Ivan Pervushin

Pervushin was born in Perm Oblast, a district in the southeast of European Russia. He claimed his birthplace to be the town of Lysva (where his grandfather, John Pervushin, was a priest) but other sources suggest Pashii, in Gornozavodsk.[2] Though, according to recently found archival parish registers of 1827 from Lysva church, he was born in Lysva.[3] He graduated from Kazan clerical academy in 1852. Upon graduation, Pervushin was required to become a priest; he stayed for some time in Perm, then moved to a remote village of Zamaraevo, some 150 miles from Ekaterinburg, where he lived for 25 years.[4]

In Zamaraevo, Pervushin founded a rural school in 1859.[2] He moved to the nearby town of Shadrinsk in 1883, where he published an article that ridiculed the local government. As a punishment, he was exiled to the village of Mehonskoe in 1887.

Pervushin died in Mehonskoe at the age of 73.

The priest's job provided for Pervushin's life and left him plenty of free time to spend on mathematics. Pervushin was particularly interested in number theory. In 1877 and in the beginning of 1878 he presented two papers to the Russian Academy of Sciences. In these papers, he proved that the 12th and 23rd Fermat numbers are composite:[5]

${\displaystyle 2^{2^{12}}+1}$ is divisible by ${\displaystyle 7\times 2^{14}+1=114689}$

and

${\displaystyle 2^{2^{23}}+1}$ is divisible by ${\displaystyle 5\times 2^{25}+1=167772161.}$

In 1883 Pervushin demonstrated that the number

${\displaystyle 2^{61}-1=2305843009213693951}$

is a Mersenne prime, and that correspondingly

${\displaystyle 2^{60}(2^{61}-1)=2658455991569831744654692615953842176}$

is a perfect number. At the time, these were the second largest known prime number, and the second largest known perfect number, after ${\displaystyle 2^{127}-1}$ and ${\displaystyle 2^{126}(2^{127}-1)}$, proved prime and perfect by Édouard Lucas seven years earlier. They remained the second largest until 1911, when Ralph Ernest Powers proved that ${\displaystyle 2^{89}-1}$ is prime and ${\displaystyle 2^{88}(2^{89}-1)}$ is perfect.[6]

Pervushin was a contributor to the International World Congress of Mathematicians of 1893, a part of the World's Columbian Exposition in Chicago that became a precursor to the later International Congresses of Mathematicians. However, he did not attend.[7]