It's interesting since 0004 is technically just as random as any other lock combination on paper. If you choose a random number between 0000 and 9999, every number has the same chance.

Same with the private key of 4. It was still 47 bytes of 0 and one byte of 4 as storage for P-384.

So if you randomly tested keys, you would take as long to find it on average as any other key.

The problem is that, similar to cracking a number lock, one of the things to check first is weak patterns. This means people on a number lock would start at 0000 and turn one dial. Simlar things happened with the certificates afaik. Someone checked if those certs keys were any low integer and indeed they were.