This is https://jim-quinn8.blogspot.com
See also https://jim-quinn4.blogspot.com
The value of the natural logarithm e with 110 e terms in my Long Number Calculator with just 1510 digits for the calculation (the assigned limit to speed it up!) inside the
.exe file (which took only 2 minutes 6 seconds on my desktop!) is:
2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738 this has 159 accurate digits
while
The value of the natural logarithm e with 2570 digits after the decimal point and it is accurate upon reading, and as a result of my Visual Basic Version 2.5 Long Number calculation, with 1100 e-terms is:
1100 e terms v2.5 with an accurate 2570 digits after decimal point:
2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193200305992181741359662904357290033429526059563073813232862794349076323382988075319525101901157383418793070215408914993488416750924476146066808226480016847741185374234544243710753907774499206955170276183860626133138458300075204493382656029760673711320070932870912744374704723069697720931014169283681902551510865746377211125238978442505695369677078544996996794686445490598793163688923009879312773617821542499922957635148220826989519366803318252886939849646510582093923982948879332036250944311730123819706841614039701983767932068328237646480429531180232878250981945581530175671736133206981125099618188159304169035159888851934580727386673858942287922849989208680582574927961048419844436346324496848756023362482704197862320900216099023530436994184914631409343173814364054625315209618369088870701676839642437814059271456354906130310720851038375051011574770417189861068739696552126715468895703503540212340784981933432106817012100562788023519303322474501585390473041995777709350366041699732972508868769664035557071622684471625607988265178713419512466520103059212366771943252786753985589448969709640975459185695638023637016211204774272283648961342251644507818244235294863637214174023889344124796357437026375529444833799801612549227850925778256209262264832627793338656648162772516401910590049164499828931505660472580277863186415519565324425869829469593080191529872117255634754639644791014590409058629849679128740687050489585867174798546677575732056812884592054133405392200011378630094556068816674001698420558040336379537645203040243225661352783695117788386387443966253224985065499588623428189970773327617178392803494650143455889707194258639877275471096295374152111513683506275260232648472870392076431005958411661205452970302364725492966693811513732275364509888903136020572481765851180630364428123149655070475102544650117272115551948668508003685322818315219600373562527944951582841882947876108526398139559900673764829224437528718462457803619298197139914756448826260390338144182326251509748279877799643730899703888677822713836057729788241256119071766394650706330452795466185509666618566470971134447401607046262156807174818778443714369882185596709591025968620023537185887485696522000503117343920732113908032936344797273559552773490717837934216370120500545132638354400018632399149070547977805669785335804896690629511943247309958765523681285904138324116072260299833053537087613893963917795745401613722361878936526053815584158718692553860616477983402543512843961294603529133259
1100 terms ends in: 133259428
1000 terms ends in: 133259179
The equation is e = 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! +.............+ 1/1100!
The screenshot below shows the first 160 digits - you have to copy to the right to obtain all digits, for there are actually 7010 in there, but as you have seen only 2570 count!
It took 7 hours 25 minutes to perform this calculation on my Windows XP desktop computer:
Intel(R) Core(TM)2 CPU 6300@1.86GHz 1.58GHz 1.97GB RAM
Physical Address Extension
Microsoft Windows XP Professional Version 2002 Service Pack 3
Jim
1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703029969945094998952478811655512094373648528093231902305582067974820101084674923265015312343266903322886650672254668921837971227047131660367861588019049986537379859389467650347506576050756618348129606100947602187190325083145829523959832997789824508288714463832917347224163984587855397667958063818353666110843173780894378316102088305524901670023520711144288695990956365797087168498072899493296484283020786408603988738697537582317317831395992983007838702877053913369563312103707264019249106768231199288375641141422016742752102372994270831059898459475987664288897796147837958390228854852903576033852808064381972344661059689722872865264153822664698420021195484155278441181286534507035191650016689294415480846071277143999762926834629577438361895110127148638746976545982451788550975379013880664961911962222957110555242923723192197738262561631468842032853716682938649611917049738836395495938145757671853373633125910899655424624834787197605235997769192323570220305302840385915414971072429559206706202509520175963185872766359975283663431080150665853710647328538625922260582220510403680270297504798728079461658100417052681940019095733462175943893670249320422691034369812463720111185261084268910299720311202100063507176374582405203847555197279933797614906107894985544223326004018851303631561144886847281589288163245187265066645384877599162576642872111240842068016763517100102943180715515190961642460907039408129216903517492961364004139670431041253632327030922577327960292376597745537095469115742140424230781992327617401906424512454877516862696105333694216213605394604