This question popped to my head when I watched Pi where the mathematican told the Jews "Didnt you calculate every 216 digit number allready?"

So I want to find every possible 216 digit number possible.

Here is an example


What I want.

A computer that finds 216 digit numbers and puts them on hard storage.

How long would it take with todays computers like IBM Summit? How much storage would be required to store all these numbers? And also how much data storage would be needed to store all these numbers with an index system? Like Index No 547 is

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    $\begingroup$ Script from the movie Pi MAX: It's more than God...it's everything. It's math and science and nature...the universe. I saw the Universe's DNA. MAX: It's just a number. I'm sure you've written down every two hundred sixteen number. You've translated all of them. You've intoned them all. Haven't you? But what's it gotten you? The number is nothing! It's the meaning, the syntax. It's what's between the numbers. If you have not understood it, it’s not for you. I've got it, I’ve got it and I understand it, I'm going to see it! Rabbi...I was chosen $\endgroup$
    – John L.
    Jun 13, 2019 at 14:00
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    $\begingroup$ I claim that all 216-digit numbers are stored in my computer. For example, you want to see all of them, my computer can demonstrate that. If you want to see a specific one either by its value or its location, my computer will print that one. My computer just store them compressed by an algorithm that can be decompressed on the fly. $\endgroup$
    – John L.
    Jun 15, 2019 at 10:00
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    $\begingroup$ This depends a lot on what you mean by 'find' or 'calculate'. How to formally argue this can be rather involved and non-obvious, see for instance Is there any data structure that cant be represented or described inside a comp and Andrej's answer to that question in particular. $\endgroup$
    – Discrete lizard
    Jun 15, 2019 at 14:36
  • $\begingroup$ @Discretelizard I want a computer to find every 216 digit number and store it on disc. $\endgroup$ Jun 15, 2019 at 15:50
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    $\begingroup$ @JonathanIrons Storing a number on a disc too, can be done in different ways. For instance, you do not exclude the method Apass.Jack mentioned, and I have the feeling that that isn't what you're looking for. $\endgroup$
    – Discrete lizard
    Jun 15, 2019 at 16:16

1 Answer 1


$1.0531229 \times 10^{65}$ is approximately $2^{216}$ so when you say " every possible $216$ digit number " I assume you mean every possible sequence of $216$ binary digits i.e. bits.

Each sequence occupies $216$ bits, so the minimum storage for all possible sequences (if we ignore factors like aligining on word boundaries) is $216 \times 1.0531229 \times 10^{65} \approx 2.27 \times 10^{67}$ bits. That's around $10^{40}$ yottabytes.

By my rough calculation, it will take a time of the order of the current age of the universe to generate all these combinations, and something around the size of the solar system to store all of them !

  • $\begingroup$ So much data for some combinations composed of 1 2 3 4 5 6 7 8 9 0... $\endgroup$ Jun 13, 2019 at 10:42
  • $\begingroup$ I meant you were wrong. I just wanted every possible number combination with 216 numbers. not every single one zero state $\endgroup$ Jun 13, 2019 at 10:59
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    $\begingroup$ So where does "1.0531229e+65" in your question come from ? If you mean every possible sequence of $216$ decimal digits then the numbers get even large since there are $10^{216}$ possible sequences. If you mean something else then you need to make your questions much clearer. $\endgroup$
    – gandalf61
    Jun 13, 2019 at 12:20
  • $\begingroup$ Its what someone told me. Let me edit question $\endgroup$ Jun 13, 2019 at 12:31

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