Number

4

4 — The number East Asia leaves out

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

Four is the mirror image of eight: avoided for exactly the same reason eight is chased. In Mandarin 四 (sì) sits a tone away from 死 (sǐ), “death,” and the collision repeats across the region — shi in Japanese, sa in Korean, sei in Cantonese. The resulting tetraphobia shapes the built environment for something close to a quarter of the world's population.

The evidence is architectural. Lift panels jump from 3 to 5, or relabel the floor “F”; buildings skip 4, 14, 24 and 34 together. Japanese hospitals avoid room numbers containing four, gift sets are boxed in threes and fives but never fours, and Nokia — selling hard into Asia — never shipped a 4-series handset.

The Western analogue is 13, but the contrast is the interesting part: dread of 13 grew out of story and scripture, while fear of 4 is a pure accident of phonetics, a superstition built on a rhyme. Mathematically 4 is the first composite number, the only integer equal to the number of letters in its own English name, and the answer to the four-colour theorem — the minimum number of colours needed to shade any map, and in 1976 the first major theorem ever proved with the help of a computer.

Sources https://en.wikipedia.org/wiki/Tetraphobia · https://en.wikipedia.org/wiki/Four_color_theorem

Cake Number Centered Triangular Cube-Free Curated Deficient Number Harshad / Niven Highly Abundant Highly Composite Number Lazy Caterer Number Lucas Motzkin Number Narcissistic / Armstrong Odious Number Padovan Number Perfect Square Power of Two Powerful Number Practical Number Recamán's Sequence Semiprime Smith Number Superperfect Number Tetrahedral Tetranacci Number Tribonacci Number Unlucky Number Zuckerman Number

Interestingness

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24 notable facts · grade A

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Historical context — 4 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 →

Notable events — 4 BC

Undated Likely birth year of Jesus of Nazareth (modern scholarship).

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 4
Ended on: Friday
December 31, 4
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 0s
0–9
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,022
2022 years before 2026.

In other calendars

Hebrew: 3764 / 3765 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Wood zodiac:Rat
Sexagenary cycle position 1 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 547 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: -4 / -3 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -74 / -75 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese unlucky

Considered very unlucky — buildings often skip the 4th floor.

四 (sì, "four") sounds almost identical to 死 (sǐ, "death").

Wikipedia ↗

Japanese unlucky

Avoided in hospitals and gifts.

Pronounced "shi" — the same as the word for death (死).

Korean unlucky

Hospital floors and room numbers often skip 4.

사 (sa) shares its pronunciation with the Hanja for death.

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

Properties

Parity: Even
Digit count: 1
Digit sum: 4
Digital root: 4
Palindrome: Yes
Bit width: 3 bits
Recamán's sequence: a(131) = 4
Square (n²): 16
Cube (n³): 64
Square root (√n): 2
Divisor count: 3
σ(n) — sum of divisors: 7
φ(n) — Euler's totient: 2
Sum of prime factors: 4

Primality

Prime factorization: 2 ²

Nearest primes: 3 (−1) · 5 (+1)

Divisors & multiples

All divisors (3)

1 · 2 (half) · 4

Aliquot sum (sum of proper divisors): 3

Factor pairs (a × b = 4)

1 × 4

2 × 2

First multiples

4 · 8 (double) · 12 · 16 · 20 · 24 · 28 · 32 · 36 · 40

Sums & aliquot sequence

As a sum of two squares: 0² + 2²

Aliquot sequence: 4 → 3 → 1 → 0 — terminates at zero

Representations

In words: four
Ordinal: 4th
Roman numeral: IV
Binary: 100
Octal: 4
Hexadecimal: 0x4
Base64: BA==
One's complement: 251 (8-bit)

In other bases

ternary (3) 11

quaternary (4) 10

quinary (5) 4

senary (6) 4

septenary (7) 4

nonary (9) 4

undecimal (11) 4

duodecimal (12) 4

tridecimal (13) 4

tetradecimal (14) 4

pentadecimal (15) 4

As an angle

4°

4° ≈ 0.07 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺𓏺
Greek (Milesian): δʹ
Mayan (base 20): 𝋤
Chinese: 四
Chinese (financial): 肆

In other modern scripts

Eastern Arabic ٤ Devanagari ४ Bengali ৪ Tamil ௪ Thai ๔ Tibetan ༤ Khmer ៤ Lao ໔ Burmese ၄

Digit at this position in famous constants

π — Pi (π): Digit 4 = 1
e — Euler's number (e): Digit 4 = 8
φ — Golden ratio (φ): Digit 4 = 8
√2 — Pythagoras's (√2): Digit 4 = 4
ln 2 — Natural log of 2: Digit 4 = 3
γ — Euler-Mascheroni (γ): Digit 4 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 4, here are decompositions:

2 + 2 = 4

ASCII character

As an ASCII codepoint, 4 is control character (0x04). ASCII control character.

Hex color

#000004

RGB(0, 0, 4)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.4.

Address: 0.0.0.4
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.4

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

US numbered highway

Matches numbered highway designation:

I-4 — Tampa to Daytona Beach across central Florida.

Interstate 4 on Wikipedia ↗

Musical pitch

As a MIDI note number, 4 is E-1 (10.3 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 4 is Beryllium (Be) — period 2.

Beryllium on Wikipedia ↗