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To understand this, you need to know that computers are devices that solve problems, abstracted into code readable by the physical computing device, based on the principles put forth by Alan Turing. Solving problems takes a number of steps and a certain amount of time, with the amount of time required increasing as the problem grows larger.
If a problem is solvable in n 2 time and you double the size of the input, then the amount of time it would take to solve would go up by four. Yet there are plenty of problems where one can determine that a given answer is correct in polynomial time, but actually getting to that answer may or may not be possible in polynomial time. Sudoku is an NP problem—hard to solve, easy to check.
Another important example today is factoring large numbers into prime numbers. Indeed, this exact idea is the basis of modern encryption, which relies on generating security keys that are easy to verify but hard to crack. Newer mathematical proofs have found, and might continue to find, P solutions to some of these NP problems.
It seems like it should be obvious that P does not equal NP, but it is not rigorously mathematically proven. And if you happen to prove that P does equal NP, you will have also demonstrated that there are polynomial-time algorithms for a whole lot of very important computer problems. You could make yourself very rich—bitcoin mining and security keys rely on hard-to-solve, easy-to-check NP problems. Quantum computers , which are based on different mathematics than classical computers, do not promise P solutions to every NP problem.
These prime numbers do have potential scientific value, but the value of Primecoin is not linked to the value of the prime numbers. The prime numbers are publicly available, and value again comes from supply, demand and usefulness. The goal is that the computation involved in "proof of work", which must be done anyway, should have a side-benefit. Mining essentially tries to brute force decrypt an encryption.
This is not so much a complex mathematical problem as rather systematically trying a multitude of potential solutions until one fits the current prerequisites context and difficulty. The purpose of mining is to validate the transactions of the network.
The more computational effort is applied to mining, the more resilient is the network against attacks. Therefore the Bitcoin protocol has been designed to dispense rewards among the miners to incentivize behavior that is beneficial to the network — whoever finds the winning solution is allowed to transmit a number of newly created coins to an address of his choice. Sign up to join this community. The best answers are voted up and rise to the top. How does solving math problems create bitcoins?
Asked 7 years, 4 months ago. Active 4 years, 11 months ago. Viewed 65k times. Improve this question. Add a comment. Active Oldest Votes. Improve this answer. David Schwartz David Schwartz Stephen Gornick Stephen Gornick Chinthamani Chinthamani 5 5 bronze badges. There are two mistakes in your answer: 1 There will be only 21M Bitcoin 2 The last Bitcoin will be created whenever block 6,, is found. This would be if the network actually found one block every ten minutes, but our average time is much quicker, we will be way ahead schedule.
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Both Chevalley and Harish-Chandra were, I believe, persuaded that their vocation as mathematicians was to reveal those principles that God had declared inviolable, at least those of mathematics for they were the source of its beauty and its truths. They certainly strived to achieve this.
If I had the courage to broach in this paper genuine aesthetic questions, I would try to address the implications of their standpoint. Question Which kind of mathematical problems do you have to solve in order to mine bitcoins? Let me clarify that I'm not interested in mining, only in knowing whether the problems are divine or devilish. Bitcoin mining is based on hash functions. Specifically the SHA hash function, which maps arbitrary bit strings to bit outputs in such a way that nobody knows how to find a collision two inputs with the same output , although the pigeonhole principle implies collisions exist.
Bitcoin mining doesn't involve finding collisions, which would be way too hard. Instead, one has to find inputs that lead to outputs with special properties, namely a lot of consecutive zeros. This is a scaled-down version of inverting the hash function. Of course there's no proof that any of this is actually computationally difficult, and some earlier hash functions have turned out to be weaker than expected for example, MD5 and SHA-1 , but it certainly seems to be.
