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{{Short description|Russian clergyman and mathematician}}
{{family name hatnote|Mikheevich|Pervushin|lang=Eastern Slavic}}
{{Infobox scientist
| name              = Ivan Mikheevich Pervushin
| native_name       = Иван Михеевич Первушин
| native_name_lang  = ru
| image             = Первушин Иван Михеевич.jpg
| birth_date        = {{OldStyleDate|27 January|1827|15 January}}
| birth_place       = [[Lysva]], [[Permsky Uyezd]], [[Perm Governorate]], [[Russian Empire]]<br>(now [[Perm Krai]], [[Russia|Russian Federation]])
| death_date        = {{death date and age |1900|6|30 |1827|1|27}}
| death_place       = {{ill|Mehonskoe|ru|Мехонское}}, [[Shadrinsky Uyezd]], [[Perm Governorate]], [[Russian Empire]]<br>(now [[Shatrovsky District]], [[Kurgan Oblast]], [[Russia|Russian Federation]])
| citizenship       = {{flag|Russian Empire}}
| alma_mater        = {{ill|Kazan Theological Academy|ru|Казанская духовная академия}}
}}

'''Ivan Mikheevich Pervushin''' ({{langx|ru|Иван Михеевич Первушин}}, sometimes transliterated as Pervusin or Pervouchine) ({{#statements:P569}}—{{#statements:P570}}) 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 number]]s, 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]], [[Adrien-Marie Legendre|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".<ref>{{citation|first=A. D.|last=Nosilov|title=Priest-mathematician|magazine=New time|date=July 6, 1896}}.</ref>

==Life==
Ivan Pervushin was born on {{OldStyleDate|27 January|1827|15 January}} 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, Perm Krai|Gornozavodsk]].<ref name="gorn">{{citation|title=Сельский учитель, родом из Пашии|trans-title=Rural teacher, originally from Pashii|date=September 29, 2011|url=http://gornozavodsk.su/?p=896|newspaper=Gornozavodsk Napravlenie|language=ru}}.</ref> Though, according to recently found archival parish registers of 1827 from Lysva church, he was born in Lysva.<ref>[[c:File:ГАПК Ф.37.Оп.1.Д.55а Метрическая книга Троицкой церкви Лысьвенского завода 1827 (заглавие часть о рождении).jpg|Commons: Trinity church of Lysva parish register, title, 1827]] [[c:File:ГАПК Ф.37.Оп.1.Д.55а Метрическая книга Троицкой церкви Лысьвенского завода 1827-01 (часть о рождении).jpg|Commons: Trinity church of Lysva parish register, birth record of Pervushin, 1827-01-15]]</ref> He graduated from Kazan clerical academy in 1852. Upon graduation, Pervushin was required to become a priest; he stayed for some time in [[Perm, Russia|Perm]], then moved to a remote village of {{ill|Zamaraevo|ru|Замараевское}}, some 150 miles from [[Ekaterinburg]], where he lived for 25 years.<ref>{{citation|title=ПЕРВУШИН Иван Михеевич|trans-title=PERVUSHIN Ivan Mikheevich|language=ru|encyclopedia=Ural Historical Encyclopedia|access-date=2015-05-29|url=http://www.ural.ru/spec/ency/encyclopaedia-15-1535-pervushin-ivan-miheevich.html}}.</ref>

In Zamaraevo, Pervushin founded a rural school in 1859.<ref name="gorn"/>
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 {{ill|Mehonskoe|ru|Мехонское}} in 1887.

Ivan Pervushin died on {{OldStyleDate|30 June|1900|17 June}} in Mehonskoe at the age of 73.

==Number theory==
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 number]]s are composite:<ref>{{citation|title=Prime Numbers: The Most Mysterious Figures in Math|first=David|last=Wells|publisher=John Wiley & Sons|year=2011|isbn=9781118045718|page=96|url=https://books.google.com/books?id=1MTcYrbTdsUC&pg=PA96}}.</ref>

: <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.<ref>{{harvtxt|Wells|2011}}, [https://books.google.com/books?id=1MTcYrbTdsUC&pg=PA152 p.&nbsp;152].</ref>

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 Congress of Mathematicians|International Congresses of Mathematicians]]. However, he did not attend.<ref>{{citation|title=International Mathematical Congresses: An Illustrated History 1893–1986|first1=Donald J.|last1=Albers|first2=Gerald L.|last2=Alexanderson|first3=Constance|last3=Reid|edition=2nd|publisher=Springer|year=2012|isbn=9781461387107|page=3|url=https://books.google.com/books?id=2prhBwAAQBAJ&pg=PA3}}.</ref>

==References==
{{reflist}}

{{Authority control}}

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[[Category:People from Lysva]]
[[Category:Russian mathematicians]]
[[Category:1827 births]]
[[Category:1900 deaths]]
[[Category:Russian Christians]]
[[Category:Burials in Kurgan Oblast]]