Values p, thetamin(p) for the first thetamin-champions p For x >= p, we have theta(x) >= x times thetamin(p). [ 2, 0.231049060186648436], [ 3, 0.358351893845611000], [ 5, 0.485885340237450767], [ 7, 0.486100684610678970], [ 11, 0.595769446424295324], [ 13, 0.606467774175139762], [ 17, 0.662865472418247661], [ 29, 0.703361668502724390], [ 37, 0.722812186518171388], [ 41, 0.761534090591611484], [ 59, 0.792819741089315048], [ 67, 0.807374862991198229], [ 71, 0.816017313614026186], [ 97, 0.828993964347167553], [ 101, 0.843069326295576445], [ 127, 0.849957340323199785], [ 149, 0.869454697277702206], [ 163, 0.869575625134454706], [ 223, 0.878072846592262195], [ 227, 0.894093826174344633], [ 229, 0.898037345836449608], [ 347, 0.909651242937521126], [ 349, 0.913005847827844348], [ 367, 0.913462648740895803], [ 419, 0.916058825002412670], [ 431, 0.919426718004364817], [ 557, 0.920858343105432481], [ 563, 0.922278605969241085], [ 569, 0.926449128972382654], [ 587, 0.927825739505255842], [ 593, 0.929191749458454825], [ 599, 0.936740631487071363], [ 601, 0.938022593835692087], [ 607, 0.938312312403356156], [ 809, 0.940911970408634635], [ 821, 0.944997001843194286], [ 853, 0.945581326022353676], [ 1423, 0.948018745289347676], [ 1427, 0.951774722984867719], [ 1429, 0.954187585012774485], [ 1433, 0.955003482002779113], [ 1447, 0.957386137963234225], [ 1451, 0.957669064395834946], [ 1481, 0.960096280598203254], [ 1973, 0.960970115285294515], [ 1987, 0.961887606780949332], [ 1993, 0.962945603350205642], [ 2237, 0.963211176939696092], [ 2657, 0.965452068474814716], [ 2659, 0.966962482808190476], [ 3299, 0.968830840792320194], [ 3301, 0.969523007616359890], [ 3307, 0.969626889674528764], [ 3449, 0.969739364217641466], [ 3457, 0.970972880248572139], [ 3461, 0.971078662637560079], [ 3511, 0.971303148377974440], [ 3527, 0.973067273238694220], [ 3529, 0.974277717827066848], [ 3533, 0.974758334667804693], [ 5381, 0.975267352581575362], [ 5387, 0.975775444516897275], [ 5393, 0.976282613331165815], [ 5399, 0.976427556575768914], [ 5407, 0.976933169793933960], [ 5413, 0.977490257395713850], [ 5639, 0.978674884502435310], [ 5641, 0.978862284222389874], [ 7451, 0.979036119884322541], [ 7477, 0.979704939887191492], [ 7481, 0.980111229737939356], [ 7487, 0.980922108423314043], [ 7499, 0.980947320370002182], [ 7517, 0.981100913142747822], [ 8597, 0.981294640324184892], [ 8623, 0.981890097582751668], [ 8627, 0.981994764996281353], [ 8663, 0.982286780514794428], [ 11777, 0.982915809311365611], [ 11779, 0.983377695955404762], [ 11783, 0.983466547471276992], [ 11801, 0.983760876281965405], [ 11807, 0.984054949133672449], [ 11813, 0.984182224009391859], [ 11821, 0.984202405702141664], [ 11897, 0.984417483655857736], [ 11923, 0.984874308897090460], [ 11927, 0.985009064580418118], [ 12097, 0.985093229757120907], [ 12373, 0.985139670276053413], [ 14387, 0.985511612795387883], [ 14401, 0.985765793627679482], [ 14407, 0.985787471786356433], [ 14533, 0.986081878408236137], [ 19373, 0.986285972755345768], [ 19379, 0.986693556127669980], [ 19381, 0.986897398245941746], [ 19387, 0.986897974203201613], [ 19417, 0.987203123904719643], [ 19421, 0.987609842948431531], [ 19423, 0.987914767735482461], [ 19427, 0.988215746056099024], [ 19681, 0.988416798248204822], [ 19687, 0.988416978266275494], [ 19697, 0.988625155001770116], [ 19913, 0.988727637227328595], [ 19961, 0.988785071732448003], [ 20873, 0.988977298434222572], [ 20879, 0.989074712172943097], [ 20887, 0.989077398449113163], [ 20897, 0.989080093083693957], [ 21481, 0.989268134389784701], [ 21487, 0.989548164674206952], [ 21491, 0.989835816123342130], [ 31957, 0.989845636634891915], [ 32051, 0.989984015455221352], [ 32057, 0.990245885844700968], [ 32059, 0.990339524070019154], [ 