The "crypto" in bitcoin is about being able to know that the copy of the blockchain you have is indeed the "authentic", consensus blockchain. It has nothing to do with keeping anything secret, as the entire blockchain is literally as public as it is possible for data to get.
I recall reading some article about how, when mining for bitcoin (for example), what was really being mined are progressively larger prime numbers, or scientific data, or some such data requiring lots of computation.
Isn't there something of real value being mined? If not, what is being done when people _mine_ bitcoins?
Mining is a "proof of work" event - in essence, you generate a random value so that a cryptographic hash total block would end with a particular number of zeroes. Such a block + hash is trivial to verify but very time/effort consuming to create, thus proving that you spent a large amount of (otherwise useless) work to "mine" that block.
Having a large amount of work required is what prevents a malicious actor from tampering with the chain, since doing so requires doing as much work as all the other miners together.
The only value of mining is that it is necessary for the bitcoin system to operate. Nothing of real value (outside of the bitcoin system) is being mined and as seen from space it is just a waste of electricity.
> I recall reading some article about how, when mining for bitcoin (for example), what was really being mined are progressively larger prime numbers, or scientific data, or some such data requiring lots of computation.
You're most likely thinking about Primecoin[0].
> Isn't there something of real value being mined? If not, what is being done when people _mine_ bitcoins?
"Real value" in a computational sense is difficult to articulate. Making a calculation part of a mining algorithm that ultimately results in _new_ information is challenging because it, by definition, requires a lot of effort to not just calculate, but verify. Folding proteins, searching SETI datasets, etc. presumably require the same amount of effort to verify as they do to solve in the first place. The way that cryptocurrencies that use a "proof of work" ("PoW") are typically set up is to make it very difficult to solve a computation, but very easy for others to verify that the solution is correct. The other component of PoW that makes it beneficial as a verification tool is the ability to increase or decrease the difficulty of solving the calculations required by the network. Without the concept of adjustable "difficulty," a network could not adapt or grow as more (or less) computational power is brought online. This difficulty of computation is a core component of the decentralized, distributed nature of blockchains.
If you'd like to learn more about it, here are a couple of resources to get you started:
- "Proof of Work" (Wikipedia)[1]
- "Is there a way to set up proof-of-work systems so they would be even more useful?" (StackExchange, orig. asked in Sept. 2011, updated Dec. 2017)[2]
- "The Fair Cost of Bitcoin Proof of Work" (Tomaso Aste, University College London, 2016)[3]
- "FoldingCoin" (HN discussion, Jan. 2015)[4]
Bitcoin's hashing scheme's "value" is in its ability to make it computationally difficult (and of significant real cost) to attempt to cheat the network.
Simplifying a very complex discussion, you can consider it, in a limited sense, analogous to the different ways that the World's governments and assorted financial institutions spend untold billions of USD, EUR, RMB, YEN, etc. every year to secure, confirm, compensate, and extend the underlying infrastructures that support global financial exchange.
