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Graham's Number last digits

Several years ago we did a bunch of projects on Graham's number. An attempt to explain Graham's number to kids, and . The last 4 digits of Graham's number. These projects were inspired by this fantastic Evelyn Lamb article: Graham's numbers is too big for me to tell you how bit it is. Today I thought it would be fun to revisit the calculation of a few of the last digits of Graham's number Though too large to be computed in full, many of the last digits of Graham's number can be derived through simple algorithms. The last 400 digits are these: 38814483140652526168785095552646051071172000997092 91249544378887496062882911725063001303622934916080 2545946149457887142783235082924210209182589675356 In Wikipedia, Graham's number, it is described how to calculate the last d digits of Graham's number. They introduce an algorithm simply iterating. x = 3 x mod 10 d. d times starting with x=3

Revisiting the last digits of Graham's number - Mike's

Shopping. Tap to unmute. If playback doesn't begin shortly, try restarting your device. An error occurred. Please try again later. (Playback ID: ttrvStYTo3ZfQcqs) Learn More. You're signed out. The last digit of Graham's number is its modulo 10. Its modulo 2 is clearly 1 (it's a power of 3, and thus odd). Its modulo 5, by Euler's theorem is 3 T3(x-1) mod phi(5) mod 5 pɨk garda kapɨk/. phew... that's writing the number as. (3 x 16 + 3 x 4 + 1) x 256 x 4096 x 4096. + (16 + 3 x 4 + 0) x 4096 x 4096. + (16 + 4 + 1) x 16 x 4096. + ( (3 x 4) x 16 + 2 x 4 + 3) x 256. + (3 x 16 + 2 x 4 + 3) Now this is simply insane. With such a big number a Flavan would simply list the digits This will accurately get the last 6 digits from the argument you pass. One thing to note. In SQL Server 2005, the \ (backslash) character does not return 1 by ISNUMERIC. But it does in SQL Server 2008. This function should work in both versions of SQL Server since we're simply excluding this character in the 7th piece of my test argument above Digit Number Digit; 1 (250th to last number) 2 (249th to last number) 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 4

So now that we have the toolkit, let's go through Graham's number: Graham's number is going to be equal to a term called g 64. We'll get there. First, we need to start back with a number called g 1, and then we'll work our way up. So what's g 1? g 1 = 3 ↑↑↑↑ 3. Hexation. You get it. Kind of. So let's go through it Quite surprisingly that pattern gives us enough information to infer that the last digit of Graham's number is either 3 or 7. We spend probably half of the movie arriving at that fact and then we perform a more detailed calculation to see what the last digit actually is I was reading random topics on Wikipedia the other day, and saw something about the first 500 numbers of Grahams' Number. I want to create a program (probably in C#) to calculate as many digits from it as I can, but I haven't be able to make sense of the way it is done. Would someone be able.. Since g 0 is 4 and not 3, Graham's number cannot be expressed efficiently in chained arrow notation g 64 ≈ 3 → 3 → 64 → 2 or BEAF { 3, 65, 1, 2 } < g 64 < { 3, 66, 1, 2 }. Using Jonathan Bowers' base-3 G functions it is exactly G 64 4. It can be also exactly expressed in the Graham Array Notation as [ 3, 3, 4, 64] Graham's number (last 500 Digits anyway) Essential T-Shirt Designed and sold by ShaneReid2 $19.9

&quot;Graham&#39;s number (last 500 Digits anyway)&quot; Sticker by

Therefore the first decimal digit of $A$ is $k$ iff $k \leq 10^\gamma < k+1$, or, equivalently, iff $\log_{10} k \leq \gamma < \log_{10} (k+1)$. Taking the special case where $A = G$ is Graham's number, we have $G = 3^{3^x}$ for some natural number $x$. Then $\log_{10} G = 3^x \log_{10} 3$ Graham's number, G, G, G, is much larger than N: N: N: f 64 (4), {f^{64}(4)}, f 6 4 (4), where f (n) = 3 ↑ n 3. { f(n)\;=\;3\↑ ^{n}3}. f (n) = 3 ↑ n 3. This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977

