  We show that there is a correspondence between Goldbach conjecture sequences
(GCS) and expectation values of the number operator in Fock states. We
demonstrate that depending on the normalization or not of Fock state
superpositions, we have sequences that are equivalent and sequences that are
not equivalent to GCS. We propose an algorithm where sequences equivalent to
GCS can be derived in terms of expectation values with normalized states.
Defining states whose projections generate GCS, we relate this problem to
eigenstates of quantum harmonic oscillator and discuss Fock states directly
associated to GCS, taking into account the hamiltonian spectrum and quantum
vacuum fluctuations. Finally, we address the problems of degeneracy, maps
associating GCS and Goldbach partitions.
