# The following list of lists in the form [a_1,a_2,...,a_40],[init=x,f=1..40]
#  gives the expectation time number for a prime sum where a_i corresponds to the
#  expectation time of the dice with i-faces for i=1..40 and with initial value x

L1:=[2, 1.5000000000000000000, 1.5443229620595869530, 2.0435600666103862250, 
     1.9293374144815927431, 2.4284520326112658621, 2.1364427295591266747, 
     2.5684161878790772755, 2.7287467108337090440, 2.9713015236434718196, 
     2.7823214298576667855, 3.0813596713700148118, 2.8871428933187858248,
     3.1331891995385863864, 3.2365303599726166358, 3.3899568896197398202, 
     3.2348086388882898448, 3.4533134731721223356, 3.2969917429015145572, 
     3.4722762494520863693, 3.5425771055928523256, 3.6470404036597778475, 
     3.5121823730499168464, 3.6899821553005208501, 3.7372232584201157302, 
     3.8537512829081848628, 3.8936891827095033446, 3.9877314445674274768, 
     3.8745350440001945851, 4.0320059779069223089, 3.9124570011045959493, 
     3.9961866866023480539, 4.0378275580511424770, 4.1191476686112812587, 
     4.1569072059964545156, 4.2662805932829084592, 4.1590824322452382893, 
     4.2276087068220550415, 4.2588398979275869167, 
     4.3321175425650998942], [init=0,f=1..40]:

L2:=[1, 1, 1.6330243953433124663, 1.6348399049697686813, 2.0460365740834708334, 
     2.0815221134539983888, 2.2982829470972053309, 2.6405531471277980499, 
     2.7603614909178484168, 2.7011750624518707204, 2.8407530828721843731, 
     2.8443326917298259899, 2.9788204264800176053, 3.1918825249840766525, 
     3.2711120384209690266, 3.1905481906434070533, 3.2913182548873927094, 
     3.2715606092060266167, 3.3551330029552604218, 3.5139045705913300842, 
     3.5713553771322915634, 3.4884738114910952473, 3.5470800777162008957, 
     3.7228825855874317206, 3.7681975675424617358, 3.8763492409879471911, 
     3.9156244721464092279, 3.8502237546857568697, 3.8991149461383932135, 
     3.9019415366367982930, 3.9403839527702783800, 4.0230446144839689382, 
     4.0590173652954245578, 4.1397473882295599287, 4.1726082602073276122, 
     4.1509759557463501848, 4.1775767990998716231, 4.2454124674959056125, 
     4.2727358611668562529, 4.2264563306111345368], [init= 1,f=1..40 ]:

L3:=[1, 2.3145973062313413334, 1.8991316117493152132, 2.5394625976051517091,
     2.6007638116868130538, 3.2266393958645986493, 2.8110426176114460052, 
     3.0968991615158200758, 2.8386645531030071854, 3.1462398431384509552, 
     3.2538996801954224917, 3.5831558042064096362, 3.3379019980266639491, 
     3.5172419776186651484, 3.3216182779856499239, 3.5145937382976658712, 
     3.5810074372219124313, 3.7996770964273633511, 3.6218375343015567666, 
     3.7624030938746078993, 3.8114023625178786476, 3.9101084544402247273, 
     3.9465205076886802507, 4.1173465485493810597, 3.9666251218271561460, 
     4.0717998564161887004, 3.9430695578449621996, 4.0459619718872703809, 
     4.0776116399601999776, 4.2397481264533496915, 4.2701039581813124675, 
     4.3372160937395501383, 4.2205455180619984588, 4.2987831573876001668, 
     4.3199502717032863581, 4.4322631553569131754, 4.3240858265054739721, 
     4.3896442348627685304, 4.2900020953949300219, 
     4.3695040347653656229], [init=4,f=1..40]:

L4:=[1, 2.6292243139770376583, 2.6974467904324519176, 3.0591707485760504658, 
     2.6295206341523552915, 3.2626801014121088163, 2.8459276718425864284, 
     3.1902953622672914690, 3.2698516359412240715, 3.5643093303673529017, 
     3.3075575205078484666, 3.6273187753912012708, 3.3752417723547081034, 
     3.5719399872380691830, 3.6582703364053314287, 3.8050405613778523797, 
     3.6191519825750077909, 3.8340236249252866671, 3.8659134086586115436, 
     4.0027350416129851323, 4.0237633570647386998, 4.1200629250388888526, 
     3.9651993376853728887, 4.1347966550870612383, 3.9900607894112112973, 
     4.1006217628344020583, 4.1372930968546220416, 4.2244122131579794856, 
     4.2520376045875878993, 4.4142578035775534403, 4.2831733748565140816, 
     4.3550598819508050358, 4.3784040376212172920, 4.4461242615706304605, 
     4.3320349443147854346, 4.4478561030527875006, 4.3388042087871344969,
     4.4075923817722660852, 4.4318093225949937249, 
     4.5103182098448972769],[init=6,f=1..40]:

L5:=[3, 3.2584851485479084228, 2.5077089208055138321, 3.0987627310552909525,
     2.6657974348606565895, 3.3107195024647118020, 3.4311976251461977557, 
     3.6198134766243244233, 3.3069332805479792746, 3.6250815549562569231, 
     3.3568668724025806678, 3.6686619715458693449, 3.7338797339862490682, 
     3.9106864623982566255, 3.6846171366700404892, 3.8460779722032520368, 
     3.8936685359986512046, 4.0773486084703141671, 4.1017981097664089976, 
     4.2138264216310082214, 4.0354230102525999727, 4.1400627744286815865, 
     3.9834345396670523415, 4.1595271970779653662, 4.2033147514793200703, 
     4.2950530078893526834, 4.3134165750629060008, 4.3986516123481652100, 
     4.2661583301920868817, 4.4281302857817515097, 4.4539028314398911812, 
     4.5129452892093817682, 4.3866382193717973488, 4.4588810719578750921, 
     4.3480872625995089032, 4.4632390490168290335, 4.4898372749552276329, 
     4.5492616226360389171, 4.4460479964374570056, 
     4.5276208223419954076],[init=8,f=1..40]:

L6:=[2, 2.1723169502696720209, 2.5846643570634277939, 2.4790035069780133539, 
     2.7085801861268287312, 3.3649915873934724421, 3.4135121897303273914, 
     3.2176031932687799770, 3.3831453867932790837, 3.2955200521680900848, 
     3.4023234666561109307, 3.7075791198288732347, 3.7658702519878340642, 
     3.6499744860524841056, 3.7269575857328425978, 3.8691213502138554120, 
     3.9021353084006919233, 4.0869508338327406364, 4.1010156444903333648, 
     4.0131683735921227851, 4.0567428114299883840, 3.9600500554311225453, 
     4.0100321673331109661, 4.1833291970296397760, 4.2178496799406257780, 
     4.3028773657262553856, 4.3220748058821664700, 4.2469742489204626585, 
     4.2802583710686480017, 4.4419767200268669914, 4.4623508073279328828, 
     4.3761895995112853964, 4.3995848207616358462, 4.3314846924755343518, 
     4.3637972796115361214, 4.4784185256127768974, 4.5008957192832973862, 
     4.4326141050619482078, 4.4637072222984707363, 
     4.5413866052690170025], [init=9,f=1..40]:

L7:=[1, 2.3446533667232451146, 1.9384935332012691648, 2.6589400011453075230,
     2.7732784528710779557, 3.4215141340781100402, 2.9868243311313410716, 
     3.3096465903994205278, 3.0448316093209440045, 3.3809058572649117537, 
     3.4443478123976340578, 3.7444044893821134480, 3.4968695121162845102, 
     3.6959451592658171186, 3.7665232730249600614, 3.8922704500822301847, 
     3.9113185673011606147, 4.0971165028466861186, 3.8959652334457394810, 
     4.0357156522280457541, 3.8723358730349200793, 3.9874063075340111213, 
     4.0355206470537882256, 4.2062599752588535359, 4.2321992967385556579, 
     4.3112326645029023243, 4.1677153081768116696, 4.2672152809508864756, 
     4.2943322511641942151, 4.4557710650873085173, 4.3229025971211726485, 
     4.3891899007895651357, 4.2701854876280322416, 4.3519353167330753503, 
     4.3792865692076283510, 4.4934007799161747691, 4.3824403336646467328, 
     4.4504780418842899481, 4.4810687555266428524, 
     4.5551057884453138775], [init=10,f=1..40]:

L8:=[1, 2.6893479597368536193, 2.8155366472059387291, 3.2571622753501696966,
     2.8471997772541376013, 3.4789478414643644673, 3.0900760732843607199, 
     3.4380086471895340155, 3.5434382918931863654, 3.7770416535515704552, 
     3.4835481334480170449, 3.8011865005435564327, 3.8446413873421313495, 
     4.0272192118057055409, 4.0440347681846833715, 4.1375451512861854141, 
     3.9211530365894805145, 4.1084342716323444907, 3.9186050173457970669, 
     4.0677655556659714204, 4.1057663241574196786, 4.2142878344733112181, 
     4.2526352699438806338, 4.4037209415809931391, 4.2392057199089313370, x
     4.3265663697266033163, 4.3582488747600670486, 4.4426544241591283923, 
     4.3083745080008626886, 4.4695184448625338942, 4.3358081725121713225, 
     4.4069020386923218347, 4.4377447818153462296, 4.5079948386363845453, 
     4.3945725019033153592, 4.5083029833732205418, 4.5342198537018147331, 
     4.6001665954326722007, 4.6208086557375719461, 
     4.6935764951605283173], [init=12,f=1..40]:

L9:=[3, 3.3787268908957158697, 2.6382297381593303110, 3.3786927532599313187, 
     2.9225252092471727668, 3.5989827763064771077, 3.7683997969431940836, 
     3.9374176626946996886, 3.5502712601633203342, 3.8197815581615192490, 
     3.9005332580507477231, 4.1469539640682309092, 4.1705513359703370195, 
     4.3001840965273755642, 4.0326501013317961864, 4.1488106501839747738, 
     3.9315785916887268369, 4.1329137595355405309, 4.1823338294324206070, 
     4.3014646544705470722, 4.3301235276198765397, 4.4317429556415054117, 
     4.2600722304606292997, 4.4113574597254825868, 4.4327474882248526257, 
     4.5172123255905296011, 4.3663607893532234219, 4.4575932656672372787, 
     4.3223797191551373106, 4.4832197910410654767, 4.5079372089358021690, 
     4.5749775959171595637, 4.4495299471333912756, 4.5239923454258732652, 
     4.5471682041299044830, 4.6600880459174656531, 4.6831120703478541967,
     4.7398348078726149957, 4.6316219491563522011, 
     4.7074218600304700732], [init=14,f=1..40]:

L10:=[2, 2.2524703493541515473, 2.8084243704738902084, 2.7029462352757372446,
      3.0967395411533333833, 3.6905997327682258829, 3.7596987117635896555, 
      3.4999179676251227468, 3.6001620303732194641, 3.8565461473872066563,
      3.8979845496300604136, 4.1492661241054773291, 4.1512144062657104315, 
      4.0134968973817325212, 4.0425486446982329515, 3.9047523158999505625, 
      3.9579001710139664654, 4.1563569884069414155, 4.1913775585113943552, 
      4.3108521422398563716, 4.3394106524021980388, 4.2390486602740802852, 
      4.2676087437156420998, 4.4193655124832696905, 4.4410080190785236662, 
      4.3499084831279682993, 4.3815283644216307829, 4.3038733861237444150, 
      4.3363425340174742856, 4.4968754382957260486, 4.5211798715412634274, 
      4.4363323037216984104, 4.4656216569692778930, 4.5353957401888998394, 
      4.5587058352507705311, 4.6714092531594448711, 4.6905827595248163416, 
      4.6182901863954794946, 4.6457333594569015480, 
      4.7210431968853096192], [init=15,f=1..40]:

