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The math behind cryptocurrencies. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/btc-thanks This video was also funded with help from Protocol Labs: https://protocol.ai/join/ Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact, it does: http://3b1b.co/crypto ENS: 3b1b.eth 2^256 video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat Here are a few other resources I'd recommend: Original Bitcoin paper: https://bitcoin.org/bitcoin.pdf Block explorer: https://blockexplorer.com/ Blog post by Michael Nielsen: https://goo.gl/BW1RV3 (This is particularly good for understanding the details of what transactions look like, which is something this video did not cover) Video by CuriousInventor: https://youtu.be/Lx9zgZCMqXE Video by Anders Brownworth: https://youtu.be/_160oMzblY8 Ethereum white paper: https://goo.gl/XXZddT Timestamps: 0:00 - Introduction 2:25 - Ledgers and digital signatures 7:21 - The ledger is the currency 10:06 - Decentralization 12:26 - Cryptographic hash functions 14:38 - Proof of work and blockchains 19:42 - Double spending 21:41 - Block times, halvenings, and transaction fees 24:40 - Thanks Thanks to these viewers for their contributions to translations Italian: @lcl45 ------------------ Animations are largely made using manim, a scrappy open-source python library. https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown