编程逻辑：寻找最小方程给大量 [英] Programming Logic: Finding the smallest equation to a large number
问题描述
我不知道整个很多关于数学，所以我不知道如何开始，以谷歌我所期待的，所以我依靠专家的智慧，帮助我了解我之后...
I do not know a whole lot about math, so I don't know how to begin to google what I am looking for, so I rely on the intelligence of experts to help me understand what I am after...
我想找到方程的一个特定大批最小的字符串。例如，给定数量
I am trying to find the smallest string of equations for a particular large number. For example given the number
"39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816"
"39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816"
最小的公式是64 ^ 64（据我所知）。它包含了只有5个字节。
The smallest equation is 64^64 (that I know of) . It contains only 5 bytes.
基本上，程序会扭转，而不是采取一个前pression和寻找答案的数学，它需要一个答案，并找到最简单的EX pression。简单化是这种情况，是指最小的字符串，而不是真正简单的数学。
Basically the program would reverse the math, instead of taking an expression and finding an answer, it takes an answer and finds the most simplistic expression. Simplistic is this case means smallest string, not really simple math.
这已经已创建？如果是的话我在哪里可以找到它？我期待采取极其庞大的数字（10 ^ 10000000），并打破他们有希望的前pressions，这将是像超过100个字符。这甚至可能吗？现代的CPU / GPU的没有能力做这样大的计算？
Has this already been created? If so where can I find it? I am looking to take extremely HUGE numbers (10^10000000) and break them down to hopefully expressions that will be like 100 characters in length. Is this even possible? are modern CPUs/GPUs not capable of doing such big calculations?
编辑：
确定。因此，寻找最小的公式花费了太多的时间，判断上的答案。反正是有这种暴力破解并获得最小的发现迄今？
Ok. So finding the smallest equation takes WAY too much time, judging on answers. Is there anyway to bruteforce this and get the smallest found thus far?
例如给一些超级超级大。有时取数的sqaureroot将导致在离pression比数本身较小
For example given a number super super large. Sometimes taking the sqaureroot of number will result in an expression smaller than the number itself.
至于什么EX pressions那就开始吧，好自然会尝试EX pressions那会前pression最小。我相信有万吨数学的事情我不知道，但做了一些小了很多的方法之一就是权力。
As far as what expressions it would start off it, well it would naturally try expressions that would the expression the smallest. I am sure there is tons of math things I dont know, but one of the ways to make a number a lot smaller is powers.
推荐答案
只是扔在你的谷歌斗另一个关键字，请参见柯尔莫哥洛夫复杂性。字符串的Kolmogorov复杂是最小的图灵机输出该串的大小，给定的一个空的输入。这就是你似乎是经过正式的方法之一。但是，计算给定的字符串的柯尔莫哥洛夫复杂性被称为是一个不可判定问题：）
Just to throw another keyword in your Google hopper, see Kolmogorov Complexity. The Kolmogorov complexity of a string is the size of the smallest Turing machine that outputs the string, given an empty input. This is one way to formalize what you seem to be after. However, calculating the Kolmogorov complexity of a given string is known to be an undecidable problem :)
希望这有助于
TJ
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