Number

3

3 — Three

3 is a prime, odd, a calendar year.

Three is the second prime, the first odd prime, and the first Mersenne prime (\(2^2 - 1\)). It is also the second triangular number.

Sources https://en.wikipedia.org/wiki/3

Arithmetic Number Chen Prime Circular Prime Cousin Prime Cube-Free Cullen Number Curated Deficient Number Evil Number Fermat Number Fibonacci Harshad / Niven Highly Abundant Jacobsthal Number Left-Truncatable Prime Lucas Mersenne Prime Narcissistic / Armstrong Padovan Number Palindromic Prime Partition Number Pernicious Number Perrin Number Prime Recamán's Sequence Right-Truncatable Prime Self Number Sophie Germain Prime Squarefree Triangular Twin Prime Wagstaff Prime Zuckerman Number

Interestingness

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29 notable facts · grade A

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Historical context — 3 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 — 3 BC

Calendar year

Year 3 BC was a common year starting on Wednesday or Thursday of the Julian calendar and a common year starting on Tuesday 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: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Wednesday
January 1, 3
Ended on: Wednesday
December 31, 3
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: 2,023
2023 years before 2026.

In other calendars

Hebrew: 3763 / 3764 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Water zodiac:Pig
Sexagenary cycle position 60 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 546 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: -5 / -4 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -75 / -76 Saka
Indian national calendar; year starts in March.

Cultural significance

Christian sacred

The Holy Trinity — Father, Son, and Holy Spirit.

Threefold deity is central to Christian theology.

Western significant

The "rule of three" — third time's the charm; three wishes; three little pigs.

Triadic patterns recur throughout Western folklore and storytelling.

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

Properties

Parity: Odd
Digit count: 1
Digit sum: 3
Digital root: 3
Palindrome: Yes
Bit width: 2 bits
Recamán's sequence: a(2) = 3
Square (n²): 9
Cube (n³): 27
Divisor count: 2
σ(n) — sum of divisors: 4
φ(n) — Euler's totient: 2

Primality

3 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 3

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 3)

1 × 3

First multiples

3 · 6 (double) · 9 · 12 · 15 · 18 · 21 · 24 · 27 · 30

Sums & aliquot sequence

As consecutive integers: 1 + 2

Continued fraction of √n

√3 = [1; (1, 2)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: three
Ordinal: 3rd
Roman numeral: III
Binary: 11
Octal: 3
Hexadecimal: 0x3
Base64: Aw==
One's complement: 252 (8-bit)

In other bases

ternary (3) 10

quaternary (4) 3

quinary (5) 3

senary (6) 3

septenary (7) 3

nonary (9) 3

undecimal (11) 3

duodecimal (12) 3

tridecimal (13) 3

tetradecimal (14) 3

pentadecimal (15) 3

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺
Greek (Milesian): γʹ
Mayan (base 20): 𝋣
Chinese: 三
Chinese (financial): 參

In other modern scripts

Eastern Arabic ٣ Devanagari ३ Bengali ৩ Tamil ௩ Thai ๓ Tibetan ༣ Khmer ៣ Lao ໓ Burmese ၃

Digit at this position in famous constants

π — Pi (π): Digit 3 = 4
e — Euler's number (e): Digit 3 = 1
φ — Golden ratio (φ): Digit 3 = 1
√2 — Pythagoras's (√2): Digit 3 = 1
ln 2 — Natural log of 2: Digit 3 = 9
γ — Euler-Mascheroni (γ): Digit 3 = 7

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 2 (gap of 1)
Next prime: 5 (gap of 2)

Pair status: twin with 5.

ASCII character

As an ASCII codepoint, 3 is control character (0x03). ASCII control character.

Hex color

#000003

RGB(0, 0, 3)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.3.

Address: 0.0.0.3
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.3

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

Musical pitch

As a MIDI note number, 3 is D♯-1 (9.7 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 3 is Lithium (Li) — period 2.

Lithium on Wikipedia ↗