32297, 0.990599657528562769], [ 32299, 0.990798412842894716], [ 32303, 0.990889116876221407], [ 32321, 0.991149046159363380], [ 32323, 0.991192838452899795], [ 32353, 0.991329965836336094], [ 32359, 0.991528319746820321], [ 32363, 0.991665352128279130], [ 32369, 0.991924893870869244], [ 32371, 0.991968034579683496], [ 32401, 0.991982420566530703], [ 32411, 0.992055548295123163], [ 40751, 0.992109135646671471], [ 40813, 0.992223398639964111], [ 40819, 0.992360668943600311], [ 41113, 0.992442985555193974], [ 41131, 0.992460002339388097], [ 41141, 0.992518449212700682], [ 47269, 0.992536182783130891], [ 47279, 0.992595893317506069], [ 47287, 0.992639222213259070], [ 47491, 0.992740543563346583], [ 47497, 0.992745314755791795], [ 48463, 0.992763079341264608], [ 48473, 0.992821488169499039], [ 48731, 0.992857010570909011], [ 48751, 0.992956223790049046], [ 48757, 0.993096146662030780], [ 48761, 0.993102264793213887], [ 48989, 0.993185336604212630], [ 51131, 0.993253259668229408], [ 51193, 0.993314854696413184], [ 69991, 0.993389089775247398], [ 69997, 0.993491697613762122], [ 70001, 0.993524282084376062], [ 70111, 0.993598396625598498], [ 70117, 0.993685810891986079], [ 70841, 0.993815404805094384], [ 70843, 0.993888875552897809], [ 70849, 0.993951622232705640], [ 70867, 0.993968962751316086], [ 70877, 0.994087762955257852], [ 70891, 0.994094362701381820], [ 70913, 0.994167751255596413], [ 70919, 0.994219663621108040], [ 70949, 0.994239565771382765], [ 88789, 0.994323097804137012], [ 88793, 0.994384226020786068], [ 88799, 0.994490141069215860], [ 88801, 0.994551253507917346], [ 88807, 0.994634756854807603], [ 88811, 0.994649324636017257], [ 88993, 0.994732672565670971], [ 88997, 0.994793658845963624], [ 89003, 0.994854637661621991], [ 89009, 0.994867671404917721], [ 89363, 0.994906179652940102], [ 89371, 0.994922419007246058], [ 89381, 0.994983178725063712], [ 89387, 0.995043931037486020], [ 89393, 0.995076373566122647], [ 89413, 0.995100883363859240], [ 89491, 0.995111068241853803], [ 89513, 0.995171742207555615], [ 89519, 0.995214304032448851], [ 89561, 0.995245239395007972], [ 89753, 0.995251766469445263], [ 92173, 0.995268698766734792], [ 119549, 0.995339285498814111], [ 119611, 0.995380773118841443], [ 119653, 0.995436437806919470], [ 120551, 0.995483944045064468], [ 120557, 0.995531445967585019], [ 120563, 0.995554250064987742], [ 120619, 0.995566672241969322], [ 120641, 0.995595595135306223], [ 120661, 0.995610054154360992], [ 120671, 0.995655466039223334], [ 120689, 0.995684369035572991], [ 120709, 0.995715433158534988], [ 120811, 0.995762841139373683], [ 120817, 0.995798837659063298], [ 175621, 0.995810897575401640], [ 175631, 0.995835732552567844], [ 175663, 0.995837170591101413], [ 175687, 0.995857145978541025], [ 175829, 0.995880522230655100], [ 175837, 0.995915223808626036], [ 175843, 0.995918099311207794], [ 175891, 0.995932300656614181], [ 175937, 0.995989627438362859], [ 175939, 0.996001664996681753], [ 175949, 0.996002380663672396], [ 175961, 0.996028596432328878], [ 176017, 0.996074580840294607], [ 176021, 0.996098639081929105], [ 176041, 0.996108880863257396], [ 177883, 0.996154440380177305], [ 177887, 0.996211198217454834], [ 177889, 0.996233738965677561], [ 178067, 0.996235256346243566], [ 178091, 0.996243144442500634], [ 178393, 0.996257379029112172], [ 178439, 0.996293174270442178], [ 178469, 0.996293939909946700], [ 178481, 0.996297846917243204], [ 181711, 0.996331593818801115], [ 181717, 0.996353592984750496], [ 181871, 0.996388162156993442], [ 181889, 0.996443790943275207], [ 181891, 0.996444636654419211], [ 181903, 0.996456437803817024], [ 181913, 0.996490148110068538], [ 181919, 0.996512901168312597], [ 181927, 0.996528907218295577], [ 181997, 