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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1Do you mean $\frac{2^{80}}{2} = 2^{80-1} = 2^{79}$? or something else? – DDS Jul 16 '19 at 05:07
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@mlchristians yes exactly. – R1w Jul 16 '19 at 05:09
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Well, there you have it. – DDS Jul 16 '19 at 05:09
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@mlchristiansThanks. – R1w Jul 16 '19 at 05:09
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@mlchristians how about dividing it to 100? the answer would be (2/5)^2*2^76? – R1w Jul 16 '19 at 07:37
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1$\frac{2^{80}}{100} = \frac{2^{80}}{2^{2}5^{2}} = \frac{2^{78}}{5^{2}}.$ – DDS Jul 16 '19 at 08:18
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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.
Ross Millikan
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1$1000 \approx 2^{10}$ so it still doesn't help much. $2^{80}$ is really big. – Ross Millikan Jul 16 '19 at 05:12
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1Computing 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. – Ross Millikan Jul 16 '19 at 05:24
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I am looking for an idea or at least a clue to compute that big number using too many computers but with your good answer, I think it is somehow impossible. – R1w Jul 16 '19 at 05:33
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1To 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 – Ross Millikan Jul 16 '19 at 13:50
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When you started it sounded like you wanted to compute $2^{80}$ different things, which is wildly different. No array of computers can reasonably do that. – Ross Millikan Jul 16 '19 at 13:52
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It is actually part of my project about cracking RSA 1024, to do that I have to compute all combination but it takes many years as you mentioned then I decide to break it to many computers to reduce the computing time, here is the link to the original question: How long does it take to crack RSA 1024 with a PC? – R1w Jul 16 '19 at 14:00
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My second comment is very rough but in the spirit of your linked question. $10^{12}$ operations per second seems large to me. With $30000$ computers you could be done in a year. – Ross Millikan Jul 16 '19 at 14:06
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But is it not possible that maybe one of these 30000 computers has the answer before all possibility being computed? – R1w Jul 16 '19 at 14:13
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Absolutely. You could hit it on the first guess. Very unlikely, though. – Ross Millikan Jul 16 '19 at 14:31