Buy Graham's number (last 500 Digits anyway) by ShaneReid2 as a Sticke Due to the method, for any natural number d, the last d digits D(d) of Graham's number in base 10 could be computed in the following recursive way: D(d) = {3 (d = 0) 3N (d − 1) mod 10d (d > 0) Note that the recursion starts from d = 0, but the result of D(0) is not meaningful because the last 0 digit of Graham's number does not make sense 0. Another interesting way to do it which would also allow more than just the last number to be taken would be: int number = 124454; int overflow = (int)Math.floor (number/ (1*10^n))*10^n; int firstDigits = number - overflow; //Where n is the number of numbers you wish to conserve</code>. In the above example if n was 1 then the program would. All these numbers pale in comparison to Graham's number, a number so large that simply trying to remember all the digits would turn your head into a black hole

Graham's Number Brilliant Math & Science Wik

GS1 Check Digit Calculator can calculate the last digit of a barcode number, making sure the barcode is correctly composed. Calculate a check digit Graham's Number Escalates Quickly - Numberphile - YouTube. Gillette Deodorant | 72Hr Sweat Protection | Gillette Invisible Solid. Watch later. Share. Copy link. Info. Shopping. Tap to unmute. If. Mind sufficiently blown. I like really big numbers. When I say really big I don't mean numbers like a million or a billion, I mean numbers like Graham's number which is so big that if you were try to store every digit in your brain it would sooner turn into a black hole before you could get it all in there Graham Firestone 587 (rare name: not sure of the last 4 digits) Greg Napster 404-394 (for more common names add an area code) Greg Napster 404-394 (Narrow search with name in Quotes) Graham 678-587 Roswell (first name w/ city) Graham 587 lawyer (first name w/ profession

Slight confusion about the calculation of the last digits

How do we know the last digit of Graham's number? - Quor

  1. The last 7625597484986 digits are the same as those of Graham's number. ~ 10^^(2.6448990072*10 22,212,093,154,093,428,529 ) The hypermega, equal to 2(*^^^3)2 in my Caret-Star notation
  2. What Graham's Number shows is that even that fails us at some point when we venture into the realms of numbers with more digits than we can even comprehend, which is rightly to be expected when we start compounding exponential operators together (the number of digits being basically the log of a number base 10)
  3. Graham's number is relatively easy to calculate, given infinite RAM xD. robosnakejr wrote: Oh look. Humanity created something they can't comprehend again.Yeah I don't get why people are so in awe of things. So you made a BFS chess bot that plays better than any person, and it's definitely incomprehensible
  4. So Graham's number G sits between these two chained numbers. Graham's number is actually a really small number compared to TREE(3). I mean it is so small, it might as well be 1. It took me a couple of months of studying before I started to understand how the TREE function worked
  5. $\begingroup$ @DavidRoberts Not the OP, but: since Graham's number is a power of 3, the first digit (mod 9) must be either 1 or 3. Since Graham's number is an odd power of 3 (it's 3 raised to another power of 3, all of which are odd), it has to be 3. $\endgroup$ - Steven Stadnicki Nov 27 '17 at 20:4
  6. Here are the instructions: Split the number N into its last digit y and the number x formed by the other digits (it can be very large). Now, consider 2y (twice the digit) and x. Subtract the smaller from the larger. The result is divisible by 7 if and only if the original number was

Graham's number was devised in 1971 by Ron Graham to answer a particular question in Ramsey theory, a subfield in combinatorics. It was later quantified around 1976 via Don Knuth's up-arrow notation. Suppose we take four vertices in a 2-dimensional square and connect them with lines. We can give them one of two colors: red or blue. Vertices: 22 = 4Lines: (4 * 3)/2 = 6Ways to Color: 26 = 64. Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is named after mathematician Ronald Graham, who used the number in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in. Graham's number is so large that if all the atoms in the universe were made into ink, the number could not be written. That is certainly disappointed for the readers of this post who wanted to see the number. However, the last digits of Graham's number are:262464195387 Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number. Indeed, like the last three of those numbers, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume Large Numbers First page. . . Back to page 3. . . Forward to page 5. . . Last page (page 9) The Mega and the Moser. These numbers were constructed by Hugo Steinhaus and Leo Moser (in the late 1960's or earlier, exact dates unknown) just to show that it is easy to create a notation for extremely large numbers