245654140128533007813633449856736406703977342229811961042925534501601405940479547154534548407271737656262366549166640233006013265744070107836858468452313160467754480500402240639911970362218602920238867150711017169400296868759663500040895316214233425227956834067013470185902028360716762147743493449563595808082130442586469468522610908263353008756612603460672195404055984128912975994810000772057440230047673258800091514371489475444879157191294659083570873961515537797640262068370848046072969382719585689759759626104159152657577790782334980567840022901532052138935373775536566427046826874289963441395743666073744445583086477893212985302148197395341478170516614952551763291993699565744522639112519093541386989366817430938226424736926202072990967831154131946484377915459915923928287714695149274026409213645654041644581490201945749419305269002613972646081065071439603206077510594187798284793986195249964165213139715293599421897416647075187235788629466108560170428869605798394052906407430811833388677881562635867156008396760245349229943938867059754315442943430957258470988215463111260766774067864571578060647447499750354544559313286549189849336572747626297414738235686914837831363361283627903824840163806671607179848728555842931349226093240565957553651136754644387834283313466644554180390821898983294626345016171122016929619460169320621033039744866231656003566781813443100896568706742965658177445572685015631594412507361198063472886466241327193669426712951450397518928313486192841303255188431169014671423794374728334344652482043796059732870616274910941596862625302558889768470417502003140262284691048046984032437906606737749627102512710602060862662843666050192890893838320006091228691881836842361693903523126930368613796811526946997891926635284389927016519825502252923579366281634568108913074112678378199449772765448294920438801301783546499213574032791577507786002296423504275996997626918738414847394773851563552091220963315839034567189415294357040653076085290174249768185502885276344949577449110422502453723156063618103504871759158032791798367510067136100066217566049573766777112925287302479926720158996418937762016114118289899682955902511656391422364995062850030696812973507251727918598301115277542298851885311763594786003123063726098369850308310852145595748359555715739356633680864821078791247051031631569581604348748829614894154585355561974999296877955099285527423590251810323766861609592552544319954907420679739157072614245328950428097351037967736660135917522627061232312589450697634813177754456066603576220483006904225389494867729521325719769245927670660765816558298675056572894658860919029644381285057859759437506402446062121456085608545249251368328754843438733720201692311630432705648060137587936856721535087816844078023292064623163811291772297752725531075161383682134604577799854625622081960631636019206330968516216231660683468863116621501323854287391304495123155216365621295187475530976570639955029880425647340557785191349533039888643071431785052007986242468481382976340802176297056457213162198306829364628682222279923816416353172598273213079714192676286915681181839966515100307010826703128664015918312719604038923540682591504595764918368552614803465109289896559961829716408498135702922729622140263750595519947501618105854474019764971593766342388569701982214045410209642908388248860987218876494800835944491934478931331080777740838035601892228537110093898091204853232990455598524096889180504497043838415045586150130902907091306156469685958969228276473764261083791700284689036668670497679170399954436330425855797794077269935288950837827114357125780631282729349883385045927110609526062879059715054945907279841681751687041505072957723365201003263831478479410794607656506369332663038206021719551471952041208479627248539111589302866641079696991524811276979149995102660574531123881393934919708926940735738491944291963007280950338654302137812339456142472424586825005490509782168419895154077663046648660253211821517058546481699010351020406040779053482395457081103662802419307833539518597508847118544793150345001580384709447854602092161934402798458912472052941776762506497961858234776556280824940544437650597779439080197924300154959936710407983913033119996866535017872308995874345981050410546853618716669008602651872709506307892209449850428619343629495429310972099408595585896796000425822959426943909574110166784798090792890754084338798997585569009471963248904323366036372887420477179897787319674789334640099238795928413280479076582258181183540591455395810029729132679714194354057353161415847980294411862031322519054091589019122255319653737392856310390787757920503439443610560728204865743914647280480723365927320176656223005701114685591214450995505364985643365509525473974996502828824922856959093188033794992264659862068823401174394496293131985985880254199347096201038949171977062258657266707618728353902334806925083435649537445628310757587186877538159397085400698899220166054425026312832880789794907045544329548492870187596100762027461311058672024649539970560477439601070677420574723587570759024726518532288910223630374462004719642400758541636765726892037163539219477428690685888815809704248358215149135699281075072307826447406718734809484544537264931062922580337258517145144805462076646086736427250483015812043421751869316708560008335295934426745872998735071625170300571157138175301302407011029660250955862422560289064674131908000682128984594
which was then squared to go back to "nearly" 3 !!
