Let’s talk about hash #00000000000000000021e800c1e8df51b22c1588e5a624bea17e9faa34b2dc4a

On June 19, 2018 a block was mined with the hash # 00000000000000000021e800c1e8df51b22c1588e5a624bea17e9faa34b2dc4a

The first tweet with this hash tag appears to have originated from Mark Wilcox, with no additional commentary.

What is the significance of this hash? Well that depends on who you ask. Only a few reasons were formally proposed:

1. There are lots of zeroes at the beginning of the hash. The first Bitcoin block mined (# 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f) had lots of zeroes as well. What are the odds of that!
2. 21e800 somehow relates to a physics theory called E8 Theory (or An Exceptionally Simple Theory of Everything). How? Well, that’s not really explained, it just does!

Beyond these two explanations, the hype seems to center around the idea that “This number is special, what are the odds of it occurring?”

From the presented facts it’s clear that “time travel is real” and “Quantum computers exist”:

Yes, of course.

I choose to believe this is just a troll.

Why the leading zeroes?

So what are the odds that this block would contain 18 leading zeroes? Well, I crunched the numbers and it turns out it’s 100%! How? Well, for starters, every block contains leading zeroes. The latest blocks (at the time of writing) are:

0000000000000000002a4f38ba94edaf3d7eae3a7b44ed58d05b1998c403989c
00000000000000000020f6658d7c4f3e7d186499058902f8ab98b0b439feebee
000000000000000000312a238a33e0622abe4fb9a76486a179ebf346aa4392a0

Note that all three contain 18 leading zeroes! But why?

These leading zeroes are the “proof-of-work” you’ve probably heard of when discussing the blockchain. The goal of the Bitcoin mining algorithm is to find inputs to a hash function that generate a hash with a certain number of leading zeroes. When difficulty increases, this means that miners must now generate hashes that have more leading zeroes. This takes a long time, and your computer must try out many, many, many inputs before it stumbles upon inputs that generate the required number of leading zeroes.

If you have more than $500 invested in cryptocurrencies, you should really set aside 25 minutes to watch this excellent explanation of the technology:

What are the odds of 21e800 occurring?

I’m still not sure what the significance of these numbers are, but that doesn’t mean we can’t double check the probability of randomly mining a block with these digits following the leading zeroes.

Each digit can randomly be one of 0–9 and a–f. This means that there are 16 possibilities for each digit. Since we’re generating six digits, the number of possible outcomes are:

16 * 16 * 16 * 16 * 16 * 16 = 16⁶ = 16,777,216 possibilities

So there are ~16.7 million possible combinations of digits for these first six digits.

Our 21e800 block was block #528,249. Let’s calculate the odds of this hash NOT appearing in any block:

((16⁶ — 1) / (16⁶))^528,249 = 0.97

The odds that the hash does appear is 1–0.97 or 3%.

So the odds aren’t great, but they also aren’t “quantum computers must’ve been invented for this to have happened”

What about simpler combinations?

I don’t really understand why 21e800 is any more significant to E8 theory than than 21e8 (they’ve both got e8 in them!), so does this simpler combination ever occur?

To answer this question, I simply downloaded a list of all of the hashes and looked at them. Here are the 18 hashes containing the rare and elusive 21e8:
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Other vanity hashes

While we’re looking for patterns in whitenoise, why stop with 21e8? Here are some others I’ve found. If you want to look through them yourself, I’ve made the list of hashes available on GitHub at: https://github.com/JoshVarty/BitcoinHashes

5teal (Steal)

000000000057ea16558140e0b3995aef6dd2641624e1c790acf78424ce4e4b83

ca11ed (Called)

000000000000ca11ed39feba1e60a1b885befafbb6532ece763ba18bdc05ffdd

1o55es (Losses)

00000000001055e54d1d11bae837d58b1b5887947c0af9147b7418675d5198b5

Steal called losses. Spooky. Someone really oughta look into that.