This very large integer is written out in words following the large number naming standards of R. K. Guy and J. H. Conway, as described on Wikipedia. Converting this to a machine-readable format may be a test of your computer programming skill!
(It can probably also be done without programming in a text editor or word processor. You could do a search-and-replace to transform the various Latin numbers in the names of the power-of-ten scales into decimal integers, confirming whether or not there are any gaps in the scale, then deleting the names of the scales, then doing another search-and-replace to transform the English number names into decimal integers.)
In more conventional decimal notation this number is
3133553981605965122843809233721715366660499888754558152396581782502292713560072273133411388651711565 2751791982437376901293085076208499357400411479715613289416668474871275537966736595657526370331659024 3726738673886376028204422390946579045833348870085663085401981457433199185794951108689863220238032388 6341940561368402751057350409889706761830512916588565518946786457591544444986342229173699327750837766 4168391583015603750294600980265076076269433681250152964864481077949988780418501107896129360469152617 7621248073260102654523707946988708303966920913130984024130372993776086739472500876076389854939794850 2459622020881855519793612896101754980433395920886295156679555233366220617098118639111733242300595927 5986540725209813415417350415602211114887343174144264948656002711358311555027825439235447088433517769 2718611444262215247477319539356887569039719699016377082793057051246207388637215663449148501751475567 4652542584570420423854104307813085217596308415514821313294387442824090231574974042137171903773517388 6153018196900065664287749158996195318646990026961683993393839418109998353463530974448200041130194317 9175061857482067448844194852895306129595276421887378938451102949340666116012172274626740004070067041 5381335277936222086606790305944261453999757045173707328644636019753914347081804105052553692055413196 2976682840981908282222319854593869812107080455731323593443666349203560157759704286818422736702789105 2037025887320792628708843780746109635760805277926808179865877073968098105865517850784365049027078546 9103051133675070926665576554138591709440147265158710911356270480288955051818998559485589260849602580 7738152863655257661252325256111421265004036295101829620043162465881027427298342580328358120911940178 8057619712884279624216177248236692768300441978766652795146824942760593920455859735046594196697673007 6084319021070002517314898980337028183192030931180395958569963713446635949500031278793755507415125142 1370188222269218842582503982132359187841911535849776111903935687962605584617322898812161066242148837 2898620951883185293680589914297112816554340233173978793339901089671113255611449391267068255720044994 9060656922189936964511610902294853340682307413842407118009738098692181921912192627229851645611466159 0469781663743815220536463304268050347998459472407023057334314577932512128925695
which is actually not all that large as integers go. (For example, it's far smaller than the Mersenne primes that have been submitted to win EFF's cooperative computing awards—those are millions of digits long, while this number is only a mere 2279 digits long!)
What's unusual about this number? Well, if you convert it to hexadecimal you might notice the value
1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000fc703800003fffffc00001f8e07000 007fffff800003f1c0e00000ffffff1fffc7038fc7fff1fffffe3fff8e071f8fffe3fffffc7fff1c0e3f1fffc7fffff8e00e 381f8e38038ffffff1c01c703f1c70071fffffe38038e07e38e00e3fffffc70071f8e3f1c01c7fffff8e00e3f1c7e38038ff ffff1c01c7e38fc70071fffffe38038e3fe38e00e3fffffc70071c7fc71c01c7fffff8e00e38ff8e38038ffffff1fffc71f8 1c7fff1fffffe3fff8e3f038fffe3fffffc7fff1c7e071fffc7fffff8000038e38e00000ffffff0000071c71c00001fffffe 00000e38e3800003fffffffffffc0007fffffffffffffffff8000ffffffffffffffffff0001fffffffffffe071f81c0ff803 81ffffffc0e3f0381ff00703ffffff81c7e0703fe00e07ffffff1c003f03ffc7fffffffffe38007e07ff8ffffffffffc7000 fc0fff1ffffffffff8e38e38e381ff1ffffffff1c71c71c703fe3fffffffe38e38e38e07fc7fffffffc0e38e07e3fff803ff ffff81c71c0fc7fff007ffffff038e381f8fffe00ffffffe001c01c7e38e38fffffffc0038038fc71c71fffffff80070071f 8e38e3fffffffffffff1c0ff8038ffffffffffffe381ff0071ffffffffffffc703fe00e3ffffff8000038e3f1c71f8ffffff 0000071c7e38e3f1fffffe00000e38fc71c7e3fffffc7fff1f8e00e07007fffff8fffe3f1c01c0e00ffffff1fffc7e380381 c01fffffe38038fc71f800003fffffc70071f8e3f000007fffff8e00e3f1c7e00000ffffff1c01c71c0ff8fc01fffffe3803 8e381ff1f803fffffc70071c703fe3f007fffff8e00e3f038ff8038ffffff1c01c7e071ff0071fffffe38038fc0e3fe00e3f ffffc7fff1c7ff8007e3ffffff8fffe38fff000fc7ffffff1fffc71ffe001f8ffffffe00000e0003fe38fffffffc00001c00 07fc71fffffff8000038000ff8e3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
appears very "special" in that it starts and ends with a whole lot of Fs, and has a seemingly very repetitive structure in the middle. This might also prompt you to try converting it to binary
1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111100000000000000000000011111100011100000011100 0000000000000000000111111111111111111111111000000000000000000000111111000111000000111000000000000000 0000001111111111111111111111110000000000000000000001111110001110000001110000000000000000000001111111 1111111111111111100011111111111111100011100000011100011111100011111111111111100011111111111111111111 1111000111111111111111000111000000111000111111000111111111111111000111111111111111111111111000111111 1111111110001110000001110001111110001111111111111110001111111111111111111111110001110000000001110001 1100000011111100011100011100000000011100011111111111111111111111100011100000000011100011100000011111 1000111000111000000000111000111111111111111111111111000111000000000111000111000000111111000111000111 0000000001110001111111111111111111111110001110000000001110001111110001110001111110001110000000001110 0011111111111111111111111100011100000000011100011111100011100011111100011100000000011100011111111111 1111111111111000111000000000111000111111000111000111111000111000000000111000111111111111111111111111 0001110000000001110001110001111111110001110001110000000001110001111111111111111111111110001110000000 0011100011100011111111100011100011100000000011100011111111111111111111111100011100000000011100011100 0111111111000111000111000000000111000111111111111111111111111000111111111111111000111000111111000000 1110001111111111111110001111111111111111111111110001111111111111110001110001111110000001110001111111 1111111100011111111111111111111111100011111111111111100011100011111100000011100011111111111111100011 1111111111111111111111000000000000000000000111000111000111000111000000000000000000000111111111111111 1111111110000000000000000000001110001110001110001110000000000000000000001111111111111111111111110000 0000000000000000011100011100011100011100000000000000000000011111111111111111111111111111111111111111 1111111000000000000000111111111111111111111111111111111111111111111111111111111111111111111111000000 0000000001111111111111111111111111111111111111111111111111111111111111111111111110000000000000001111 1111111111111111111111111111111111111111111100000011100011111100000011100000011111111100000000011100 0000111111111111111111111111111000000111000111111000000111000000111111111000000000111000000111111111 1111111111111111110000001110001111110000001110000001111111110000000001110000001111111111111111111111 1111100011100000000000011111100000011111111111100011111111111111111111111111111111111111111100011100 0000000000111111000000111111111111000111111111111111111111111111111111111111111000111000000000000111 1110000001111111111110001111111111111111111111111111111111111111110001110001110001110001110001110001 1100000011111111100011111111111111111111111111111111100011100011100011100011100011100011100000011111 1111000111111111111111111111111111111111000111000111000111000111000111000111000000111111111000111111 1111111111111111111111111110000001110001110001110000001111110001111111111111110000000001111111111111 1111111111111100000011100011100011100000011111100011111111111111100000000011111111111111111111111111 1000000111000111000111000000111111000111111111111111000000000111111111111111111111111111000000000000 1110000000001110001111110001110001110001110001111111111111111111111111111110000000000001110000000001 1100011111100011100011100011100011111111111111111111111111111100000000000011100000000011100011111100 0111000111000111000111111111111111111111111111111111111111111111111111111000111000000111111111000000 0001110001111111111111111111111111111111111111111111111111110001110000001111111110000000001110001111 1111111111111111111111111111111111111111111111100011100000011111111100000000011100011111111111111111 1111111111000000000000000000000111000111000111111000111000111000111111000111111111111111111111111000 