Hilbert number
In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form . The Hilbert numbers were named after David Hilbert.
The sequence of Hilbert numbers begins 1, 5, 9, 13, 17,... ). A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number. The sequence of Hilbert primes begins
A Hilbert prime is not necessarily a prime number; for example, 21 is a composite number since. However, 21 a Hilbert prime since neither 3 nor 7 are Hilbert numbers. It follows from multiplication modulo 4 that a Hilbert prime is either a prime number of the form , or a semiprime of the form.