0.996529750026045672], [ 182009, 0.996564283904639012], [ 182027, 0.996619872748937970], [ 182029, 0.996620710377939336], [ 182041, 0.996624062444703061], [ 182089, 0.996635847299277078], [ 182099, 0.996669748822914704], [ 302831, 0.996704842721781295], [ 302833, 0.996733353496245932], [ 302837, 0.996755280864106406], [ 302843, 0.996763996202006469], [ 302891, 0.996766174986400725], [ 302903, 0.996788097645850615], [ 302909, 0.996790228464307611], [ 302959, 0.996798986622657678], [ 302969, 0.996834065187258848], [ 302971, 0.996846830995724517], [ 303271, 0.996849007906735862], [ 303283, 0.996877479373070929], [ 303287, 0.996899376251517404], [ 303293, 0.996921272328841899], [ 303299, 0.996921941120168694], [ 312197, 0.996956078147499185], [ 312199, 0.996983827950580493], [ 312203, 0.997005190262136337], [ 312209, 0.997039325567214628], [ 312211, 0.997060686346950722], [ 312217, 0.997062885775900921], [ 312229, 0.997090631852160700], [ 312233, 0.997105603556479267], [ 312241, 0.997114187915116866], [ 312251, 0.997121796877291516], [ 313543, 0.997143078912984407], [ 313549, 0.997170720615060388], [ 313553, 0.997185640703715728], [ 313561, 0.997206920479180804], [ 313567, 0.997231672852389097], [ 315349, 0.997233875582488184], [ 315361, 0.997236078265616958], [ 315373, 0.997249009401537756], [ 315407, 0.997274584834625719], [ 315437, 0.997276786202326887], [ 315449, 0.997302635949530511], [ 315517, 0.997323379279653088], [ 316031, 0.997343481792525068], [ 316177, 0.997345682804201087], [ 316189, 0.997357583635957306], [ 407177, 0.997384407927219995], [ 407179, 0.997386737043718279], [ 407191, 0.997389066095314875], [ 407203, 0.997397081551192223], [ 463181, 0.997397425759121265], [ 463207, 0.997412670462449614], [ 463213, 0.997427914798816868], [ 463219, 0.997430239384705576], [ 463231, 0.997445482985049304], [ 463237, 0.997452113441914220], [ 463247, 0.997459085002405022], [ 463283, 0.997470020722497631], [ 463291, 0.997472069142283861], [ 463447, 0.997484324795701970], [ 467471, 0.997507984181258162], [ 467473, 0.997527375648507475], [ 467477, 0.997551034573672761], [ 467479, 0.997553354398636304], [ 467491, 0.997568477095145152], [ 467497, 0.997583599430933387], [ 467503, 0.997588237289836340], [ 467527, 0.997599830686703431], [ 467587, 0.997604467647834259], [ 467611, 0.997619586356578373], [ 467617, 0.997626171111094714], [ 467627, 0.997649822710773841], [ 467629, 0.997669207209375594], [ 467633, 0.997680057595508448], [ 467641, 0.997686640828754096], [ 467651, 0.997700417587254041], [ 467867, 0.997724057833800194], [ 467869, 0.997730637960377468], [ 467879, 0.997754277526246870], [ 467881, 0.997756591982626315], [ 467893, 0.997775965837445538], [ 467897, 0.997777418685211813], [ 468001, 0.997783996418480470], [ 468011, 0.997786673499141156], [ 468049, 0.997792145216497168], [ 468439, 0.997792878640521491], [ 468491, 0.997804443923143214], [ 468551, 0.997804810773690595], [ 468577, 0.997815596262496934], [ 470077, 0.997829467122056164], [ 470149, 0.997848757623395588], [ 470153, 0.997858001788203602], [ 470201, 0.997873045731681923], [ 470207, 0.997874671026755250], [ 486037, 0.997885588664159359], [ 486281, 0.997886090575959332], [ 486307, 0.997900705194213911], [ 486313, 0.997907111637414340], [ 486323, 0.997921725583161677], [ 486329, 0.997930933234010112], [ 486377, 0.997953752635044827], [ 486379, 0.997959851929809857], [ 486481, 0.997966255654865566], [ 486491, 0.997968556521690832], [ 486503, 0.997983165063378559], [ 486509, 0.997988264110435446], [ 486559, 0.997989759954631598], [ 486637, 0.997997894776670616], [ 487381, 0.998002005963663006], [ 643847, 0.998019679692110660], [ 643849, 0.998024025241978333], [ 643873, 0.998024372318656677], [ 644047, 0.998038941707563014], [ 644051, 0.998042359142451568], [ 644089, 0.998044531292292332], [ 644101, 0.998056000417200669], [ 644107, 0.998061271292113428], [ 644117, 0.998072740014760890], [ 644123, 0.998084208538209686], [ 644129, 0.998098324259265071], [ 678157, 0.998100462301865701], [ 678169, 0.998102571425134417], [ 678329, 0.998104709224328130], [ 678341, 0.998106041970893350], [ 678367, 0.998115397433533421], [ 678401, 0.998126362534796990], [ 678407, 0.998143212620743275], [ 678409, 0.998157119979209870], [ 678413, 0.998158695979785807], [ 678533, 0.998166716746144708], [ 678541, 0.998168853203551706], [ 678553, 0.998172195370116877], [ 757993, 0.998175495219863695], [ 758099, 0.998177312177460506], [ 758179, 0.998182003490131527], [ 758189, 0.998184061656675797], [ 758201, 0.998185544886152853], [ 758227, 0.998198134711565613], [ 758231, 0.998204308158375654], [ 758267, 0.998204920107694215], [ 758687, 0.998206977426268926], [ 758699, 0.998214297385863171], [ 758707, 0.998226879928831506], [ 758711, 0.998233403136097519], [ 759547, 0.998243344610969061], [ 759553, 0.998255914453657485], [ 759557, 0.998271112718464655], [ 759559, 0.998275796667063797], [ 759569, 0.998290994660210982], [ 759571, 0.998295678293862430], [ 759581, 0.998300181847456006], [ 760093, 0.998304290689829290], [ 760117, 0.998306345046602291], [ 760129, 0.998308399359281309], [ 760141, 0.998318333502052661], [ 760147, 0.998328267498384452], [ 760153, 0.998328384236068220], [1090697, 0.998330146747323333], [1090709, 0.998337196463375821], [1090757, 0.998342074481892288], [1090877, 0.998352988440607133], [1090879, 0.998362071983386219], [1090883, 0.998369325082084712], [1090889, 0.998380238880867499], [1090891, 0.998387491833179402], [1090897, 0.998389253539196642], [1090909, 0.998392845583442116], [1090919, 0.998398267933657647], [1090927, 0.998401859851130562], [1090937, 0.998412773150406010], [1090939, 0.998416295910860079], [1090963, 0.998423410117702575], [1090997, 0.998430593087653794], [1091017, 0.998439675312903700], [1091021, 0.998448203016799289], [1091137, 0.998451793961740377], [1091147, 0.998462705245539919], [1091149, 0.998466296028161872], [1091159, 0.998475098878629158], [1091219, 0.998482279809489515], [1091239, 0.998491290492803147], [1091257, 0.998500370699681984], [1091261, 0.998507521964376369], [1092019, 0.998512665203952050], [1092821, 0.998519906237521939], [1092827, 0.998523423717059176], [1092851, 0.998528699716191843], [1092887, 0.998535940279703860], [1092893, 0.998541353442784897], [1092901, 0.998547836326456795], [1093061, 0.998558452173155730], [1099247, 0.998565402118646748], [1099309, 0.998566838314103236], [1099391, 0.998575794337408227], [1099409, 0.998579966237365493], [1101299, 0.998585344720586099], [1101307, 0.998587096242241142], [1101319, 0.998590475301871653], [1101371, 0.998597666775339437], [1101377, 0.998599356088974312], [1101403, 0.998608360660359147], [1101407, 0.998616929762087116], [1101509, 0.998624585019288272], [1146661, 0.998628043830881672], [1146671, 0.998629736017114459], [1146697, 0.998636678196368998], [1146703, 0.998643620307538482], [1146709, 0.998645262241842409], [1146763, 0.998648720643048544], [1146773, 0.998651949908529799], [1148921, 0.998653664987128921], [1148933, 0.998657095061091983], [1148957, 0.998657952223456633], [1149487, 0.998664283657065156], [1149857, 0.998664476380106311], [1155601, 0.998667640065240234], [1155821, 0.998677990253973114], [1155823, 0.998684792338494870], [1155899, 0.998695141857501669], [1155901, 0.998702035335812003], [1155907, 0.998703744773455231], [1155919, 0.998712366101413461], [1155923, 0.998719259375585483], [1155929, 0.998724424588596779], [1155937, 0.998731317727169293], [1155943, 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