210616425053523665424341403405616531364460651354621102410235630410161563606024216331212016330364300255214355031066401006065011640544350135204510414560325026015063450124654404113261556620416420231010300106365"

6

Returns: 234802374
"344444022221553015425540521133045120012450530255023452512103500034304252503045325425420121240424010225122002134012050054354203214144400353115040500243105345334403445022315332211135022412234434022355522012315112320224315400522041051201105031440310030421321104322342552244421154054014201"

5

Returns: 2
"10122201121110200011011202122021100101201212010220222100221020001212221111212002221112111101212002112112200100111112012221201100101221121001111101210200200100111100122112202021120020022102221120102102021200"

2

Returns: 0
"22112111202000010000111021212102101012020121101021120212212221011020202100212120020002012211000200112220110212011020020102102221020101101121101112012011100101012222102102021001012211112000202212011120100100001101220112200112012020201221220202121120002202121222000012110222122"

2

Returns: 0
"1314058874406844511242566235535831454423017102372650201581762528610502751547277547524817185807122728436147706660242841575444065804638708044431423415015457251885542802062556420212643822333165625836882130846533231764017438804811247743255335363250044132261668724184026004713568036111566827421586184875630825234766344833838058221515248310756627781050505222313831"

8

Returns: 222141766
"3212112012200100332113110321131031201033012313022302332022002120112221301202030301331300201022211320301211321001202111110303223333023202133230203100313311231321030101012130020002220110010213323330031202022330101020203320013102102213313322310200111233201020111230312033232133312210030210133113213203132222101010133111313321033113221233213320122322031310000212121321221023113311101012110030112112330113122303220100030130122011030031131011101210111210231121001301122023300132012032"

3

Returns: 0
"2130142122223323020022313324104322322143114100121003410100222312424132222231013212311144331021044010140422324033411433234442421220301121234402300023010332212322332222042121003401432330302022234312300223232313444004211131043434103013033041200223000111233124024224340400014244032020023420233031021312333410213110"

4

Returns: 2
"50602554231022531422124321332053200355360645614420053502360241165326600013241315332231226245655535422446463462501242216531522642143342250030"

6

Returns: 252947979
"12411241021410114411333423013443110000112212432102120124013031431004011412403223113210343033123401023103222042213400321104214240422130201"

4

Returns: 2
"1001120102100111100120012010002022121210201002022012020200211020210101211000111111221110020002010011022220021220200002120201201221011202200001101110002102120101222122221022221021010011012101200202001100102001011021202101100211012011102112111122122211101121210211022020212202021020102010202010102200022211021212011121020202021022112100011011202111102211000011201202002101110200101201121122001212011200221122002111122012100220011220111000011022021200220011022220022201022010022022220000220210110000202101002100110001221212022200011112210002211002100111021221010021222110100120101111210102122010012200010120202022211122022220200101100001012101002210120222210120220201220221110111112210021201"

2

Returns: 0
"22332123202000321020203030122030221112212130201021210332123211"

3

Returns: 0
"5104501621317645574737250267345423377551602603545663743534612255506263617526027"

7

Returns: 997164315
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

4

Returns: 2
"104232440140222302011101101442242013100441402240413314301211442312220203130334343200324110233434311100440441431444104030442413403044231030230322440333033034231041330031422233422140332021434342233344244011322204003224142213123303043121321420040201304022423202114330431003120330141004010103322321110044241440223034440021133230122100224121023302404301313302101013142221444140010133100213320320102223124432111340242002002042444321130123431001020003"

4

Returns: 2
"43441131334531241304405403120442050131230253102452145050403313234350242032042204534434321310354445245020023003354441540403053222401105154441"

5

Returns: 2
"5105111421012510442312066310603514223141"

6

Returns: 357559054
"82344673537272638737003262600611171610631281107860358827768234174011188111531225862285176701685625054816061313558352828477301582"

8

Returns: 144482078
"3030331033332121100311000310121002002303021310023013030301232213020333123211121322120102022212032121021330132331010222311111112003022112220222103112223"

3

Returns: 0
"11111000110011111100101100101100000111000100011110100001110001111011101011"

1

Returns: 0
"5146054131461044001505540546120560562223265002301002020040660431231604243631530403354661645536220643360341353053553114256251526000132646021025252561015560556202151333564514030666166105001014440001150346316106345320141356153401400303320462535662236453240206212222112116651"

