# Ivan Mikheevich Pervushin

Ivan Mikheevich Pervushin (Russian: Иван Михеевич Первушин) (January 21, 1827 – June 29, 1900) was a Russian mathematician of the 2nd half of 19th century.

Pervushin was born in the town of Lysva of the Perm gubernia to a family of a clergyman. 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.

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:

$2^{2^{12}} + 1$ is divisible by $7*2^{14}+1=114689$

and

$2^{2^{23}} + 1$ is divisible by $5*2^{25}+1=167772161$

In 1883 Pervushin demonstrated that the number:

$2^{61}-1$ = 2305843009213693951

is a Mersenne prime. This number became known as "Pervushin's number", and remained the second largest known prime (after $2^{127}-1$, proved prime by Lucas 7 years earlier) until 1911, when Powers proved that $2^{89}-1$ is prime.

From Zamaraevo, Pervushin moved to the nearby town of Shadrinsk in 1883. Here Pervushin published an article that ridiculed the local government. As a punishment, he was exiled to the village of Mehonskoe in 1887.

A contemporary of Pervushin's, writer A.D.Nosilov, who frequently visited Pervushin in Mehonskoe, wrote a paper "Priest-mathematician", which was published in the "New time" magazine on July 6, 1896.

He wrote: "... this is the modest unknown worker of science ... All of his spacious study is filled up with the different mathematical books, ... here are the books of famous mathematicians: Chebyshev, Legendre, Riemann; not including all modern mathematical publications, which were sent to him by Russian and foreign scientific and mathematical societies. It seemed I was not in a study of the village priest, but in a study of an old mathematics professor ... Besides being a mathematician, he is also a statistician, a meteorologist, and a correspondent".

Pervushin died in Mehonskoe at the age of 73.