8,128
8,128 is a composite number, even.
8,128 (eight thousand one hundred twenty-eight) is an even 4-digit number. It is a composite number with 14 divisors, and factors as 2⁶ × 127. Remarkably, it is a perfect number: the sum of its proper divisors is exactly 8,128, equal to the number itself — a property shared by only a handful of known integers. It is the 127th triangular number. Written other ways, in hexadecimal, 0x1FC0.
Interestingness
Properties
- Parity
- Even
- Digit count
- 4
- Digit sum
- 19
- Digit product
- 128
- Digital root
- 1
- Palindrome
- No
- Bit width
- 13 bits
- Reversed
- 8,218
- Recamán's sequence
- a(10,511) = 8,128
- Square (n²)
- 66,064,384
- Cube (n³)
- 536,971,313,152
- Divisor count
- 14
- σ(n) — sum of divisors
- 16,256
- φ(n) — Euler's totient
- 4,032
- Sum of prime factors
- 139
Primality
Prime factorization: 2 6 × 127
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√8,128 = [90; (6, 2, 3, 3, 2, 1, 1, 3, 1, 4, 4, 2, 2, 2, 2, 2, 4, 4, 1, 3, 1, 1, 2, 3, …)]
Period length 28 — the block in parentheses repeats forever.
Representations
- In words
- eight thousand one hundred twenty-eight
- Ordinal
- 8128th
- Binary
- 1111111000000
- Octal
- 17700
- Hexadecimal
- 0x1FC0
- Base64
- H8A=
- One's complement
- 57,407 (16-bit)
- Scientific notation
- 8.128 × 10³
- As a duration
- 8,128 s = 2 hours, 15 minutes, 28 seconds
As an angle
Historical numeral systems
- Babylonian (base 60)
- 𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
- Egyptian hieroglyphic
- 𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
- Greek (Milesian)
- ͵ηρκηʹ
- Mayan (base 20)
- 𝋡·𝋠·𝋦·𝋨
- Chinese
- 八千一百二十八
- Chinese (financial)
- 捌仟壹佰貳拾捌
Digit at this position in famous constants
- π — Pi (π)
- Digit 8,128 = 3
- e — Euler's number (e)
- Digit 8,128 = 4
- φ — Golden ratio (φ)
- Digit 8,128 = 7
- √2 — Pythagoras's (√2)
- Digit 8,128 = 4
- ln 2 — Natural log of 2
- Digit 8,128 = 5
- γ — Euler-Mascheroni (γ)
- Digit 8,128 = 0
Also seen as
Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 8128, here are decompositions:
- 5 + 8123 = 8128
- 11 + 8117 = 8128
- 17 + 8111 = 8128
- 41 + 8087 = 8128
- 47 + 8081 = 8128
- 59 + 8069 = 8128
- 89 + 8039 = 8128
- 179 + 7949 = 8128
Showing the first eight; more decompositions exist.
UTF-8 encoding: E1 BF 80 (3 bytes).
As an unsigned 32-bit integer, this is the IPv4 address 0.0.31.192.
- Address
- 0.0.31.192
- Class
- reserved
- IPv4-mapped IPv6
- ::ffff:0.0.31.192
Unspecified address (0.0.0.0/8) — "this network" placeholder.
Heard as a frequency, 8,128 Hz is closest to:
- Concert pitch (A4 = 440 Hz): B8 (7902.1 Hz, +49¢ — about midway to C9)
- Scientific pitch (C4 = 256 Hz): C9 (8192 Hz, -14¢)
- Baroque pitch (A4 = 415 Hz): C♯9 (8365.9 Hz, -50¢ — about midway to C9)
The digit sequence 8128 first appears in π at position 147 of the decimal expansion (the 147ordinal-suffix:th digit after the integer 3).
Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.
Related reading
- Perfect numbers — Numbers exactly equal to the sum of their parts — only 52 are known, and the odd ones may not exist at all.
- Triangular numbers — 1, 3, 6, 10, 15 … the counting numbers stacked into triangles, and Gauss's famous shortcut for summing them.
- Egyptian hieroglyphic numerals — Seven hieroglyphs for every power of ten, from a single stroke to a million.