We present a theoretical study of the energetic and thermodynamic stability of selected phosphorus and arsenic clusters containing 18 to 168 atoms. For this purpose we employ MP2 as well as DFT functionals BP86 and B3LYP with extended basis sets. All procedures predict the family of one-dimensional polymers X18+12n, each with 2n−1 isomers of virtually identical energy, to be more stable than other structures investigated so far. Furthermore, islands of stability result for ring-shaped clusters X24n with Dnd symmetry for n=4 (only for arsenic), 5, 6, and 7. Phosphorus and arsenic show otherwise a very similar behavior. An investigation of basis set effects shows that a doubly polarized triple zeta valence basis (TZVPP) is both necessary and sufficient. In comparison to the reliable spin component scaled MP2 (SCS-MP2) procedure, DFT methods underestimate and MP2 overestimates the stability of larger clusters; the discrepancy increases with the number of atoms. The addition of a long-range dispersion correction to B3LYP energies does not rectify the shortcomings of DFT in comparison with SCS-MP2.