6

Returns: 732848875
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

3

Returns: 0
"7347025377267573607045657323004611546533231527002702235631624554703773641777477556157532432033746054226511724002571462777331722345011367363546730740505117313514"

7

Returns: 928686348
"22212000120201010212221212211010210002120000"

2

Returns: 0
"10401124441104131313131224404000234200121243333002111314102013112041143242213033212313130044340440232140103420333412232000204241443342401203200100212020102324411433330143243100413403402432003240141013221313210032202041331132004431120424430102134244000333401233300202232411013212434023432414200224323011231440421103434333302110133403034434422110400232444403104042300114340042033424313341242110241221330104414433302233014210101203430010324301031340043112321200243324243431132234231302330003343242311122332334100432123433103332340230422041330112200410024024100210003401201441333010302330314242202413200324234410032302311340130220232032203122214133141443342231030321433413032332411400130241422131103130110014334031122341343134330120010240033323202023311124023100240040131011023024430040130141233120210210432133002033312334102423142344131143040032024300012213342"

4

Returns: 2
"34312210420100402334334231301112211402033041200204042111413130333012032032414214234342423142433142314202343"

4

Returns: 2
"330340414431230023443134313430223104311410340310244210013"

4

Returns: 2
"33503215214303145040125500434115301402102303121411332201524432243253224344352402005322331015005204335502102204514334234303233442052102115552210042425333423410433405013111"

5

Returns: 2
"122210221101220000101122211021200201112210100120001011201012000122011210011200021021202222200212022222000121220101000122122200110101002001022011220002012201121211012001202220201211020001000112210202201201002110020200121211011122110111110211011221222101201212121012000122102201222000102200200101121102210121011222000120002022001202011101112012011202210112"

2

Returns: 0
"1110100111100100011000101001010001011010110100010011111100001001011010101101011100100010111100110011011001001010101"

1

Returns: 0
"22100021010001020111122100121120111122201101011001001122002201001210200010002102001021221000002022202010220110012222120112221001120221022102002121211021012211211000020220120200010222000002120220001002100202221121100112222122221010201112101222221020120120010221221201201"

2

Returns: 0
"10111011110010001110001100100010011000110001000001000000110010111001101111100000110101110100110010011111100011010011111111111001011010111011000110001000010101000110000100010000000110010101111010110101111001010100"

1

Returns: 0
"11010010010001110011011110011111110111111000001010000011011011011111110100100101011010000101100011111000110100111000010111001101001011100000011011011111001110111100"

1

Returns: 0
"1101111010111000000001110111110110000000000100100001110111101101100111100100000101101110100111100110001110111100000000011100000100100000001010000110011110100010100001111110011010111100100000110001011000100100011010000110001101101001111001100011011101101010010100011000010011101100100000011011100111101001111111001010110"

1

Returns: 0
"5666244254243664062261056026665134225415130636032636653031033340046664433215403255345020116562524131215030542066034314064436424043254362063204064024055305623325054402611552456000243503414531535132654321660456556352330205162405203236335154433616602634552136662310554212060032566630131306141065546213323066255454265002461420006224660635502324036131032662434302663310251365545610664611526634264010650565250363420153454214145243036354144266135026552326126542461060424556115640031165145505214034036412105025030556146556160"

6

Returns: 456386642
"32033234300222422442311333021231401141344020042420320243233120110"

4

Returns: 2
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

5

Returns: 2
"3620355025166634133234344423012142325522004251010214446410325645024310131160663053352211432002203545323654665464220"

6

Returns: 494429237
"1102012211001022212022022021020200022110201212011212221201022022121221100211121001002111121211021210222202122010110112022211211112121100221112012021111000102221122001210210122100212112222021000101012001212100021010000200210211201021121210000112100121100200110010122001202010202001121102102010011212001210212"

2

Returns: 0
"3451234144030040522345282445663326266855086511446661330225023461238380748304164344752047847266471080066524143713586756437537843314637517288258741118342335618210572604010334022638068033826856113125840053070066836172531182142187254803474381613016251315683505886387037"

