List of powers of 2

This page contains unnamed powers of 2 that used to have articles on the Googology Wiki. The former content of these articles is also included here.
== List of powers of 2 ==
512 is equal to 29. 512 is a Dudeney number, that is it is equal to the cube of the sum of its digits. It is the smallest base-10 Dudeney number (the others are 4,913, 5,832, 17,576, and 19,683).
In the Bignum Bakeoff contest, entries are limited to 512 characters (ignoring whitespace)
----
210 = 1,024
----
2,048 is a positive integer following 2,047 and preceding 2,049. It is the 11th power of 2, and equal to f2(8) and f3(2) in the fast-growing hierarchy.
It is also the largest known power of 2 where all digits are even.Pointless Gigantic List of Numbers - Part 1 (0 ~ 1,000,000) - Pointless Large Number Stuff
2048 is also the name of a web game where you slide tiles representing powers of 2 across a board and try to combine them to reach higher and higher powers of 2. The largest tile you can reach is 131072.
----
131,072 is the 17th power of 2.
In the 2048 game, it is the largest tile you can reach.
----
262,144 is the fourth expofactorial number, equal to 4321 = 432 = 49.
----
536,870,912 is the largest power of two number with distinct digits.Prime Curios!: 536870912 It is just over half a billion.
----
2,147,483,648 is a positive integer equal to \(2^{31} = 2^{2^5 - 1}\). It is notable in computer science for being the absolute value of the maximum negative value of a 32-bit signed integer, or a 32 bit integer limit; which have the range [-2147483648, 2147483647].
Its full name in English is "two billion/milliard one hundred forty-seven million four hundred eighty-three thousand six hundred forty-eight," where the short scale uses "billion" and the long scale uses "milliard."
----
263 = 9,223,372,036,854,775,808 It is the absolute value for the maximum negative value of a 64-bit signed integer, which has the range of [-9,223,372,036,854,775,808, 9,223,372,036,854,775,807].
286 = 77,371,252,455,336,267,181,195,264 is the largest known power of two not containing a zero.
----
2168 = 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856 is the largest known power of two not (in this case, the digit 2 is missing).
----
2219 = 842,498,333,348,457,493,583,344,221,469,363,458,551,160,763,204,392,890,034,487,820,288 is the largest power of two with an accepted English name.
----
21.024 = 2210 = 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 is the 64-bit floating point. In many video games using scripts, going past this number will read as "Infinity."
----
21,000,000 ≈ 9.90065623 × 10301,029
== Approximations of these numbers ==
For 131,072:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1.31072 \times 10^5\) (exact)	\(1.31072 \times 10^5\) (exact)
Arrow notation 	\(2↑17\) (exact) 	\(2↑17\) (exact)
Steinhaus-Moser Notation 	6[3] 	7[3]
Copy notation 	1[6] 	2[6]
Taro's multivariable Ackermann function	A(3,14) 	A(3,15)
Pound-Star Notation 	#*(36)*3 	#*(37)*3
BEAF 	\(\{2,17\}\) 	\(\{2,17\}\)
Hyper-E notation 	E[2]17 	E[2]17
Hyperfactorial array notation 	8! 	4!1
Fast-growing hierarchy 	\(f_2(13)\) 	\(f_2(14)\)
Hardy hierarchy 	\(H_{\omega^2}(13)\) 	\(H_{\omega^2}(14)\)
Slow-growing hierarchy 	\(g_{\omega^{17}}(2)\) 	\(g_{\omega^{17}}(2)\)
For 262,144:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(2.62144 \times 10^5\) 	\(2.62144 \times 10^5\)
Arrow notation 	\(2\uparrow18\), \(4\uparrow9\) 	\(2\uparrow18\), \(4\uparrow9\)
Steinhaus-Moser Notation 	6[3] 	7[3]
Copy notation 	2[6] 	3[6]
Chained arrow notation 	\(2\rightarrow18\), \(4\rightarrow9\)	\(2\rightarrow18\), \(4\rightarrow9\)
Taro's multivariable Ackermann function	A(3,14) 	A(3,15)
Pound-Star Notation 	#*(16)*4 	#*(16)*4
PlantStar's Debut Notation 	[3] 	[4]
BEAF 	\(\{2,18\}, \{4,9\}\) 	\(\{2,18\}, \{4,9\}\)
Hyper-E notation 	E[2]18, E[4]9 	E[2]18, E[4]9
Bashicu matrix system 	(0)[512] 	(0)[512]
Hyperfactorial array notation 	4!1 	4!1
Bird's array notation 	\(\{2,18\}, \{4,9\}\) 	\(\{2,18\}, \{4,9\}\)
Strong array notation 	s(2,18), s(4,9) 	s(2,18), s(4,9)
Fast-growing hierarchy 	\(f_2(14)\) 	\(f_2(15)\)
Hardy hierarchy 	\(H_{\omega^2}(14)\) 	\(H_{\omega^2}(15)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega 2 +1}}(4)\) 	\(g_{\omega^{\omega 2 +1}}(4)\)
For 536,870,912:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(5.36870912\times10^8\) (exact)	\(5.36870912\times10^8\) (exact)
Arrow notation 	\(2↑29\) (exact) 	\(2↑29\) (exact)
Steinhaus-Moser Notation 	9[3] 	10[3]
Copy notation 	4[9] 	5[9]
Taro's multivariable Ackermann function	A(3,25) 	A(3,26)
Pound-Star Notation 	#*(99)*4 	#*(38)*5
BEAF 	{2,29} 	{2,29}
Hyper-E notation 	E[2]29 	E[2]29
Hyperfactorial array notation 	12! 	13!
Fast-growing hierarchy 	\(f_2(24)\) 	\(f_2(25)\)
Hardy hierarchy 	\(H_{\omega^2}(24)\) 	\(H_{\omega^2}(25)\)
Slow-growing hierarchy 	\(g_{\omega^{29}}(2)\) 	\(g_{\omega^{29}}(2)\)
For 2,147,483,648:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(2.147483648\times10^9\) (exact)	\(2.147483648\times10^9\) (exact)
Arrow notation 	\(2 \uparrow 31\) (exact) 	\(2 \uparrow 31\) (exact)
Steinhaus-Moser Notation 	9[3] 	10[3]
Copy notation 	21[5] 	2[10]
Taro's multivariable Ackermann function	A(3,28) 	A(3,29)
Pound-Star Notation 	#*(2,2,3)*3 	#*(24)*6
BEAF 	{2,31} 	{2,31}
Hyperfactorial array notation 	12! 	13!
Fast-growing hierarchy 	\(f_2(26)\) 	\(f_2(27)\)
Hardy hierarchy 	\(H_{\omega^2}(26)\) 	\(H_{\omega^2}(27)\)
Slow-growing hierarchy 	\(g_{\omega^{31}}(2)\) 	\(g_{\omega^{31}}(2)\)
== Sources ==
Category:Numbers
 
Category:Lists
Category:Class 1
Category:Unnamed numbers with 4 to 6 digits
Category:Class 2
Category:Unnamed numbers with 7 to 29 digits
Category:Numbers with 30 to 100 digits