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There are $~2^{80}~$ possibilities to calculate and I want to divide it by $~2~$ to process it by two computers at the same time to find the answer maybe sooner.

How can I divide $~2^{80}~$ by $~2~$?

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    $\begingroup$ Do you mean $\frac{2^{80}}{2} = 2^{80-1} = 2^{79}$? or something else? $\endgroup$ – mlchristians Jul 16 '19 at 5:07
  • $\begingroup$ @mlchristians yes exactly. $\endgroup$ – R1w Jul 16 '19 at 5:09
  • $\begingroup$ Well, there you have it. $\endgroup$ – mlchristians Jul 16 '19 at 5:09
  • $\begingroup$ @mlchristiansThanks. $\endgroup$ – R1w Jul 16 '19 at 5:09
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    $\begingroup$ $\frac{2^{80}}{100} = \frac{2^{80}}{2^{2}5^{2}} = \frac{2^{78}}{5^{2}}.$ $\endgroup$ – mlchristians Jul 16 '19 at 8:18
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$$\frac {2^{80}}2=\frac{2^{80}}{2^1}=2^{80-1}=2^{79}$$ Having two computers does not make much of a dent.

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  • $\begingroup$ How about 1000 Computer? Army of Zombies. $\endgroup$ – R1w Jul 16 '19 at 5:11
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    $\begingroup$ $1000 \approx 2^{10}$ so it still doesn't help much. $2^{80}$ is really big. $\endgroup$ – Ross Millikan Jul 16 '19 at 5:12
  • $\begingroup$ Is there any way to compute this big number by using parallel processing? $\endgroup$ – R1w Jul 16 '19 at 5:19
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    $\begingroup$ Computing the number is easy. Alpha gives $1208925819614629174706176$ instantly. It will do much larger numbers as well. If you know $2^{10}=1024$ it only takes three more multiplies to get there, which is reasonable to do by hand. Doing that many operations in a computer is hard. If you can do $10^{12}$ per second it will take about $10^{12}$ seconds, which is about $30000$ years. $\endgroup$ – Ross Millikan Jul 16 '19 at 5:24
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    $\begingroup$ To compute the number you just need some software that works with numbers that do not fit into $64$ bits. Wolfram Alpha does that and is available at www.wolframalpha.com. You can just type in 2^80 and get the result. You can do much larger numbers. The programming language Python switches seamlessly into large integers when required. It does $2^{8000}, which has about $2400$ digits instantly. There is an add-on package to C that will handle large numbers, but I am not familiar with it. Maple and Mathematica will do this. I suspect there are add-ons for any popular programming language $\endgroup$ – Ross Millikan Jul 16 '19 at 13:50

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