8

Returns: 752684098
"230020301011013311022201333230031310332032300133311000212233230032013023121311323001322303031300111011112010113032122300211002332131103003332102300210313210232011111330313311101133130231302211230212323012020103201213100311303133200100333212322032000233131002212223221013131131200023100210013003112332200112031330031022103002333011130321111233103201212200330233022333223012033122300332331010122130202221033130211011112321133222223302122023002230012033130112221303223110321120132302322112012332220110230111311002200033323322121213102311032103231312300011102200032202000130102222301233232023221203132103102130322123210010212300023222220233122201001232113012022000311003022221110200331132030011232132021023012322002122312010013313312113111013322221012013211001121333320133221111320230202123122232131330003121213010100013310313231112120332003013321232110221210323220212123210323221331122102321202330200233112233203232211"

3

Returns: 0
"20736456430432154655002103765112350221"

7

Returns: 275630954
"11201200120100100200022101222002201011022200201102221010111201202110122022211120221120010001220221202211220122021202211021221221101111222120211212200220211222212201122100111122101200021112000111111201102211100221111110110221201100021122111010210210110100001002222011101110120211000100022010210220120101211000010000210121201210201210001201101220102021201202100011110212120100112111210011022010000101221222010201220201012020202122101120200021010111002201201102021211022022102020002210210011121211102020012222112102110212002101102012101011221001210110020212111200220022022220002210112002102202010210200221022212021211012010020202002100100020102120101121201120101002212102210100012100212210212001002001211221110101000200110101101212012111122201010001"

2

Returns: 0
"206211563144500403222034364024631406251030341"

6

Returns: 453812249
"424846538861031634546145016421684526382136134121654538731657834738016677504352156876165118737203871465356053887742204243665074753686166843171658384822630101653572100177660234841833013126526022732221385808001218278721380285763355012520587511745204138122331820444265081003363275302413511058225506548436562264135736004386086037231083403855127270783787507766446043321480126877557068517157426263762361003376178820700462824563674734784360555517378864574873604500266415856304770254432763512383505704730704451304084038707654372173578478187274644701644271232783308312615266052347"

8

Returns: 846759470
"22241442435164263536564141456426004253245004654045541204363322160405061104350615115604361401451051511046260513113232462454400351533101160204012555350512030124556626020626016026500104156652261665544052552443331065303205302016152214343005031146354466066531635415015616305664652556621555625302235021355365451561544565625205231346006610225160120551144611102416316014525254041153101002634222535652250053644202220233166035065406404223142534346254540656223204251566026331412511521550162363315146140326362426132312406120666361344460042135341633113"

6

Returns: 173651503
"1100100100000001010100000001111101011101110110101011000111110000100100111000100101011000100110001111100010111101"

1

Returns: 0
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

5

Returns: 2
"214040042325235315254235220312020545302434223055333155000542440524250434512015331123140003223400232351325455413022042015212044355111155431202223014523010553005124243232403340440445214303205351002513322055041200112352455453252255020201104504500454525154002243245324325524520253024451514434"

5

Returns: 2
"323421004332501103143521514152134515534131153040454425334"

5

Returns: 2
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

5

Returns: 2
"176531361413312772247761032670443471661570400612362054733717300246106400533303017440341764650635737506277234675601714002042"

7

Returns: 599223769
"201"

2

Returns: 0
"7740210316014174214634757755735723211612327403044150306703676233444"

7

Returns: 396421099
"637244245062652474225640156147251337571543063411763741747220303652005117376147231750531336213567350170051010224704263500307462467431731322466651053020431063404276074137554577117304501432122010127336221706631352113746050200765576003116252027421013551662233072741166410332346330751655143061072253324225010311212415204573712160011665560063114003765533766167305636136510046044055300060576"

7

Returns: 841704318
"43313114432400130404031434224442131412341122441144341410403304131124004302232230413432121104303234102344302012421430000440023232313140411132221100311002420140044042"

4

Returns: 2
"10001100011100001000110010010001100000110001111110011010100011111110001111010001111011001000011110010011000100111111000000110000111010001001001001110011110011001110000000001011100100000111101010001001010100101110111010110000000001101101001001100010110011010"

1

Returns: 0
"122122000000100202011000021201121221101111121120020100102022211121110022212221020200221112221020202110201202111212201101221121202022202101110120022210222021211001010111212211022212121212101000111201011021111112211212101121110102001022121122200220000020201100011012012222020212222121121102221100200202000001221020021112001010"

