  All solid phases of bismuth under pressure, but one, have been experimentally
found to superconduct. From Bi-I to Bi-V, avoiding Bi-IV, they become
superconductors and perhaps Bi-IV may also become superconductive. To
investigate the influence of the electronic properties N(E) and the vibrational
properties F({\omega}) on their superconductivity we have ab initio calculated
them for the corresponding experimental crystalline structures, and using a BCS
approach have been able to determine their critical temperatures Tc obtaining
results close to experiment: For Bi-I (The Wyckoff Phase) we predicted a
transition temperature of less than 1.3 mK and a year later a Tc of 0.5 mK was
measured; for Bi-II Tc is 3.9 K measured and 3.6 K calculated; Bi-III has a
measured Tc of 7 K and 6.5 K calculated for the structure reported by Chen et
al., and for Bi-V Tc ~ 8 K measured and 6.8 K calculated. Bi-IV has not been
found to be a superconductor but we have recently predicted a Tc of 4.25 K.
