Aleksander Prystor was born in Vilnius, now the capital of Lithuania and then called Vilna under the Russian Empire, to a railroad worker Feliks Prystor and Maria (née Olejnik). In 1894 he graduated from the Second High School in Vilna, and began studying mathematics and physics at Imperial Moscow University. Lacking financial support of his family, Prystor lived in poverty. After graduation in 1900, he decided to study medicine at the University of Tartu. In the summer of 1902, he returned to Vilna, taking a job in a bank. Between November 1903 and September 1904, Prystor served in the 16th Sapper Battalion of the Imperial Russian Army.