How was it possible to calculate the last digits of Graham

Graham's number is a very big natural number that was defined by a man named Ronald Graham.Graham was solving a problem in an area of mathematics called Ramsey theory.He proved that the answer to his problem was smaller than Graham's number Recently, when we were writing our book Numericon, we came across what has now become one of our very favourite numbers: Graham's number. One of the reasons we love it is that this number is big. Actually, that's an understatement. Graham's number is mind-bendingly huge. The observable Universe is big, but Graham's number is bigger Graham's number is a power tower of the form 3 n (with a very large value of n), so its rightmost decimal digits must satisfy certain properties common to all such towers. One of these properties is that all such towers of height greater than d (say), have the same sequence of d rightmost decimal digits Our human brain can't imagine such a huge number, we do not even know the first digit of this number although we know the last five hundred digits. But even though Graham's number is so big, so huge there are still infinite numbers bigger than Graham's number. We are still basically at the same distance from infinity as any other number. Rayo's. Graham's problem. Graham's number is connected to the following problem in the branch of mathematics known as Ramsey theory:. Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2 n vertices.Then colour each of the edges of this graph using only the colours red and black

Is this the correct way to compute the last $n$ digits of

First 100 Digits of Graham's Number in Base 3. Name the first 100 digits of Graham's Number in Base 3. You only have two minutes! Quiz by Sudoku00. Profile Quizzes Subscribed Subscribe? Rate: Nominate. Nominated. Spotlight. Last updated: May 25, 2021. More quiz info >> First submitted: May 25, 2021: Times taken: 11: Report this quiz.

Graham's Number is, or was for a long time, the largest number ever cited in a mathematical journal. If you want to know what it actually represents, there's a great Numberphile video about it here. For our purposes, we only care about the value: it's our target. To get to Graham's number, you start with a very large number: 3^^^^3 Graham's number, although smaller than TREE(3), is much larger than many other large numbers such as Skewed´number andMosesś number, both of which are in turn much larger than a googolplex. Though too large to be computed in full, many of the last digits of Graham's number can be derived through simple algorithms We know TREE(3) exists, and we know it's finite, but we do not know what it is or even how many digits there are. The number comes from a simple game of trees—meaning the charts used in graph.

Last month, American reality show entertainer turned American political system entertainer Donald Trump publicized presidential rival Sen. Lindsey Graham's cell number, urging his supporters to. b. . f and where the number of 3s in each tower, starting from the leftmost tower, is specified by the value of the next tower to the right. 64 A Government and the Minister of Education are responsible for setting challenging targets for improvement that will require a comprehensive, national effort focused on improving numeracy skills of every child during all stages of the education system. Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number. Indeed, like the last three of those numbers, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume The Ackermann numbers are incredibly modest compared to Graham's number. Even though there is no hope of ever being able to compute a tiny tiny fraction of its digits, the last 500 digits are known:: Whether these digits are random or not is another question. Click here for more information. Other interesting fac The next layer has that many arrows between 3s. Then take that answer and put that many arrows into the next layer between 3s, and this goes on for 64 layers. If you're interested the last ten digits of Grahams Number are 2464195387, no one, not even Graham himself knows what the first digit is

