user80259: The description states:
A script hash is the hash of the binary bytes of the locking script (ScriptPubKey), expressed as a hexadecimal string. The hash function to use is given by the “hash_function” member of server.features() (currently sha256() only). Like for block and transaction hashes, when converting the big-endian binary hash to a hexadecimal string the least-significant byte appears first, and the most-significant byte last.

For example, the legacy Bitcoin address from the genesis block:

1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa
has P2PKH script:

76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac
with SHA256 hash:

6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b
which is sent to the server reversed as:

8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161
By subscribing to this hash you can find P2PKH payments to that address.

Can anybody explain what these numbers are:
6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b
8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161
and how to get them?

user100185: Using the bx command line tool,
the Satoshi address: 
1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa
looks like this decoded (using bx)
$ bx base58-decode 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa

outputs:
0062e907b15cbf27d5425399ebf6f0fb50ebb88f18c29b7d93

The first 2 digits (00) is the version number, the last 8 digits (c29b7d93) is the checksum. Leaving 62e907b15cbf27d5425399ebf6f0fb50ebb88f18 as your payload (pubkey in this instance).
Now if I were to make a basic P2PKH locking script with the above pubkey it would look like this:
dup hash160 [62e907b15cbf27d5425399ebf6f0fb50ebb88f18] equalverify checksig

and now encode it in base16:
bx script-encode "dup hash160 [62e907b15cbf27d5425399ebf6f0fb50ebb88f18] equalverify checksig"

result:
76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac

sha256 this:
bx sha256 76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac

result is your number:
6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b

The second number, 
8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161

is serialized in the little-endian (least-significant-byte-first) order. As stated in the link:

When transactions are transmitted over the network or exchanged between applications, they are serialized. Serialization is the process of converting the internal representation of a data structure into a format that can be transmitted one byte at a time, also known as a byte stream. Serialization is most commonly used for encoding data structures for transmission over a network or for storage in a file. 

so they're the same number, except byte by byte backwards (I exploded the last 3 bytes of the first to make it apparent).
6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364e df 01 8b
8b 01 df ...


80259: <p>The <a href="https://electrumx.readthedocs.io/en/latest/protocol-basics.html#script-hashes" rel="nofollow noreferrer">description</a> states:</p>

<pre><code>A script hash is the hash of the binary bytes of the locking script (ScriptPubKey), expressed as a hexadecimal string. The hash function to use is given by the “hash_function” member of server.features() (currently sha256() only). Like for block and transaction hashes, when converting the big-endian binary hash to a hexadecimal string the least-significant byte appears first, and the most-significant byte last.

For example, the legacy Bitcoin address from the genesis block:

1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa
has P2PKH script:

76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac
with SHA256 hash:

6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b
which is sent to the server reversed as:

8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161
By subscribing to this hash you can find P2PKH payments to that address.
</code></pre>

<p>Can anybody explain what these numbers are:</p>

<p><strong>6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b</strong></p>

<p><strong>8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161</strong></p>

<p>and how to get them?</p>
 100185: <p>Using the <a href="https://github.com/libbitcoin/libbitcoin-explorer" rel="nofollow noreferrer">bx command line tool</a>,
the Satoshi address: </p>

<p><code>1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa</code></p>

<p>looks like this decoded (using bx)</p>

<pre><code>$ bx base58-decode 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa
</code></pre>

<p>outputs:</p>

<pre><code>0062e907b15cbf27d5425399ebf6f0fb50ebb88f18c29b7d93
</code></pre>

<p>The first 2 digits (<code>00</code>) is the version number, the last 8 digits (<code>c29b7d93</code>) is the checksum. Leaving <code>62e907b15cbf27d5425399ebf6f0fb50ebb88f18</code> as your payload (pubkey in this instance).</p>

<p>Now if I were to make a basic P2PKH locking script with the above pubkey it would look like this:</p>

<pre><code>dup hash160 [62e907b15cbf27d5425399ebf6f0fb50ebb88f18] equalverify checksig
</code></pre>

<p>and now encode it in base16:</p>

<pre><code>bx script-encode "dup hash160 [62e907b15cbf27d5425399ebf6f0fb50ebb88f18] equalverify checksig"
</code></pre>

<p>result:</p>

<pre><code>76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac
</code></pre>

<p>sha256 this:</p>

<pre><code>bx sha256 76a91462e907b15cbf27d5425399ebf6f0fb50ebb88f1888ac
</code></pre>

<p>result is your number:</p>

<pre><code>6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364edf018b
</code></pre>

<p>The second number, </p>

<pre><code>8b01df4e368ea28f8dc0423bcf7a4923e3a12d307c875e47a0cfbf90b5c39161
</code></pre>

<p>is <a href="https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch06.asciidoc#transaction-serializationoutputs" rel="nofollow noreferrer">serialized in the little-endian</a> (least-significant-byte-first) order. As stated in the link:</p>

<blockquote>
  <p>When transactions are transmitted over the network or exchanged between applications, they are serialized. Serialization is the process of converting the internal representation of a data structure into a format that can be transmitted one byte at a time, also known as a byte stream. Serialization is most commonly used for encoding data structures for transmission over a network or for storage in a file. </p>
</blockquote>

<p>so they're the same number, except byte by byte backwards (I exploded the last 3 bytes of the first to make it apparent).</p>

<pre><code>6191c3b590bfcfa0475e877c302da1e323497acf3b42c08d8fa28e364e df 01 8b
8b 01 df ...
</code></pre>
