No piece of data that does have significance to the Bitcoin consensus can be memorable because it occurs (about) every ten minutes. In order to get something memorable to provide sanity (let's say, anti-sybil-attack) checking, it has to be rare, but recurrent.  The opportunity is actually already there, but it usually goes by without providing the benefits.

For example, I found this blog post by Ken Shirriff who describes artifacts that can be found in the blockchain. These artifacts are not intimately tied to their location in the blockchain, so anyone building an alternative blockchain can relatively easily add the artifacts with the same timestamp and at the same height, masking the counterfeit.  In order to prevent that, the memorable thing has to be intimately tied to work-intensive results, like the ratio of the hash to the target.  Nelson Mandela's image appearing in the blockchain does NOT prove to me it's the blockchain I can see at blockchain.com right now, but if the smallest block hash in that blockchain, on 12/13/13, after all the zeroes, starts with 3da1 (144 * 65536 times as much work) and is one of the three block hashes from that day that have two occurrences of a double-e (about 256 times more work), then it will.  The problem is that I'll probably forget most of those details - but not that Mandela's image went in the blockchain near the end of 2013.

On Sat, Apr 13, 2019 at 12:09 PM Peter Todd <pete@petertodd.org> wrote:
On Wed, Apr 03, 2019 at 02:39:32PM -0700, Dave Scotese via bitcoin-dev wrote:
> Every block's hash is smaller than the difficulty at that time.  Block
> 569927's hash was VERY small (started with 21 zeros).  The ratio of block
> hash to difficulty requirement (0xffffffff - difficulty, I think) could be
> used to identify blocks as "special," thus providing the opportunity to
> popularize unimportant but memorable-and-therefore-useful details.  How can
> they be useful if they are unimportant?  They are useful for sanity
> checking.  For example, if the drunken bishop walk (or some other popular
> randomart) produced by block 569927's hash looked like a face, that would
> be memorable: "The block with the smallest hash in 2019 (maybe ever?) looks
> like a face after the drunken bishop walk."

As hashest smaller than the target have no significance to the Bitcoin
consensus I'd suggest not basing any features on that property. It's just as
arbitrary as picking whole decimal number block heights, yet has the additional
downsides of being harder to compute, and being likely to confuse people as to
how the Bitcoin consensus works.

--
https://petertodd.org 'peter'[:-1]@petertodd.org