From 1,000,000 to Graham&#39;s Number - Wait But Why

Graham's Number is another contender for the most well-known large number, claimed to be the largest number ever used in a serious mathematical proof. In the form of an upper bound to a problem in Ramsey Theory , this number can't be expressed in digits even if each digit was planck's length and it was written across the observable universe 1011 (100 billion) - This is about the number of stars in the Milky Way and the number of galaxies in the observable universe (100-400 billion)—so if a computer listed one observable galaxy every second since Christ, it wouldn't be anywhere close to finished currently. Well who asked you anyway? Other specific integers (such as TREE(3)) known to be far larger than Graham's number have. Graham's number is a power tower of the form 3↑↑n (with a very large value of n), so its rightmost decimal digits must satisfy certain properties common to all such towers. One of these properties is that all such towers of height greater than d (say), have the same sequence of d rightmost decimal digits Graham's number is a very, [/math]; this number is so huge, its digits would fill up the universe and beyond. Although this number may already be beyond comprehension, this is barely the start of this giant number. The next step like this is [math] This page was last changed on 3 November 2014, at 16:52

&quot;Graham&#39;s number (last 500 Digits anyway)&quot; T-shirt by

Graham's Number: Page 1 of 1 o Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation.. (This answer assumes you know how Graham's number is obtained - if you don't, check the Wikipedia page about it.)Graham's number is inconceivably huge - in fact, 3↑↑↑3 is many orders of. We can't represent Graham's number with any familiar notation - even if we used the entire universe to write it down - but I can tell you right now what the last twelve digits of Graham's Number. And It's a way bigger than the 3638334640025 decimal digits you explained. If you go the way down from the top, you'll have: 3, 27, 7.625.597.484.987, a number which has approx. ~ 6,9 x 10^12 digits and not 3,6 x 10^12 digits, and so on. I've calculated that one between number out, therefore I know this. But I didn't came beyond that number

Calculating last digits. The final digits of Graham's number can be computed by taking advantage of the convergence of last digits, because Graham's number is a power tower of threes.Here is a simple algorithm to obtain the last \(x\) digits \(N(x)\) of Graham's number The last digit of Graham's number, and the rarest digit among the 500 rightmost decimal digits of Graham's number (these 500 digits include 56 0s, 56 2s, 56 9s, 55 5s, 54 8s, 49 1s, 47 3s, 46 4s, 46 6s, but only 35 7s)

How to Count to the Largest Number Ever Used – Math with

How do we know the last digit of Graham's number is 7

Graham's number is not only too big to write down all of its digits, it is too big even to write in scientific notation. In order to be able to write it down, we have to use Knuth's up-arrow notation. We will write down a sequence of numbers that we will call g1, g2, g3, and so on Graham's number is a very, very big number that was discovered by a man called Ronald Graham. It is the answer to a problem in an area of mathematics called Ramsey theory, and is one of the biggest number ever used in a mathematics study. Even if every number in the number was written i Graham's number is divisible by 3 and ends in a 7, its last 12 digits are 262464195387 but it can't be expressed in a standard way and is too big to be worked out in full Graham's number is defined like this: The number of arrows in each layer is given by the result of evaluating the arrows in the layer below, until after 64 layers, the final number is reached. To give you some idea of the size of this, we can look at the first layer alone: where the number of threess in the expression on the right i

Video: How were the last N digits of Graham's Number calculated

The last 12 digits of Graham's number : conlang

In the last Ramona Quimby book, Graham's number is on the low end of the numbers listed there. (4,3) has 6.031*10^19727 digits). Now imagine Graham's number as the input. AUGHHH indeed. Although this number is still provably less than g65, so it's really not actually a huge improvement. In approaching Graham's problem, it is natural to first consider alternative or related forms. In [23, Section 4], Pomerance gave a heuristic argument that leads to the following conjecture. Conjecture 1.9. Let N be an integer. Denote G (N) to be the number of positive integers n ≤ N such that (2 n n) is coprime with 105 So, when we see a number like 0.999 (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s. Subsequently, question is, what does last number of your like mean? It is a common method of engaging users to like the photo so that the number increases by one, and the number at the end is your result for whatever short answer test they have created Graham's number G is an upper bound in a problem in Ramsey theory, first mentioned in a paper by Ronald Graham and B. Rothschild. The Guinness Book of World Records calls it the largest number ever used in a mathematical proof. Graham's number is too difficult to write in scientific notation, so it is generally written using Knuth's arrow-up notation 101 digits. What is larger than Graham's number? There are whole sets of numbers that have been conceived of that are as mind-bendingly larger than Graham's Number as Graham's Number is itself large. Obviously, even Rayo's Number is not in any sense the largest number. There is no such thing

