Algorithmic improvements to the parallel, distributed-memory multilevel fast multipole algorithm (MLFMA) have resulted in implementations with favorable weak scaling properties. This allows for the simulation of increasingly larger electromagnetic problems, provided that sufficient computational resources are available. This is demonstrated by presenting the full-wave simulations of extremely large perfectly electrically conducting (PEC) sphere and Thunderbird geometries. Both problems are formulated using the combined field integral equation (CFIE) and discretized in over respectively 3 and 2.5 billion unknowns. They are solved using 4096 CPU cores and 25 TByte of memory. To the best of our knowledge, this is the largest number of unknowns and the highest amount of parallel processes reported to date, for this type of simulation. Additionally, it is demonstrated that the implementation attains a high parallel speedup and efficiency.