-1

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 

001234686486484642341234567876345675433586484545856856752856846845685468523253523253253623547568768786858866567895445665446654600912323131231547568568568823568658561223133257857857131233118765432100542533525223552000

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 

235346098435790863409863405364908736409364235253348902340983548796439082409348974369807324354364398706430253435354925364545685634754865498769675222321214241526343987230544533604234234236409340983543534460534523253532
Delta Oscar Uniform
  • 99
  • 3
  • 2
    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 – John L. Jun 13 '19 at 14:00
  • 1
    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. – John L. Jun 15 '19 at 10:00
  • 1
    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. – Discrete lizard Jun 15 '19 at 14:36
  • @Discretelizard I want a computer to find every 216 digit number and store it on disc. – Delta Oscar Uniform Jun 15 '19 at 15:50
  • 1
    @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. – Discrete lizard Jun 15 '19 at 16:16

1 Answers1

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 !

gandalf61
  • 1,589
  • 4
  • 11