A Hilbert number can mean either the Gelfond-Schneider constant or an integer in the following class.
Flannery and Flannery (2000, p. 35) define a Hilbert number as a positive integer of the form 
(i.e., a positive integer 
such that 
). The first few are then 1, 5, 9, 13, 17, 21, 25,
... (OEIS A016813). The number 1 is the unit. A Hilbert number 
that is not divisible by
a smaller Hilbert number other than 1 is called a Hilbert prime (or S-prime; Apostol
1976, p. 101); otherwise, 
is called a Hilbert composite. The first few Hilbert primes
are 5, 9, 13, 17, 21, 29, 33, 37, 41, 49, ... (OEIS A057948),
and the first few Hilbert composites are 25, 45, 65, 81, 85, ... (OEIS A054520,
with its initial unit 1 omitted).
Factorization with respect to Hilbert primes is not necessarily unique, as illustrated by the example
 |
The first few such examples are 441, 693, 1089, 1197, 1449, ... (OEIS A057949).