L11:=[1, 2.5049739592003454471, 2.1063102919825794539, 2.9470367736986874558, 
      3.2168379713915462610, 3.7606788072064837467, 3.2897279269411203071, 
      3.5559810744695311352, 3.6406933676300556423, 3.8884380574410975618, 
      3.8977162094231530425, 4.1527251325556344189, 3.8546996525792445177, 
      4.0214176422342726979, 3.7898802626545218537, 3.9310043600486349255, 
      3.9829078709753987595, 4.1788237782543626296, 4.2002545357119700682, 
      4.3201834687457400305, 4.1421551700522157037, 4.2555596488978722108, 
      4.2756112442190985699, 4.4277142423777339645, 4.2702003608461419950, 
      4.3649547278061130017, 4.2250349414511830588, 4.3240719807942318115, 
      4.3502577015596236581, 4.5104851930467731338, 4.3798932276826851202, 
      4.4529768335112335314, 4.4813635080236144453, 4.5468425053551684826, 
      4.5702576693260337704, 4.6827166810125113547, 4.5671465978164571606, 
      4.6327850891664960626, 4.6596126507827545898,  
      4.7344444149452983891], [init=16,f=1..40]:

L12:=[1, 3.0099848981290615769, 3.3190047895632371063, 3.8648336174054624297, 
      3.2991190955081918532, 3.8235158270218154816, 3.8128718015881308852, 
      4.0460284005323097944, 4.0690959307745677964, 4.2327369496363375701, 
      3.8993003031919054274, 4.1573060435196106369, 3.8606872359496071027, 
      4.0508111858808269511, 4.0791253325875404693, 4.2151607192442838800, 
      4.2520338150358629884, 4.4168955443536142338, 4.2090453725905140875, 
      4.3401478998815680686, 4.3664529873931879316, 4.4555685879082642299, 
      4.2840324351701959905, 4.4437756887638244623, 4.2850215769263778106, 
      4.3870675807563378880, 4.4173858626332495037, 4.5012322658581363303, 
      4.3641373796430409197, 4.5291995158945257174, 4.5515729346448488909, 
      4.6204869179352581152, 4.6354871978904232980, 4.7000823742215447886, 
      4.5818140400512573187, 4.6941117793467868116, 4.7169303778990000450, 
      4.7802012367997419297, 4.8035319123194953661, 
      4.8699959677786794308], [init=18,f=1..40]:

L13:=[3, 4.0200081497027698529, 3.3867461776335643314, 3.9233939711924733220,
      3.9678476416332682817, 4.3192276844781414234, 4.2893784477337012345, 
      4.4648539845645657134, 4.0177903386196397276, 4.2347026304873380433, 
      3.9023768167288069411, 4.1648121387904978064, 4.2043600955191518568, 
      4.3377541729396261881, 4.3561652920394821424, 4.4841034283453180079, 
      4.2474890139806612544, 4.4265411924333397563, 4.4598758506225475347, 
      4.5638415537302914488, 4.3651107523856509671, 4.4648269536373872548, 
      4.3012824077066137724, 4.4595444056709462620, 4.4948513689274367933, 
      4.5790635901282005433, 4.4253573684252729033, 4.5159883487991959748, 
      4.5487453605311688833, 4.7011580214727356818, 4.7186714928796860567, 
      4.7742713215644978231, 4.6427042759030936619, 4.7122931364984591691,
      4.7326253222508387367, 4.8439730300925629498, 4.8636305672498862226, 
      4.9243209187625463446, 4.8104453755146822462, 
      4.8800979741941123095], [init=20,f=1..40]: