Ivan Mikheevich Pervushin (, sometimes transliterated as Pervusin or Pervouchine) (—) was a Russian clergyman and mathematician of the second half of the 19th century, known for his achievements in number theory. He discovered the ninth perfect number and its odd prime factor, the ninth Mersenne prime. Also, he proved that two Fermat numbers, the 12th and 23rd, were composite.
A contemporary of Pervushin's, writer A. D. Nosilov, 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".
Life
Ivan Pervushin was born on in Lysva, Permsky Uyezd, Perm Governorate, a district in the east 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. Though, according to recently found archival parish registers of 1827 from Lysva church, he was born in Lysva. 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 , some 150 miles from Ekaterinburg, where he lived for 25 years.
In Zamaraevo, Pervushin founded a rural school in 1859.
: <math>2^{2^{12 + 1</math> is divisible by <math>7\times2^{14}+1=114689 </math>
and
: <math>2^{2^{23 + 1</math> is divisible by <math>5\times2^{25}+1=167772161.</math>
In 1883 Pervushin demonstrated that the number
: <math>2^{61}-1 = 2305843009213693951 </math>
is a Mersenne prime, and that correspondingly
: <math>2^{60}(2^{61}-1) = 2658455991569831744654692615953842176 </math>
is a perfect number. At the time, these were the second largest known prime number, and the second largest known perfect number, after <math>2^{127}-1</math> and <math>2^{126}(2^{127}-1)</math>, proved prime and perfect by Édouard Lucas seven years earlier. They remained the second largest until 1911, when Ralph Ernest Powers proved that <math>2^{89}-1</math> is prime and <math>2^{88}(2^{89}-1)</math> is perfect.
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.