sql - Stored Procedure to SELECT Last 6 Digits of Number

On top of that, the dictionary I use most often has the word NUMBER as the last keyword on page 1227, and it is the first keyword on the following page, 1228. These are the two position numbers required to designate both digits in the 19 th appearance of 19, and 12:27 is the official time of drawing of the NUMBERS in Texas This number is too big for writing in scientific notation, or even power towers; it can be defined recursively (see the definition in the Wikipedia, for example), or approximated with special. Graham's Number used to be the biggest number I could name, but now I understand that C Compilers Disprove Fermat's Last Theorem. semi-extrinsic on Jan 26 I can't tell you how many digits it has. I also can't tell you how many digits its number of digits has, or how many digits the number of digits of its number of digits. Graham's number is bigger the number of atoms in the observable Universe, which is thought to be between 1078 and 1082. It's bigger than the 48th Mersenne prime, 2/sup>-1, the biggest prime number we know, which has an impressive digits

Now, Graham's number is so much bigger than a googolplex as to make comparison pretty much meaningless. You and I would not be able to wrap our heads around it in any meaningful way, and yet if you patiently go back to how this number is CONSTRUCTED, it's not really hard to follow the steps The truly wonderful thing about Graham's number is that it's possible to calculate the last few digits and we know it ends in a 7. 8. Smallest Integer. Unknowable Thing: What's the smallest positive integer not definable in under eleven words? This is a problem in the philosophy of mathematics

Graham's Number Quiz - By gainerthegophe

Graham's number will always present a maximum stock price given a company's EPS and BVPS. As a result, any stock price below that figure should signal a good buy for a value investor. What is the. Graham's number is mind-bendingly huge. the biggest prime number we know, which has an impressive 17,425,170 digits. And it's bigger than the famous googol, 10100 (a 1 followed by 100 zeroes), which was defined in 1929 by American mathematician Edward Kasner and named by his nine-year-old nephew, Milton Sirotta When numbers get huge, they get names like googol, TREE(3), and Graham's number. The latter is a 64-step calculation that grinds to a halt after a few steps. By then, there are trillions of digits. Graham's number is a tiny speck next to TREE(3). Capturing its full capacity or reach is said to be impossible Smorynski then defines Graham's number to be G(64). However, this definition gives a vastly smaller number than what I've seen in other places. In fact, as I'll show below, Smorynski's function G(n) has the growth rate of a constant base with a linear hyper-tetrated exponent, whereas the functio Graham's number, which can't be written with conventional notation, was developed by mathematician R.L. Graham. It's so large that, even if all the matter in the universe was converted to pens and ink, it still wouldn't be enough to write out the number in its entirety

From 1,000,000 to Graham's Number — Wait But Wh

115. Ibix said: Which is almost as big as the 213th triangle number, which is 225+212. Triangle numbers make me think of Pascal's triangle, in particular a Pascal's triangle with. 2 13. rows. That's an even number of rows, so the two middle elements of the last row will be the largest elements in the triangle, so counting from 0, these. But there exists a number that is the biggest ever used. It is so big that even so-called power towers are useless to describe it. Prof Hugh Woodin, University of California, USA - Graham's number is much, much bigger than a googolplex. In fact, it's as large relative to a googolplex as a googolplex is to the number 10

