Prokhorov was born in Moscow to Tamara and Dmitri Prokhorov. He has one sibling, an elder sister, Irina. His maternal grandmother, Anna Belkina, was a Jewish microbiologist who remained in Moscow during World War II to make vaccines while her daughter Tamara was moved east to safety. His paternal grandparents were relatively wealthy peasant farmers (known as kulaks) who were persecuted as class enemies under the Bolsheviks and again under Stalin. His father, one of eight children, grew up poor, after his family "lost everything and was forced to flee from one part of Siberia and restart life in another".