Number

8

8 — The luckiest number in China

8 is a composite number, even, a calendar year.

Eight is the most sought-after digit in the Chinese-speaking world, and the reason is pure sound. 八 (bā) is a near-homophone of 发 (fā), the fa of 发财 (fācái), “to make a fortune”; in Cantonese the pairing is 八 (baat) against 發 (faat). A number that sounds like getting rich becomes, by a kind of linguistic gravity, a number people will pay for.

And they do pay. The Beijing Olympics opened on 8 August 2008 at 8:08 in the evening. Phone numbers and licence plates carrying runs of eights command real premiums at auction — Sichuan Airlines reportedly paid 2.33 million yuan for the number 8888-8888 in 2003 — and economists studying Hong Kong plate auctions have measured the effect rather than merely noted it. Developers price eighth-floor apartments higher, and quietly skip the floors nobody wants.

The mathematics is just as distinguished. 8 is the first cube after 1 (2³) and a Fibonacci number, and by Mihailescu's theorem — Catalan's conjecture, finally proved in 2002 — 8 and 9 are the only two consecutive perfect powers anywhere in the integers. The number an entire culture prizes for prosperity also happens to be the one cube in all of arithmetic sitting directly beneath a square.

Sources https://en.wikipedia.org/wiki/Numbers_in_Chinese_culture · https://en.wikipedia.org/wiki/Catalan%27s_conjecture

Cake Number Curated Deficient Number Fibonacci Flippable Harshad / Niven Highly Abundant Leyland Number Lucky Number Narcissistic / Armstrong Octagonal Odious Number Perfect Cube Power of Two Powerful Number Practical Number Recamán's Sequence Refactorable Number Strobogrammatic Tetranacci Number Zuckerman Number

Interestingness

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18 notable facts · grade A

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Historical context — 8 AD

First 9 years of the Common Era

The 0s began on January 1, AD 1 and ended on December 31, AD 9, covering the first nine years of the Common Era.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Historical context — 8 BC

Calendar year

Year 8 BC was either a common year starting on Friday or Saturday or a leap year starting on Thursday of the Julian calendar and a common year starting on Wednesday of the Proleptic Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Tuesday
January 1, 8
Ended on: Wednesday
December 31, 8
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 0s
0–9
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,018
2018 years before 2026.

In other calendars

Hebrew: 3768 / 3769 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Earth zodiac:Dragon
Sexagenary cycle position 5 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 551 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 0 / 1 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -70 / -71 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese lucky

Extremely lucky — sought after in addresses, phone numbers, license plates.

八 (bā) sounds like 发 (fā, "prosper, get rich"). The Beijing Olympics opened on 08/08/08 at 8:08 PM.

Wikipedia ↗

Japanese lucky

Lucky — represents prosperity broadening like an opening fan.

The shape of the kanji 八 widens outward.

Hindu sacred

Associated with Lakshmi and the eight forms of wealth (Ashta Lakshmi).

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Even
Digit count: 1
Digit sum: 8
Digital root: 8
Palindrome: Yes
Bit width: 4 bits
Recamán's sequence: a(16) = 8
Square (n²): 64
Cube (n³): 512
Cube root (∛n): 2
Divisor count: 4
σ(n) — sum of divisors: 15
φ(n) — Euler's totient: 4
Sum of prime factors: 6

Primality

Prime factorization: 2 ³

Nearest primes: 7 (−1) · 11 (+3)

Divisors & multiples

All divisors (4)

1 · 2 · 4 (half) · 8

Aliquot sum (sum of proper divisors): 7

Factor pairs (a × b = 8)

1 × 8

2 × 4

First multiples

8 · 16 (double) · 24 · 32 · 40 · 48 · 56 · 64 · 72 · 80

Sums & aliquot sequence

As a sum of two squares: 2² + 2²

Aliquot sequence: 8 → 7 → 1 → 0 — terminates at zero

Continued fraction of √n

√8 = [2; (1, 4)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: eight
Ordinal: 8th
Roman numeral: VIII
Binary: 1000
Octal: 10
Hexadecimal: 0x8
Base64: CA==
One's complement: 247 (8-bit)

In other bases

ternary (3) 22

quaternary (4) 20

quinary (5) 13

senary (6) 12

septenary (7) 11

nonary (9) 8

undecimal (11) 8

duodecimal (12) 8

tridecimal (13) 8

tetradecimal (14) 8

pentadecimal (15) 8

As an angle

8°

8° ≈ 0.14 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ηʹ
Mayan (base 20): 𝋨
Chinese: 八
Chinese (financial): 捌

In other modern scripts

Eastern Arabic ٨ Devanagari ८ Bengali ৮ Tamil ௮ Thai ๘ Tibetan ༨ Khmer ៨ Lao ໘ Burmese ၈

Digit at this position in famous constants

π — Pi (π): Digit 8 = 6
e — Euler's number (e): Digit 8 = 8
φ — Golden ratio (φ): Digit 8 = 9
√2 — Pythagoras's (√2): Digit 8 = 5
ln 2 — Natural log of 2: Digit 8 = 1
γ — Euler-Mascheroni (γ): Digit 8 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 8, here are decompositions:

3 + 5 = 8

ASCII character

As an ASCII codepoint, 8 is BS (backspace). ASCII control character.

Hex color

#000008

RGB(0, 0, 8)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.8.

Address: 0.0.0.8
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.8

Unspecified address (0.0.0.0/8) — "this network" placeholder.

US numbered highway

Matches numbered highway designation:

I-8 — San Diego, CA to Casa Grande, AZ.

Interstate 8 on Wikipedia ↗

Musical pitch

As a MIDI note number, 8 is G♯-1 (13 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 8 is Oxygen (O) — period 2.

Oxygen on Wikipedia ↗