# Why are Hilbert Numbers Called Hilbert Numbers?

It is my understanding that a Hilbert number is any number of the form $$4n + 1$$.

According to

https://en.wikipedia.org/wiki/Hilbert_number#CITEREFFlanneryFlannery2000

it seems that these numbers were named in honor of Hilbert almost twenty years ago.

My question is: Does anyone know why; or what connection they may have had to David Hilbert who was not a number theorist; and so, I am imagining, did not study them.

Or did he?

Does anyone know for sure?

To this end, we introduce Hilbert numbers (which indeed have a rather silly definition out of context) and Hilbert primes (which are Hilbert numbers $$n$$ whose only Hilbert number divisors are $$1$$ and $$n$$ itself). Hilbert primes are not Hilbert numbers which are prime in the ordinary sense: for example, $$9$$ is a Hilbert prime because its only nontrivial factor, $$3$$, is not a Hilbert number.
Every Hilbert number has a "prime factorization" into Hilbert primes. But that factorization is not unique; for example, $$441$$ has two prime factorizations $$441 = 21 \cdot 21 = 9 \cdot 49.$$