SHA is not a nice or simple function - it was designed to be hard to analyze - so I'd say this is a devilish problem. Another way to earn bitcoin is not to mine them, but to have them wired to you from other bitcoin accounts. So if you solve the discrete logarithm problem in an elliptic curve for bitcoin this is the curve Secpk1 , then you potentially can earn many bitcoins illegally of course Personally I find this problem much more beautiful than finding lot of zeroes in the SHA hash function.
So you need to know what hash functions are to understand the problem, don't worry its easy and anyone can understand it because solving this puzzle doesn't require intelligence but patience. A hash function is just a function that when you give it an input of X byte size data, image, text, anything Hash functions have some properties and one of them is when you give it different input it always produces a completely different output, so if change only one bit in that 5gb video the output of the hash function is going to change radically.
So in bitcoin, miners keeps listening for transactions and from these transaction they create a block but in order for all participating nodes to accept this block they have to change a specified region in the block and see if the resulting output starts with x number of zero's because in computers everything is ones and zeroes.
If the result is not correct output string does not start with 30 zeroes they change that region again and check the output, until they finally find the right combination of bits in that region that when you pass that block to the hash function it will produce a string that starts with 30 zeroes. Sign up to join this community. The best answers are voted up and rise to the top.
Which hard mathematical problems do you have to solve to earn bitcoins? Ask Question. Asked 7 years, 9 months ago. Active 6 months ago. Viewed 19k times. The difference is best explained by the following beautiful quotation from Langlands : [T]here is an appealing fable that I learned from the mathematician Harish-Chandra, and that he claimed to have heard from the French mathematician Claude Chevalley. Improve this question. There are now at least two cryptocurrencies Primecoin and CureCoin which do solve somewhat useful problems, and I just asked this question calling for new proof-of-work problems that solve useful mathematics problems.
The second step is to get the idea of a proof of work. It might be impossible to find a hash specifically with a string consisting of nothing but the letter "a" but what if we asked for a hash with a single zero at the front? Altering the last letter of hello world took 26 attempts to finally get hello worlC which equates to 0d7eae0fab3abc2cccc0bb4aabb24ffaf8c.
Why is this useful? Because it creates a puzzle whose difficulty is measurable and which it's impossible to perform better than blind guessing. That second property is important because it's the only way to create a fair "mining" system. Miners solve such puzzles as above but which are far more difficult. For example, find a hash that looks like this: xxxx Each hash is can be considered to be just a number. For example, the hash ab3abc2cccc0bb4aabb24ffaf8c has a numeric value of So in mining, the miners have to achieve a hash with a numeric value lower than a specified number.
This number is called the target. If your hash attempt gives you a number less than the target, which is the same thing as having a bunch of zeros at the front of the hash, then you win and you get to "mine the block". To find such a small hash takes millions of attempts, or more accurately, the whole mining network, with everyone trying at the same time, needs millions of billions of tries to get it right.
The part of the content that they are hashing and are allowed to change, a single number, in order to try and get a hash beginning with zeros, is called the nonce. The current block reward of 25 Bitcoins is given to the miner who successfully "mines the block" finds the appropriate hash.
It's not really that mining "generates" the Bitcoin in any sense, it's just that it's written into Bitcoin code that a transaction block starts with a unique transaction called a "coinbase" transaction, which is the only type of transaction with no inputs. It only has an output, consisting of the reward plus the transaction fees. To make any sense of Bitcoin's solution to this problem, you need to understand also what is meant by "distributed timestamp server" and how proof of work hashes can be used to construct this.
It is, very briefly, explained in Sections 3 and 4 of the bitcoin whitepaper. You're creating a sequence of blocks, tied to each other by including the hash of the last one in the next one. This proves that the next block knew about the last block remember, hashes are totally unpredictable , which proves that it came afterwards. However, that's not enough; you might know that block 8 comes after block 7, but what if a different block 8, put in by a different miner, also comes after block 7?
Worse still, what if these two competing blocks, 8a and 8b contain different transactions, spending money to different places? Which one is the "true" block of transactions? The reason miners did the complicated proof of work process above is exactly to solve this problem.
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