2

Returns: 0
"2000331220122230331301322012303233031000303313102212101003133331123021"

3

Returns: 0
"41350402041016236243105510224454404345031266460160415161321043464565604466341325636101064166121366523406532020402"

6

Returns: 229918708
"210101020112010100011100011101002022002121201111020112220011021002001101202222210022202020111110211101102021122001002011201011022021002211001011220022001101202021002000022210021002002112112002212211"

2

Returns: 0
"111111111001011010110011011001000010110011010101100001100101010000111000000101110010001101101011101001111011111101101001101101010101100000000111100100111110010111110001110100101101100011101000001000110101101110010101100111100000101000001101100011111100110110001010011101001011100011111011000111110111000000000111101010010100101100101110011110010101100001011100110100101111110001100001111100110101101001100001111011110101011110011000000100011011101011101110001111001101001000000100001011111100010011000100001100111101110001101100011010000011001000000001000000010110111101000010001011110011000001010101011011010111101110101101000001010100101110011100001111010100011000110010110100001110111110010101010100110010111011111010000100001110010111111010100000010110000001000110101010110011110100101100111011110011111000000111111000000011110111011010010111000000110000111010111100001001000010010000001001000100"

1

Returns: 0
"60330604442043234632724551305243030355052033767713021402337156423371466131521263766403706663264056110350447175632445145142310223066525045211410211132115633717300112275321711213244157315102063433053730452144061065173713003627763754401703006212144574353204113526"

7

Returns: 349826496
"15543422624441111135445403412565316062406445456055345114412250613461513156213451444020142324065255314040661234531465022460265163613640244533001222230330443115064022135615302106403033433254464065113441510503011202"

6

Returns: 767382794
"1200212011021102001211211002020200100211102000222022220011101110110122201122101220110101222201021112211120211210222101120001110211202001221120220101001010020101020221011121020000012221122211211121001120012200"

2

Returns: 0
"54256253200055411344233216555266123422300314526423465360364154501053100610005205564162402455153336653304220251563500201334551441145341043464656532451534026133364241421301231303560435613343526150664234313312346316513062526326322123013415350125153160540441116565446202601645231263601032426555632410150140663122536022132112100433265501561154662004263355310201246432556443640425133202633423126023636333366301514255360505260550022432450445446050050154036600053664604154414163441012443506526336323561605634656136302145322066015256135463620331624542155333045115163026301605013020614443160465543545662126106622033433256340363422512"

6

Returns: 270313778
"5202454010140342242105415502201020253324515302202514341343540230"

5

Returns: 2
"12210222110110102001021201012102011212210112101011002212200200111022101212121202202010221110122200000121112210000111012011221012201120200011201020201121111122220022022120211102000021212011011222202101211110121212021100120000"

2

Returns: 0
"222211212120201010110211211010112001120200121011011112212100120121000022222102210012001022122021101222100022010220210110100221021200012211020212122102112022201111220010222011221120121110010212222010111122221121211112021022010120120112220022110001021102201021012121001000000021101110001001201222100102101110112001110012112121120210122202010110002220021001201201022110222"

2

Returns: 0
"400200412301333320441311212342142444233342311331421"

4

Returns: 2
"1203312302020011201123233330131210002001132220321320112211220122300023233313112133213102033301132130302111121220133032000213021301210101002032122302220230231101333110013300300030033111120110312"

3

Returns: 0
"511765054548854064464237808621214264330731320015605576848177477325864453377686821062665160883651124651676242100878858108871880662070224651561270266435164331086472762626863437538840504863760836027813838478470885232148273813"

8

Returns: 970747428
"2021101111120020202021100221122222220110212100022002121210022001111122011212102011200211221001222121012112100101021100010012001102011120000020122112000001212110021201222200111021100110110020112122201220201202021220210210112020210201000000022001021110010212001002121212222120211202011101002010210001210112012200"

2

Returns: 0
"74554651361157341373603016774175514754527452552433161110706104101152226052164011065463322715362742032664527431761606711644"

7

Returns: 233998131
"32112020210111011302332321103230012133120300100112122010212330032323022102101133013120320232210231221230010111120323211030303102002112102313032122000223100303210321113010033331222012123320001133303300031213210012323203221202031112123210110110023223033220102331312123122033111332102031300032211330131002131212203021010112022212333320202212032110121003133233232012110301112232122031130013112103101132133331101212021210121213"

3

Returns: 0
"4000413010203141313413204200131001242412040201"

4

Returns: 2
"33230432132323344034304213212141110212442340404201110203341014000134302110231233041344233001410431041230332104442211133244234401242303214121004020040430010211434044021033230223413312413031314112434422042102331320"

4

Returns: 2
"2021330231303101032013032131210330120332302221003133011103101321"

3

Returns: 0
"38775404077442042410031755336818874187741384764613212700362652506135414607712354012538247677670620220777775551577445381601158060044416785384872306783841520181344046582142613020162567406606242362434220558731534581460656680206528288872107152871521017735350387304754468100147085687552630347443253346441185326070186238883208508776368600736142702320268451166632816838815247764445037460352304166147288648803144457123142843687568705876466643168547804008725414158485735364320330103114811064617785571557676543727568120486178565321776615664243713864078755722315733373728563668811426746624814815827348655807385586661647745380660856350175865708033113100203042857561452636386513831076213304531885074213713702111257614377164365178826381473013263258475665316370576477703330040512021855663277721483472062052076683183681834"

8

Returns: 705305637
"110000000001001110"

1

Returns: 0
"15106735721166753667101040317466675750100324752172437743444162125576567673760417762440375617041432344720067204005455415614016452162120037203021663466512425131240260540110001714304266704720027572514337010345272736431721122500767157216014002134001014254362677650620111647122525212627652072730243502642006231253445641266402447736120467770762442042633507231666120656670554141554266123656447625001005035607075416272737225520502670212332566207332027615143001512406754336617701171622031626216402736016452301301411174175750012456553556272010121502174326746014626210717707337515770066126626541322004671220543267062335063570343023561342410630254206733770066303556443312227266577137270123154111654734215213102507153315135541576214771445770230230407375"

7

Returns: 534952169
"5233434345250530122210102332320212441021414514042332210312221124435054355304444213022133244003250114051210150142402255025430550051342230053331055303052225442424140001425055554350000014113242400404340312521542113055203520252200145104041041441452533550031401152120303040012500120225510334002512321333523420424554533034040203052440205202251335332054322340045514442510114"

5

Returns: 2
"21020022220221222222122210211201211202022021011012201100121110012211022010010022021210010102102111010111020122200022201110120012000002112021001021212122221210011202020200020002121112211100000000221211221021112021201201022020000101211120202202110010201022121111121120012101020010220020100212012012202212110012200212200101211022122200120101101000020111102210210100110202011212221221220212221121020222021212222221201120010112022121221210101110101200001122222010212222211120202222221002001101021210010121000110202112011110211202102212212210012212"

2

Returns: 0
"34230124311341410420201121332030402240212130233000223241203024314040222333424411200243331433333003040440010433103411010331321130101343012123423110322201234240334411303323223111434444311030034112004132040223103014330314200124201221423004024402210031242433141422130030444132013044300133031443131214442311013032132132222023334310441440003402333140130020343133204323331424300002132344234221311432344122322303003323441442431431300222004401140111321334213041301440042331042322001303312043214423"

4

Returns: 2
"10006033043673034252066654535426214415760110732214617205326737247662524704"

7

Returns: 856847214
"110021222021120102121122210222222122212201222010200011111100120111120122200020102011210022022000102001110220121211100121202120112022002101"

2

Returns: 0
"1"

5

Returns: 2

We are interested in 1-digit numbers that only use digits 1 through 5. Among those, there are two antiprime numbers: 1 and 4.
"2"

4

Returns: 2

Here the two antiprime numbers are 14 and 44.
"2"

3

Returns: 0

There are no antiprime numbers among the numbers 11, 12, 13, 21, 22, 23, 31, 32, and 33.
"1"

5

Returns: 2
"2"

7

Returns: 6
"1000000006"

8

Returns: 444444449
"1000000005"

6

Returns: 750000006
"3"

8

Returns: 39
"2"

8

Returns: 13
"11111111111111111188888888888888888888777777777755555555555555666666666666666663333333333322222222222228888888888877777777"

8

Returns: 572766777

Statistics

Problem Statement for "AntiprimeNumbers"

Problem Statement

Definition

Notes

Constraints

Examples