Number

5

5 is a prime, odd, a calendar year.

5 (five) is an odd 1-digit number. It is a prime number — divisible only by 1 and itself. It is a Fibonacci number and a Catalan number. Written other ways, in Roman numerals it is V and in binary, 101.

Arithmetic Number Automorphic Number Balanced Prime Bell Number Binary Palindrome Catalan Number Centered Square Chen Prime Circular Prime Cube-Free Deficient Number Evil Number Fermat Number Fibonacci Harshad / Niven Jacobsthal Number Left-Truncatable Prime Markov Number Narcissistic / Armstrong Padovan Number Palindromic Prime Partition Number Pell Number Pentagonal Pentatope Number Pernicious Number Perrin Number Prime Pythagorean Prime Recamán's Sequence Right-Truncatable Prime Safe Prime Self Number Sexy Prime Sophie Germain Prime Square Pyramidal Squarefree Twin Prime Wilson Prime Year Zuckerman Number

Interestingness

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Historical context — 5 BC

Calendar year

5 BC was a common year starting on Monday or Tuesday of the Julian calendar and a leap year starting on Saturday 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: Saturday
January 1, 5
Ended on: Saturday
December 31, 5
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: 2,021
2021 years before 2026.

In other calendars

Hebrew: 3765 / 3766 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Wood zodiac:Ox
Sexagenary cycle position 2 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 548 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: -3 / -2 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -73 / -74 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese significant

Associated with the Five Elements (wood, fire, earth, metal, water).

Wǔxíng — the foundational schema of traditional Chinese cosmology.

Islamic sacred

The Five Pillars of Islam.

Shahada, prayer, alms, fasting, pilgrimage.

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

Properties

Parity: Odd
Digit count: 1
Digit sum: 5
Digital root: 5
Palindrome: Yes
Bit width: 3 bits
Recamán's sequence: a(129) = 5
Square (n²): 25
Cube (n³): 125
Divisor count: 2
σ(n) — sum of divisors: 6
φ(n) — Euler's totient: 4

Primality

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

Divisors & multiples

All divisors (2)

1 · 5

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 5)

1 × 5

First multiples

5 · 10 (double) · 15 · 20 · 25 · 30 · 35 · 40 · 45 · 50

Sums & aliquot sequence

As a sum of two squares: 1² + 2²

As consecutive integers: 2 + 3

Continued fraction of √n

√5 = [2; (4)]

Period length 1 — the block in parentheses repeats forever.

Representations

In words: five
Ordinal: 5th
Roman numeral: V
Binary: 101
Octal: 5
Hexadecimal: 0x5
Base64: BQ==
One's complement: 250 (8-bit)

In other bases

ternary (3) 12

quaternary (4) 11

quinary (5) 10

senary (6) 5

septenary (7) 5

nonary (9) 5

undecimal (11) 5

duodecimal (12) 5

tridecimal (13) 5

tetradecimal (14) 5

pentadecimal (15) 5

Palindromic in base 2

As an angle

5°

5° ≈ 0.087 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): εʹ
Mayan (base 20): 𝋥
Chinese: 五
Chinese (financial): 伍

In other modern scripts

Eastern Arabic ٥ Devanagari ५ Bengali ৫ Tamil ௫ Thai ๕ Tibetan ༥ Khmer ៥ Lao ໕ Burmese ၅

Digit at this position in famous constants

π — Pi (π): Digit 5 = 5
e — Euler's number (e): Digit 5 = 2
φ — Golden ratio (φ): Digit 5 = 0
√2 — Pythagoras's (√2): Digit 5 = 2
ln 2 — Natural log of 2: Digit 5 = 1
γ — Euler-Mascheroni (γ): Digit 5 = 2

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 3 (gap of 2)
Next prime: 7 (gap of 2)

Pair status: twin with 3, twin with 7.

ASCII character

As an ASCII codepoint, 5 is control character (0x05). ASCII control character.

Hex color

#000005

RGB(0, 0, 5)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.5.

Address: 0.0.0.5
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.5

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

US numbered highway

Matches numbered highway designation:

I-5 — Mexico border (San Diego) to Canada border (Blaine, WA) — the Pacific coast spine.

Interstate 5 on Wikipedia ↗

Musical pitch

As a MIDI note number, 5 is F-1 (10.9 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 5 is Boron (B) — period 2.

Boron on Wikipedia ↗