A thermal breeder reactor is fueled with a mixture of a fertile nucleus A (fraction 1 − x) which breeds a fissile nucleus B (fraction x). To breed more of B it is essential that the reproduction factor η(B) in thermal-neutron induced fission of B is greater than two. Express the maximum possible value of η(B) in terms of cross sections and the average number of fast neutrons in B-fission. Evaluate η(B)|_max for the two possible breeding systems, (²³⁸U,²³⁹Pu) and (²³²Th, ²³³U). Which is the most promising for a thermal breeder reactor?