The Square of the Square Root of 3 to 7010 digits:
2.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
Note that if you enter -1 into the number 1 slot, and square it you will see 100 as the answer - so there are a couple of unrectified snags on the very simple stuff, but the big stuff works well.
And here is the Visual Basic long number calculator v2.5 programme - just a part:
Public Class fclsLongNumCalc
Inherits System.Windows.Forms.Form
Public Const maxdigits As Integer = 7010
Public Const limit As Integer = 7055
Public Const Pi As String = "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631"
Public Const e_ As String = "2.71828182845904523536028747"
Public Const c_km_per_sec As String = "299792.458"
' Throughout I have used the arrays starting at 1,
' to avoid confusion with the text start point.
Public intNum1(limit + 1) As Integer ' Number1
Public intNum2(limit + 1) As Integer ' Number2
Public intAnswer(limit + 1) As Integer ' Answer
Public lenNum1 As Integer ' length of number1
Public lenNum2 As Integer ' length of number2
Public length As Integer ' length of answer
Public dp1posn As Integer ' dpposn points to Number1 array position after dp
Public dp2posn As Integer ' dpposn points to Number2 array position after dp
Public dpAposn As Integer ' dpposn points to Answer array position after dp
Public failure As String ' failure is "0" for success, "1" or "2" otherwise
Public sign1 As Integer ' sign will be -1 if number is negative
Public sign2 As Integer ' and sign = 0 if number is positive
Public signA As Integer
etc etc etc
Private Sub btn_e_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btn_e.Click
Call WarningText(0, "0") ' Reset warning
Call calculate_e()
Call AnswerText() ' e is the result
End Sub
Private Sub calculate_e() ' Calculates e - the base of natural logs
Dim PrevTerm(limit + 1) As Integer ' Previous term of the series
Dim PrevSum(limit + 1) As Integer ' Previous sum of the series
Dim counter As Integer
Dim counter2 As Integer
Dim dpPrevTerm As Integer ' DP of previous term
Dim lenPrevTerm As Integer ' Length of previous term
Dim dpPrevSum As Integer ' DP of previous sum
Dim lenPrevSum As Integer ' Length of previous sum
Dim strN2 As String
Dim lenN2 As Integer
PrevTerm(1) = 1 ' Set values of the first term to start
dpPrevTerm = 2 ' in e = 1+1/1!+1/2!+1/3!+.....+1/n!+...
lenPrevTerm = 1
PrevSum(1) = 1
dpPrevSum = 2
lenPrevSum = 1
sign1 = 0
sign2 = 0
For counter2 = 1 To 1100 ' 1100 terms required for 2000+ digits
For counter = 1 To limit + 1 'Transfer prevterm to n1 array
intNum1(counter) = PrevTerm(counter)
Next counter
dp1posn = dpPrevTerm
lenNum1 = lenPrevTerm
strN2 = Trim(Str(counter2)) ' Now n2 array = counter
lenNum2 = Len(strN2)
Call transfer(lenNum2, strN2, failure, dp2posn, intNum2, sign2)
Call Divide() ' Divide n1 by n2 to obtain next term in series
For counter = 1 To limit + 1 ' Transfer asnwer to n1 and prevterm
intNum1(counter) = intAnswer(counter)
PrevTerm(counter) = intAnswer(counter)
Next counter
dp1posn = dpAposn
dpPrevTerm = dpAposn
lenNum1 = length
lenPrevTerm = length
For counter = 1 To limit + 1 ' transfer prevsum to n2
intNum2(counter) = PrevSum(counter)
Next counter
dp2posn = dpPrevSum
lenNum2 = lenPrevSum
Call Padding() ' Add n1 and n2 to obtain new sum of series
Call Adding()
For counter = 1 To limit + 1 ' Transfer sum to previous sum array
PrevSum(counter) = intAnswer(counter) ' gives e on buildup
Next counter
dpPrevSum = dpAposn
lenPrevSum = length
Next counter2 ' Now loop back for next term
End Sub
Private Sub btnAbout_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnAbout.Click
Dim sMessage As String
sMessage = "Long Number Calculator" & ControlChars.CrLf & _
"Designed by Jim Quinn BSc CEng(1985) FIMechE - I also have C&G C++, but I prefer Visual Basic for I learnt that on my Sinclair Soectrum 48k in the 1980's!" & ControlChars.CrLf & _
"Version 2.5, 1100 e terms, June 2023"
MessageBox.Show(sMessage, "About", MessageBoxButtons.OK, MessageBoxIcon.Information)
End Sub
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