Homework sagemath（5） ChengXu.sagews

#5 (a) when k=6
   #(b) p=2,3,5,7,13,17,19,31,61,89
def N(k):
    N=product(nth_prime(i) for i in (1..k)) +1
    return N
for k in range(1,100):
    if is_prime(k):
        print  N(k), 'is prime', k
    else:
        print N(k), 'is composite',k

3 is composite 1 7 is prime 2 31 is prime 3 211 is composite 4 2311 is prime 5 30031 is composite 6 510511 is prime 7 9699691 is composite 8 223092871 is composite 9 6469693231 is composite 10 200560490131 is prime 11 7420738134811 is composite 12 304250263527211 is prime 13 13082761331670031 is composite 14 614889782588491411 is composite 15 32589158477190044731 is composite 16 1922760350154212639071 is prime 17 117288381359406970983271 is composite 18 7858321551080267055879091 is prime 19 557940830126698960967415391 is composite 20 40729680599249024150621323471 is composite 21 3217644767340672907899084554131 is composite 22 267064515689275851355624017992791 is prime 23 23768741896345550770650537601358311 is composite 24 2305567963945518424753102147331756071 is composite 25 232862364358497360900063316880507363071 is composite 26 23984823528925228172706521638692258396211 is composite 27 2566376117594999414479597815340071648394471 is composite 28 279734996817854936178276161872067809674997231 is prime 29 31610054640417607788145206291543662493274686991 is composite 30 4014476939333036189094441199026045136645885247731 is prime 31 525896479052627740771371797072411912900610967452631 is composite 32 72047817630210000485677936198920432067383702541010311 is composite 33 10014646650599190067509233131649940057366334653200433091 is composite 34 1492182350939279320058875736615841068547583863326864530411 is composite 35 225319534991831177328890236228992001350685163362356544091911 is composite 36 35375166993717494840635767087951744212057570647889977422429871 is prime 37 5766152219975951659023630035336134306565384015606066319856068811 is composite 38 962947420735983927056946215901134429196419130606213075415963491271 is composite 39 166589903787325219380851695350896256250980509594874862046961683989711 is composite 40 29819592777931214269172453467810429868925511217482600306406141434158091 is prime 41 5397346292805549782720214077673687806275517530364350655459511599582614291 is composite 42 1030893141925860008499560888835674370998623848299590975192766715520279329391 is prime 43 198962376391690981640415251545285153602734402721821058212203976095413910572271 is composite 44 39195588149163123383161804554421175259738677336198748467804183290796540382737191 is composite 45 7799922041683461553249199106329813876687996789903550945093032474868511536164700811 is composite 46 1645783550795210387735581011435590727981167322669649249414629852197255934130751870911 is prime 47 367009731827331916465034565550136732339800312955331782619462457039988073311157667212931 is composite 48 83311209124804345037562846379881038241134671040860314654617977748077292641632790457335111 is composite 49 19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740191 is composite 50 4445236185272185438169240794291312557432222642727183809026451438704160103479600800432029464271 is composite 51 1062411448280052319722448549835623701226301211611796930357321893850294264731624591303255041960531 is composite 52 256041159035492609053110100510385311995538591998443060216114576417920917800321526504084465112487731 is prime 53 64266330917908644872330635228106713310880186591609208114244758680898150367880703152525200743234420231 is composite 54 16516447045902521732188973253623425320896207954043566485360902980990824644545340710198976591011245999111 is composite 55 4343825573072363215565699965702960859395702691913457985649917484000586881515424606782330843435957697765931 is composite 56 1168489079156465704987173290774096471177444024124720198139827803196157871127649219224446996884272620699035171 is composite 57 316660540451402206051523961799780143689087330537799173695893334666158783075592938409825136155637880209438531071 is composite 58 87714969705038411076272137418539099801877190558970371113762453702525982911939243939521562715111692818014473106391 is prime 59 24647906487115793512432470614609487044327490547070674282967249490409801198254927547005559122946385681862066942895591 is composite 60 6975357535853769564018389183934484833544679824821000822079731605785973739106144495802573231793827147966964944839451971 is prime 61 2043779758005154482257388030892804056228591188672553240869361360495290305558100337270153956915591354354320728837959427211 is composite 62 627440385707582426053018125484090845262177494922473844946893937672054123806336803541937264773086545786776463753253544153471 is composite 63 195133959955058134502488637025552252876537200920889365778484014616008832503770745901542489344429915739687480227261852231729171 is composite 64 61076929465933196099278943388997855150356143888238371488665496574810764573680243467182799164806563626522181311132959748531230211 is composite 65 19361386640700823163471425054312320082662897612571563761906962414215012369856637179096947335243680669607531475629148240284399976571 is composite 66 6408618978071972467109041692977377947361419109761187605191204559105169094422546906281089567965658301640092918433248067534136392244671 is prime 67 2159704595610254721415747050533376368260798239989520222949435936418441984820398307416727184404426847652711313512004598759003964186453791 is composite 68 749417494676758388331264226535081599786496989276363517363454269937199368732678212673604332988336116135490825788665595769374375572699465131 is composite 69 261546705642188677527611215060743478325487449257450867559845540208082579687704696223087912212929304531286298200244292923511657074872113330371 is composite 70 92325987091692603167246758916442447848897069587880156248625475693453150629759757766750033011164044499544063264686235401999614947429856005620611 is prime 71 33145029365917644537041586451002838777754047982048976093256545773949681076083753038263261851007891975336318712022358509317861766127318306017798991 is composite 72 12164225777291775545094262227518041831435735609411974226225152299039532954922737365042617099319896354948428967312205572919655268168725818308532229331 is prime 73 4537256214929832278320159810864229603125529382310666386381981807541745792186181037160896178046321340395764004807452678699031415026934730229082521540091 is composite 74 1719620105458406433483340568317543019584575635895742560438771105058321655238562613083979651479555788009994557822024565226932906295208262756822275663694111 is composite 75 658614500390569664024119437665618976500892468548069400648049333237337193956369480811164206516669866807827915645835408481915303111064764635862931579194844131 is composite 76 256201040651931599305382461251925781858847170265198996852091190629324168449027728035542876334984578188245059186229973899465052910204193443350680384306794366571 is composite 77 101711813138816844924236837117014535397962326595284001750280202679841694874264008030110521904988877540733288496933299638087626005351064797010220112569797363528291 is composite 78 40786437068665554814618971683922828694582892964708884701862361274616519644579867220074319283900539893834048687270253154873138028145776983601098265140488742774844291 is prime 79 16681652761084211919179159418724436936084403222565933843061705761318156534633165693010396587115320816578125913093533540343113453511622786292849190442459895794911314611 is composite 80 6989612506894284794136067796445539076219364950255126280242854713992307588011296425371356170001319422146234757586190553403764537021369947456703810795390696338067840821591 is composite 81 2942626865402493898331284542303571951088352644057408163982241834590761494552755795081340947570555476723564832943786222982984870085996747879272304344859483158326560985889391 is composite 82 1268272178988474870180783637732839510919079989588742918676346230708618204152237747680057948402909410467856442998771862105666479007064598335966363172634437241238747784918327091 is prime 83 549161853502009618788279315138319508227961635491925683786857917896831682397918944745465091658459774732581839818468216291753585410058971079473435253750711325456377790869635629971 is composite 84 241082053687382222648054619345722264112075157980955375182430625956709108572686416743259175238063841107603427680307546952079823995015888303888838076396562271875349850191770041556831 is composite 85 106799349783510324633088196370154963001649294985563231205816767298822135097700082617263814630462281610668318462376243299771362029792038518622755267843677086440779983634954128409675691 is composite 86 47952908052796135760256600170199578387740533448517890811411728517171138658867337095151452769077564443190074989606933241597341551376625294861617115261811011811910212652094403655944384811 is composite 87 21914478980127834042437266277781207323197423785972676100815159932347210367102373052484213915468446950537864270250368491409985088979117759751759021674647632398042967182007142470766583858171 is composite 88 10102574809838931493563579754057136575994012365333403682475788728812063979234193977195222615030954044197955428585419874540003126019373287245560908992012558535497807870905292679023395158616371 is prime 89 4677492136955425281519937426128454234685227725149365904986290181439985622385431811441388070759331722463653363435049401912021447346969831994694700863301814601935485044229150510387831958439379311 is composite 90 2184388827958183606469810778001988127598001347644753877628597514732473285653996655943128229044607914390526120724168070692914015911034911541522425303161947419103871515655013288351117524591190137771 is composite 91 1046322248591969947499039362662952313119442645521837107384098209556854703828264398196758421712367190993062011826876505861905813621385722628389241720214572813750754455998751365120185294279180075991831 is composite 92 509558935064289364432032169616857776489168568369134671296055828054188240764364761921821351373922822013621199759688858354748131233614846920025560717744496960296617420071391914813530238313960697008021211 is composite 93 250193437116566077936127795281877168256181767069245123606363411574606426215303098103614283524596105608688009082007229452181332435704889837732550312412548007505639153255053430173443347012154702230938414111 is composite 94 124846525121166472890127769845656706959834701767553316679575342375728606681436245953703527478773456698735316531921607496638484885416740029028542605893861455745313937474271661656548230159065196413238268640891 is composite 95 62797802135946735863734268232365323600796854989079318289826397214991489160762431714712874321823048719463864215556568570809157897364620234601356930764612312239892910549558645813243759770009793795858849126367671 is composite 96 31964081287196888554640742530273949712805599189441373009521636182430667982828077742788853029807931798207106885718293402541861369758591699412090677759187666930105491469725350718941073722934985042092154205321144031 is prime 97 16653286350629578936967826858272727800371717177698955337960772451046378019053428503992992428529932466865902687459230862724309773644226275393699243112536774470584961055726907724568299409649127206930012340972316039631 is composite 98 8709668761379269784034173446876636639594408083936553641753483991897255703964943107588335040121154680170867105541177741204814011615930342030904704147856733048115934632145172739949220591246493529224396454328521288726491 is composite 99