0000000000000000001110001110001111110001110001110001111110001111111111111111111111110000000000000000 0000011100011100011111100011100011100011111100011111111111111111111111100011111111111111100011111100 0111000000000111000000111000000000111111111111111111111111000111111111111111000111111000111000000000 1110000001110000000001111111111111111111111110001111111111111110001111110001110000000001110000001110 0000000011111111111111111111111100011100000000011100011111100011100011111100000000000000000000011111 1111111111111111111000111000000000111000111111000111000111111000000000000000000000111111111111111111 1111110001110000000001110001111110001110001111110000000000000000000001111111111111111111111110001110 0000000011100011100011100000011111111100011111100000000011111111111111111111111100011100000000011100 0111000111000000111111111000111111000000000111111111111111111111111000111000000000111000111000111000 0001111111110001111110000000001111111111111111111111110001110000000001110001111110000001110001111111 1100000000011100011111111111111111111111100011100000000011100011111100000011100011111111100000000011 1000111111111111111111111111000111000000000111000111111000000111000111111111000000000111000111111111 1111111111111110001111111111111110001110001111111111110000000000001111110001111111111111111111111111 1100011111111111111100011100011111111111100000000000011111100011111111111111111111111111100011111111 1111111000111000111111111111000000000000111111000111111111111111111111111111000000000000000000000111 0000000000000001111111110001110001111111111111111111111111111110000000000000000000001110000000000000 0011111111100011100011111111111111111111111111111100000000000000000000011100000000000000011111111100 0111000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111
where its appearance is even more striking, with lots of 1s at the beginning and end, and lots of apparent structure in the middle. What's the length of that binary number?
You could play around with it in a resizable text terminal, noticing patterns that appear to be drawing a picture as you adjust the size, or you could check explicitly and see that it's 7569, which is a perfect square (87×87). If you print out this binary number in an 87×87 grid (that is, 87 lines of 87 bits each) (for example, with something like print("\n".join(b[i*87:(i+1)*87] for i in range(87))) in Python) it looks like this:
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111000000000000000000000111111000111000000111000000000000000000000111111111111 111111111111000000000000000000000111111000111000000111000000000000000000000111111111111 111111111111000000000000000000000111111000111000000111000000000000000000000111111111111 111111111111000111111111111111000111000000111000111111000111111111111111000111111111111 111111111111000111111111111111000111000000111000111111000111111111111111000111111111111 111111111111000111111111111111000111000000111000111111000111111111111111000111111111111 111111111111000111000000000111000111000000111111000111000111000000000111000111111111111 111111111111000111000000000111000111000000111111000111000111000000000111000111111111111 111111111111000111000000000111000111000000111111000111000111000000000111000111111111111 111111111111000111000000000111000111111000111000111111000111000000000111000111111111111 111111111111000111000000000111000111111000111000111111000111000000000111000111111111111 111111111111000111000000000111000111111000111000111111000111000000000111000111111111111 111111111111000111000000000111000111000111111111000111000111000000000111000111111111111 111111111111000111000000000111000111000111111111000111000111000000000111000111111111111 111111111111000111000000000111000111000111111111000111000111000000000111000111111111111 111111111111000111111111111111000111000111111000000111000111111111111111000111111111111 111111111111000111111111111111000111000111111000000111000111111111111111000111111111111 111111111111000111111111111111000111000111111000000111000111111111111111000111111111111 111111111111000000000000000000000111000111000111000111000000000000000000000111111111111 111111111111000000000000000000000111000111000111000111000000000000000000000111111111111 111111111111000000000000000000000111000111000111000111000000000000000000000111111111111 111111111111111111111111111111111111000000000000000111111111111111111111111111111111111 111111111111111111111111111111111111000000000000000111111111111111111111111111111111111 