Pervushin's number

Pervushin's number is \(2,305,843,009,213,693,951 = 2^{61}-1\), the ninth Mersenne prime. It is traditionally denoted as \(M(61)\).
This number was first proven to be prime by Ivan Mikheevich Pervushin in November of 1883 (hence the designation of Pervushin's number).PrimePages Prime Curios! - 2305843009213693951 Retrieved 2023-09-14. At the time of its discovery, it was the second largest known prime, holding that position until 1911.
The number 61 is one of only nine known numbers holding all three conditions of the .
==Approximations==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(2.305\times10^{18}\) 	\(2.306\times10^{18}\)
Arrow notation 	\(12\uparrow17\) 	\(2\uparrow61\)
Steinhaus-Moser Notation 	15[3] 	16[3]
Copy notation 	2[19] 	3[19]
Taro's multivariable Ackermann function	A(3,58) 	A(3,59)
Pound-Star Notation 	#*(0,3,2,2)*4 	#*(6,3,1)*7
BEAF 	{12,17} 	{2,61}
Hyper-E notation 	2E18 	E[2]61
Bashicu matrix system 	(0)(0)[38967] 	(0)(0)[38968]
Hyperfactorial array notation 	19! 	20!
Fast-growing hierarchy 	\(f_2(55)\) 	\(f_2(56)\)
Hardy hierarchy 	\(H_{\omega^2}(55)\) 	\(H_{\omega^2}(56)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega+3}3+\omega^{\omega+2}6}(13)\)	\(g_{\omega^{\omega2+4}2}(8)\)
==Sources==
Category:Numbers
Category:Class 2
Category:Eponymous numbers
Category:Numbers with 7 to 29 digits
Category:Prime numbers