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2047 is the number following 2046 and preceding 2048[1].
Properties[]
- 2047 is a Mersenne number; it is equal to \(2^{ 11}-1\).[10]
- 2047 is deficient.[11]
- Its prime factorization is 231 × 891.
- 2047 is the smallest Mersenne number with prime index that is not a prime number.
Approximations[]
| Notation
|
Lower bound
|
Upper bound
|
| Up-arrow notation
|
45 ↑ 2
|
| Scientific notation
|
2.047 x 103
|
2.048 x 103
|
| Slow-growing hierarchy
|
\(g_{\omega^{\omega}}(4)\)
|
\(g_{\omega^{\omega}}(5)\)
|
| Copy notation
|
20[2]
|
21[2]
|
| Chained arrow notation
|
45 → 2
|
| Bowers' Exploding Array Function/Bird's array notation
|
{45,2}
|
|
| Fast-growing hierarchy
|
f2(7)
|
f2(8)
|
| Hardy hierarchy
|
Hω(1023)
|
Hω(1024)
|
| Middle-growing hierarchy
|
m(ω,10)
|
m(ω,11)
|
| Hyper-E notation
|
E3.3111
|
| Hyper-E notation (non-10 base)
|
\(E[45]2\)
|
| Hyperfactorial array notation
|
6!
|
7!
|
| X-Sequence Hyper-Exponential Notation
|
45{1}2
|
|
| Steinhaus-Moser Notation
|
4[3]
|
5[3]
|
| PlantStar's Debut Notation
|
[1]
|
[2]
|
| H* function
|
H(0.1)
|
H(0.2)
|
| Bashicu matrix system with respect to version 4
|
(0)[45]
|
(0)[46]
|
| m(n) map
|
m(1)(4)
|
m(1)(5)
|
| s(n) map
|
\(s(1)(\lambda x . x+1)(1022)\)
|
\(s(1)(\lambda x . x+1)(1023)\)
|
Sources[]
