Largest known perfect number

The largest known perfect number is \(M_{51?}(\frac{M_{51?}+1}{2}) \approx 1.108478 \cdot 10^{49,724,094}\), where \(M_{51?}\) is \(2^{82,589,933} − 1\), the largest known Mersenne prime, which is suspected to be the 51st Mersenne prime.C. Caldwell, The Largest Known Primes. Accessed 2021-06-02.C. Caldwell, Characterizing all even perfect numbers. Accessed 2021-06-02.
==Approximations in other notations==
For 1.108478 \cdot 10^{49,724,094}\):
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1.108\times10^{49724094}\) 	\(1.109\times10^{49724094}\)
Up-arrow notation(Fish's definition for non-integers)	\(10 \uparrow\uparrow 2.8\) 	\(10 \uparrow\uparrow 2.9\)
Chained arrow notation 	\(10\rightarrow49724094\) 	\(10\rightarrow49724095\)
Bowers' Exploding Array Function 	{10, 49724094} 	{10, 49724095}
Steinhaus-Moser Notation 	7[3][3] 	8[3][3]
Fast-growing hierarchy 	\(f_2(f_2(22))\) 	\(f_2(f_2(23))\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^7}}(10)\)	\(g_{\omega^{\omega^8}}(10)\)
Hyper-E notation 	E49724094 	E49724095
Factorial 	(10!)! 	(11!)!
== Sources ==
ja:知られている最大の完全数
Category:Numbers
Category:Class 3
Category:Perfect numbers
Category:Numerical records
Category:Lower class 3
Category:Dynamic googolisms