The chemical universe database GDB-17 contains 166.4 billion molecules of up to 17 atoms of C, N, O, S, and halogens obeying rules for chemical stability, synthetic feasibility, and medicinal chemistry. GDB-17 was analyzed using 42 integer value descriptors of molecular structure which we term "Molecular Quantum Numbers" (MQN). Principal component analysis and representation of the (PC1, PC2)-plane provided a graphical overview of the GDB-17 chemical space. Rapid ligand-based virtual screening (LBVS) of GDB-17 using the city-block distance CBD(MQN) as a similarity search measure was enabled by a hashed MQN-fingerprint. LBVS of the entire GDB-17 and of selected subsets identified shape similar, scaffold hopping analogs (ROCS > 1.6 and T(SF) < 0.5) of 15 drugs. Over 97% of these analogs occurred within CBD(MQN) ≤ 12 from each drug, a constraint which might help focus advanced virtual screening. An MQN-searchable 50 million subset of GDB-17 is publicly available at www.gdb.unibe.ch .