how do I show 12 numbers from a huge number?

[SheeppOSU]

The expression "2^2^34", or "2**2**34" in Python, could be written as 2(2 * 2 * 2 * 2...). The program can't do this because it doesn't have enough space. I haven't tried this yet, but you could try doing it the way a person would do it on paper. It would be a bit complicated to explain, so I'll do an example.
2426
x_53
['7', '2', '7', '8']
['1', '2', '1', '3', '0', '0']
Then the code should line them up and add like this

list1 = ['7', '2', '7', '8']
list2 = ['1', '2', '1', '3', '0', '0']
stringAnswer = ''
for x in range(0, len(list2)) + 1):
    if x < len(list2) - len(list1):
        stringAnswer += list2[x]
    else:
        stringAnswer += str(int(list2[x + (len(list2) - len(list1))]) + int(list1[x]))

I didn't test it so idk if my example code here will work properly, but I hope you get the idea of what I'm trying to do.
EDIT: The code on line 8, could possibly output a 2 digit number, and I didn't work that out, also, the code above would be adding backwards as well as adding the number to stringAnswer backwards. There are a few problems with the code, but again, it's just to give the idea of what can be done.

[anabeatriz]

Guys, I also had the idea of ​​buying a virtual machine that contains a lot of memory for me to try to execute python code (I want to see the number that contains 5 billion digits), can you give me tips?

[jefsummers]

Whether you do the virtual machine or not, think again about my original tongue in cheek answer (base 2). Bit shifting is really really fast and is the equivalent to raising by a power of 2. I've been playing with this a bit this afternoon and benchmarking it. I can get 2 to the 100,000 power in less than 0.02 seconds (IPython). Here's the gist of the code:

import datetime as dt
start = dt.datetime.now()
alpha = 1<<100000
print(alpha)
stop = dt.datetime.now()
print(start,stop)

Result follows. Note that you start with 1, not 2, as you are shifting that one bit from the one place all the way through.

Output:
runfile('C:/Users/summersj/Downloads/aaa.py', wdir='C:/Users/summersj/Downloads')
99900209301438450794403276433003359098042913905418169177152927386314583246425734832748733133244965040316439444555585493001879966076561765629084713542474928751988896298736710932463504273731124792658002785312410887370856052872283901645686910268506759235179146970528576446968015248323454755432502927865208069577709717411022320429763512053307779968979251166198707717857759555217200813202952046179492292592956239209657978735581586675254957973131448062492602618379413050805826860315351341787396228349908863577580621046066363721305877953223449720108084863695414018358513598580356035740218729081555665806071864612689728397946218422675793496388933572475887619591376567624111250207087048704651793963987101092003639347456180906016133778985602968635985580247614489330470522228601313770959583573194858984964045723838751707022423326334368944232973818777331532869442179361253019078689036036632831615027261399341528040711719149239033418749353944558963012921972564177172335435447515523793108922681824024527557520947046421859438628656327442313320847422215514933150027177500642288262118225493496005574573349646784832691809518959557691745096732244177404328404558821091379053756467721399766217852650571698548345624875183223832503186455054721143699341679816781702551228129780651948062954053391546574799412974991903485075443364145056316573960066933824273164340395801212802609842122475142078347122248314103040686037196401618557416564394722534649452497003145098900931622689527444287054764254722531675145211822314553883743082326422006330251375331293651643417252062561553117947386191429047614456549271284181751835313270529754953705614382395732279396730301060774568484774278321953492279838364361637647429695459066723691241363259321233356431358944652191018821238297409079163860232354509593887667364032295779939011521544480036372150691155911119960015305891077294210322304242620356934932160529275696258584458223545946452769231081973058062803265167364493437617324097533423332897302829591735692730132864233117596052304951716770331637095222569524604021433876551976440165281480223483318810975594219604764793885201985410173489859485110054692466172341431353099384059232689535865388869744270086070286355020855620295493524800507965215649196832651067441009678229519541616177175429975200098873073778762106858907709694116104380286239504453237895918707602892603934898261007748876728529181064684891438936490647845912116121933007079005370590421880128565594036990708880329668716116559612323319983109232250828661803218804394475729867620969358197843859279692501233269351946932077243355273655662482237878338880749992768316334403186044636187037897843130328438234704109443065914719283411909751852392123276743849905615636884329390394420026175309768506051329371014490863961416205560535473355699267009413752718291424072342679375650697655674759341013102253428300804090795873295442135513073020501715984242307604692097329072901416063539608805592023573768856478522400927771114891344924169956071717862984365339781808694741067511113535237115404365993108896974856588008878619749343579292462040517672460122506184040119662898726738030704983612179744846791007478463561946648292247361341151355671792917819680560537264841411283478582412591219546011844124093497829633170420025304186616949623187358606524854102222118695442237882891897120805145751413619648053697231645705649984795376571745481285974060773391587753323552156094359192751993510142222469630170137174193375049192953632951011152929518362828191918216516764559465158280489842561167481503678052678786627169996492969493770457948761466281109299820207370133303244510053853785511888034741481986651145793226849009930002367361685552941734420599253719652449979254831593437063439703718096114703230741869850350547222890271748503333683283002811329108416931504573899331839345932929949427960153097561187089189295284490742432847670062431711716227317666067961019678022045645890158995247047410011581109636337313293883568689494087593341769093878063985846473005889281759988444774861300631530687600700848372675277897773568300427789027721056838330214702797285953363321105640642639097245799496861629080196041417539357688765879924285499121517379242703432486484142474568388895418932414509875057594030132496975416969553302968802193048741635010979200362102387682751763699809776149796360967043481401241306835768799049974365962964957054595247353820003637703248949821033313329135623151698544104153170541939282347233988484535521732036880883121009439414349382822035496502815307510870986046812248029738256312449893319652962023726085865090503079933086520012316719151827657420956895131361840954121214737863110428977178614481583169658487669495548262525049612270447147122296202746823629098038774693769873589421254417923552983874798304502539097887334697326030975441564748054737327327672486527590349953363541269539004588549886835749278646152520408004901147858922890854433539969947808674716135197858385714564215831711930041179894407902683463575503398880867251278835772976264992138274365739929273022387925769242327854872012972553860719683037824830637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8131048296612979081477663269791394570357390537422769779633811568396223208402597025155304734389883109376
2019-09-12 14:25:55.975741 2019-09-12 14:25:55.990701

The timestamps at the bottom show this was done in less than 0.02 seconds. I'm gently ramping this up, I think the answer could be had by letting it run overnight on a decent machine (without investing in a virtual box).

[jefsummers]

Time estimate to get the whole number using that method is just under 84 hours. I'm starting it now and will look for the answer Monday morning.

[anabeatriz]

Time estimate to get the whole number using that method is just under 84 hours. I'm starting it now and will look for the answer Monday morning.

thank you! When you're done, let me know.

[anabeatriz]

I have to look in my Math-book. Maybe there is a solution: http://weitz.de/KMFI/
The book is good, but it's only in German. He uses Python to explain math.

---

With modular arithmetic you get the last x digits of the solution.
The built-in function pow supports it.

The equation is: 2 ** (2 ** 34)

pow(2, 2**34, 10**12)

This should calculate the last 12 digits of 2 ** (2**34)

---

The other solution to get the first x digits can may be done with iteration.

def ipow(x, y, digits):
    for _ in range(y - 1):
        x *= x
        # do something to truncate x?
        # maybe working with math.log10

By the way, this question is very old: https://stackoverflow.com/questions/6351...e-required

Another solution is the usage of math.log10: https://stackoverflow.com/questions/3873...nentiation

def get_first_digits(a, b, n):
    x = b * math.log10(a)
    y = math.floor(pow(10, x - math.floor(x) + n - 1))
    return int(y)

Output:
In [65]: get_first_digits(2,2**34,12)                                                  
Out[65]: 927436539881

I showed these numbers yesterday to my teacher and he said they are not the correct ones. I have to buy a virtual machine soon to see the full number...

[DeaD_EyE]

Shit :-/

[jefsummers]

Reviving this old thread, after about 10 days of waiting I still had no answer so I broke the problem apart to see where the slowdown is. It's in the conversion from integer to string. I get the integer answer in less than 1 second. But, it's a huge integer. Conversion to a string so I can display it or write it to a file takes forever.

import datetime as dt
start = dt.datetime.now()
target = 2**34
alpha = 1<<target
stop = dt.datetime.now()
print(start, stop)
input("Calculated value: ")
start = dt.datetime.now()
outstr = str(alpha)
stop = dt.datetime.now()
print(start, stop)
input("Converted to string: ")
start = dt.datetime.now()
with open('c:\\Users\\summersj\\bignum.txt', 'w') as file : 
    file.write(outstr)
stop = dt.datetime.now()
print(f"Wrote to file {start} {stop}")

Output:
2019-09-24 10:15:24.725485 2019-09-24 10:15:25.651044
Calculated value: 

[anabeatriz]

Reviving this old thread, after about 10 days of waiting I still had no answer so I broke the problem apart to see where the slowdown is. It's in the conversion from integer to string. I get the integer answer in less than 1 second. But, it's a huge integer. Conversion to a string so I can display it or write it to a file takes forever.

import datetime as dt
start = dt.datetime.now()
target = 2**34
alpha = 1<<target
stop = dt.datetime.now()
print(start, stop)
input("Calculated value: ")
start = dt.datetime.now()
outstr = str(alpha)
stop = dt.datetime.now()
print(start, stop)
input("Converted to string: ")
start = dt.datetime.now()
with open('c:\\Users\\summersj\\bignum.txt', 'w') as file : 
    file.write(outstr)
stop = dt.datetime.now()
print(f"Wrote to file {start} {stop}")

Output:
2019-09-24 10:15:24.725485 2019-09-24 10:15:25.651044
Calculated value: 

Did you get the whole number in less than 1 second? If you can send me its photo, it would be awesome (at least the first 12 and last 12 digits)! Because, turning it into a string is really complicated!