costs, and miners thus have to balance their technology and energy investment so that their activities are profitable. As the price of Bitcoin increased, miners invested in more hardware, increasing their computational capability. However, the Bitcoin network then increased the difficulty of the cryptographic problem, in order to keep blocks published in regular intervals. Figure \[fig:difficultyblocksize\] shows the evolution in both the difficulty of the cryptographic problem over time, as well as the block size. We note the exponential increase in the difficulty for a sustained period of time. As Bitcoin prices had been steadily declining in the latter part of this period, it is likely that mining became less profitable, which explains the plateau in difficulty.

With regards to the increase in blocksize, this corresponds to an increase in Bitcoin transactions over time. A blocksize of 0.4 MB corresponds to approximately 3 Bitcoin transactions per second. A summary of other Bitcoin related trends is also provided in reports such as by [@bohme2015bitcoin].

Crypto-currency real world usage
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The projected future use of crypto-currencies like Bitcoin is discussed at length by [@brito2014bitcoin], with regard to securities, options, swaptions, forwards, bonds that may be developed going forward based on virtual currencies 