The radioactivity of aluminum-26 in two cores of Pacific sediments is an order of magnitude higher than was expected, as a result of its production by cosmic-ray interactions in the terrestrial environment. The higher activity can be explained only by postulating influx with extraterrestrial cosmic dust that had been exposed to significant flux of energetic particles capable of producing nuclear interactions. These particles may well be the "solar" cosmic rays that are sporadically accelerated by Sun during certain solar flares, since the steady galactic cosmic-ray flux is inadequate. The long-term average flux of low-energy protons in interplanetary space, required to yield the observed rate of influx of aluminum-26, is deduced on the basis of certain assumptions.