Ivan Pervushin

Ivan Mikheevich Pervushin (1827 - 1900) Russian priest and mathematician, best known for finding factors of the Fermat numbers 2212+1 and 2223+1 and finding the ninth Mersenne primeMathworldPlanetmath, 261-1.

Born in Perm, he studied to be a priest in Kazan and later moved to practice in Zamaraevo. When Pervushin was not saying Mass, he devoted himself to studying number theoryMathworldPlanetmathPlanetmath. It was in Zamaraevo that Pervushin pondered Marin Mersenne’s list of prime numbers of the form 2p-1 and discovered that Mersenne was mistaken to exclude 61, for 2305843009213693951 is in fact prime. Today computers can verify this practically instantaneously, but in Pervushin’s day, it took Hudelot 54 hours in 1887 to confirm Pervushin’s result, performing the Lucas-Lehmer primality test by hand.

The same year that Pervushin discovered the ninth Mersenne prime, he visited Shadrinsk and wrote an article critical of the government there. The government exiled him to Mehonskoe, where he spent the rest of his life. Still, the ninth Mersenne prime, the largest prime numberMathworldPlanetmath known at the time, was for a while known as “Pervushin’s number.”


  • 1 Eric Bach & Jeffrey Shallit, Algorithmic Number Theory: Volume 1: Efficient Algorithms. Cambridge: MIT Press (1996): 7
Title Ivan Pervushin
Canonical name IvanPervushin
Date of creation 2013-03-22 18:04:53
Last modified on 2013-03-22 18:04:53
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 5
Author Mravinci (12996)
Entry type Biography
Classification msc 01A55
Synonym Ivan Mikheevich Pervushin