111111111111111111111111111111111111000000000000000111111111111111111111111111111111111 111111111111000000111000111111000000111000000111111111000000000111000000111111111111111 111111111111000000111000111111000000111000000111111111000000000111000000111111111111111 111111111111000000111000111111000000111000000111111111000000000111000000111111111111111 111111111111000111000000000000111111000000111111111111000111111111111111111111111111111 111111111111000111000000000000111111000000111111111111000111111111111111111111111111111 111111111111000111000000000000111111000000111111111111000111111111111111111111111111111 111111111111000111000111000111000111000111000111000000111111111000111111111111111111111 111111111111000111000111000111000111000111000111000000111111111000111111111111111111111 111111111111000111000111000111000111000111000111000000111111111000111111111111111111111 111111111111000000111000111000111000000111111000111111111111111000000000111111111111111 111111111111000000111000111000111000000111111000111111111111111000000000111111111111111 111111111111000000111000111000111000000111111000111111111111111000000000111111111111111 111111111111000000000000111000000000111000111111000111000111000111000111111111111111111 111111111111000000000000111000000000111000111111000111000111000111000111111111111111111 111111111111000000000000111000000000111000111111000111000111000111000111111111111111111 111111111111111111111111111111111111000111000000111111111000000000111000111111111111111 111111111111111111111111111111111111000111000000111111111000000000111000111111111111111 111111111111111111111111111111111111000111000000111111111000000000111000111111111111111 111111111111000000000000000000000111000111000111111000111000111000111111000111111111111 111111111111000000000000000000000111000111000111111000111000111000111111000111111111111 111111111111000000000000000000000111000111000111111000111000111000111111000111111111111 111111111111000111111111111111000111111000111000000000111000000111000000000111111111111 111111111111000111111111111111000111111000111000000000111000000111000000000111111111111 111111111111000111111111111111000111111000111000000000111000000111000000000111111111111 111111111111000111000000000111000111111000111000111111000000000000000000000111111111111 111111111111000111000000000111000111111000111000111111000000000000000000000111111111111 111111111111000111000000000111000111111000111000111111000000000000000000000111111111111 111111111111000111000000000111000111000111000000111111111000111111000000000111111111111 111111111111000111000000000111000111000111000000111111111000111111000000000111111111111 111111111111000111000000000111000111000111000000111111111000111111000000000111111111111 111111111111000111000000000111000111111000000111000111111111000000000111000111111111111 111111111111000111000000000111000111111000000111000111111111000000000111000111111111111 111111111111000111000000000111000111111000000111000111111111000000000111000111111111111 111111111111000111111111111111000111000111111111111000000000000111111000111111111111111 111111111111000111111111111111000111000111111111111000000000000111111000111111111111111 111111111111000111111111111111000111000111111111111000000000000111111000111111111111111 111111111111000000000000000000000111000000000000000111111111000111000111111111111111111 111111111111000000000000000000000111000000000000000111111111000111000111111111111111111 111111111111000000000000000000000111000000000000000111111111000111000111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
This is a bitmap image of a QR code. As a more conventional image, it looks something like this:
If you scan it, you'll get the text value 4294967295, which is hexadecimal FFFFFFFF, indeed the largest possible number in our 32-bit unsigned integer data type.
This puzzle is dedicated to the memory of Guy and Conway, creative mathematicians and frequent collaborators who died in 2019 and 2020, respectively. (Their coauthor for the classic Winning Ways for Your Mathematical Plays, E. R. Berlekamp, also died in 2019 but happened not to be involved in Guy and Conway's 1996 The Book of Numbers, where the project to systematize the names of large numbers appears.) This puzzle is partly inspired by Eben Moglen's 1999 observation in that a computer file, of any sort, can be regarded as a single mathematical integer, which was also soon taken up by people proposing the existence of "illegal numbers", including "illegal primes".