Therefore Moser's number, although incomprehensibly large, is vanishingly small compared to Graham's number: TREE(3): appears in relation to a theorem on trees in graph theory. Representation of the number is difficult, but one weak lower bound is AA(187196)(1), where A(n) is a version of the Ackermann function. Graham's number, fo Donald Trump reads out rival Lindsey Graham's mobile number at rally; supporters instantly jam his phone line. Mr Trump is now just one point behind favourite Jeb Bush in the poll I was thinking. Rayo's number, which is meant to be the largest finite number ever concieved, is defined as: The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10^100) symbols. Rayo's number must exist somewhere. Presumably we don't have the symbols to express it yet Graham's number achieved a kind of cult status, thanks to Martin Gardner, as the largest finite number appearing in a mathematical proof. (It may no longer hold that record, but that is not my concern here.) I was surprised to learn relatively recently that it is not actually the best known bound for that particular Euclidean Ramsey problem, and that the original paper by Graham and Rothschild. Graham's number is usually defined as 3^^64 [see M. Gardner and Wikipedia], in which case only its 62 lowermost digits are guaranteed to match this sequence. To avoid such confusion, it would be best to interpret this sequence as a real-valued constant 0.783591464..., corresponding to 3^^k in the limit of k->infinity, and call it Graham's constant G(3)

17 Facts That Are 100% True And 100% Freaky. Most people have an above-average number of arms. 1. In a room with just 23 people in it, there's a 50% chance two of them share a birthday. You might. Chris Johnson dialed up an odd play Wednesday, retweeting rookie TE Cameron Graham's phone number to half a million people, in an apparent joke When in 1964, Ronald Graham (of Graham's number fame) proved that this kind of sequence is possible, his example had initial terms with more than thirty digits each (in base 10). Donald Knuth found a 17-digit pair in 1990, and later that same year Herbert Wilf found this sequence with slightly smaller initial terms

Graham's number - Mike's Math Pag

Lindsey Graham's new China lab-leak theory: That critics' dismissals cost Trump reelection. It was always likely to come to this. After weeks of the media and the scientific community. The beginning of Googolplex, in print, looks just like Googol, starting with 1 and a lot of zeroes. But this time, the zeroes are stretching out to infinity and beyond. Well, this is not entirely accurate, of course the number is much less than infinity. The fact alone that it was conceived is a proof of its finiteness Graham's last stand? Senator leads Barrett acutely aware that the president won his states by double digits, and a liberal, and famously made public the senator's cell phone number Johnson's old college number, 92, isn't available from the Giants, who plan to retire the number, last worn by Hall of Fame defensive end Michael Strahan in 2007, this fall. IOL Brett Heggie, No. 6 Graham's last stand? Senator leads Barrett court hearings FILE - In this June 9, 2020, file photo Chairman Sen. Lindsey Graham, R-S.C., speaks during a Senate Judiciary Committee hearing on.

Calculating digits of Grahams' Number Physics Forum

Donald Trump gave Lindsey Graham's cell phone numbers to millions of his supporters. Speaking at a campaign event in South Carolina, Trump blasted the senator — and then proceeded to give out. Graham's Wholesale - opening hours, address, telephone number, reviews and more The number (coincidentally prime) of known positive integers which are not the sum of two semiprimes. The smallest 2-digit number that produces the most primes by altering one digit of decimal expansion of n (without changing the number of digits). A set of eight primes can be produced in this manner {11, 17, 19, 23, 43, 53, 73, 83} Sen. Lindsey Graham of South Carolina is wielding the gavel in the performance of his political life. Once a biting critic of President Donald Trump, the Senate Judiciary Committee chairman on Monday launched confirmation hearings for Judge Amy Coney Barrett in a bid to seal a 6-to-3 conservative majority on the Supreme Court. For Graham, the Republican Senate majority and Trump himself, the. And Graham's own career appears in jeopardy like never before. For Graham, the Republican Senate majority and Trump himself, the hearings three weeks before Election Day could be a last stand

By comparison, the number of elementary particles in the observable universe has a meager 85 digits, give or take. Three 9's, when stacked exponentially, already lift us incomprehensibly beyond all the matter we can observe—by a factor of about 10 369,693,015 And Graham's own career appears in jeopardy like never before. For Graham, the Republican Senate majority and Trump himself, the hearings three weeks before Election Day could be a last stand. The proceedings are a display for voters of what it means to control the presidency and the Senate What is the very last number? A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents by saying a googol is 10^100. The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That's written as a one followed by googol zeroes

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