Number

666

666 — The Number of the Beast

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

Six hundred sixty-six is the Number of the Beast in the Book of Revelation. Mathematically, it is the sum of the squares of the first seven primes ((2^{2 + 3}2 + 5^{2 + 7}2 + 11^{2 + 13}2 + 17^2)) and is a triangular number ((T_{36})).

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

Abundant Number Curated Flippable Harshad / Niven Lucky Number Odious Number Palindrome Pernicious Number Practical Number Recamán's Sequence Repdigit Semiperfect Number Smith Number Triangular Unlucky Number

Historical context — 666 AD

Calendar year

Year 666 (DCLXVI) was a common year starting on Thursday of the Julian calendar.

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

Historical context — 666 BC

Calendar year

The year 666 BC was a year of the pre-Julian Roman calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback 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: Monday
January 1, 666
Ended on: Monday
December 31, 666
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 660s
660–669
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,360
1360 years before 2026.

In other calendars

Hebrew: 4426 / 4427 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 45 / 46 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Fire zodiac:Tiger
Sexagenary cycle position 3 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1209 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 44 / 45 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 658 / 659 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 588 / 587 Saka
Indian national calendar; year starts in March.

Cultural significance

Christian unlucky

The "Number of the Beast" — associated with the Antichrist.

Revelation 13:18: "Let him who has understanding calculate the number of the beast, for it is the number of a man, and his number is six hundred and sixty-six."

Wikipedia ↗

Chinese lucky

Triple-six — "smooth, smooth, smooth."

六 (liù) carries the "flowing/smooth" meaning; tripling intensifies the good fortune.

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

Properties

Parity: Even
Digit count: 3
Digit sum: 18
Digit product: 216
Digital root: 9
Palindrome: Yes
Bit width: 10 bits
Flips to (rotate 180°): 999
Recamán's sequence: a(2,292) = 666
Square (n²): 443,556
Cube (n³): 295,408,296
Divisor count: 12
σ(n) — sum of divisors: 1,482
φ(n) — Euler's totient: 216
Sum of prime factors: 45

Primality

Prime factorization: 2 × 3 ² × 37

Nearest primes: 661 (−5) · 673 (+7)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 6 · 9 · 18 · 37 · 74 · 111 · 222 · 333 (half) · 666

Aliquot sum (sum of proper divisors): 816

Factor pairs (a × b = 666)

1 × 666

2 × 333

3 × 222

6 × 111

9 × 74

18 × 37

First multiples

666 · 1,332 (double) · 1,998 · 2,664 · 3,330 · 3,996 · 4,662 · 5,328 · 5,994 · 6,660

Sums & aliquot sequence

As a sum of two squares: 15² + 21²

As consecutive integers: 221 + 222 + 223 165 + 166 + 167 + 168 70 + 71 + … + 78 50 + 51 + … + 61

Aliquot sequence: 666 → 816 → 1,416 → 2,184 → 4,536 → 9,984 → 18,632 → 18,628 → 13,978 → 7,802 → 4,294 → 2,546 → 1,534 → 986 → 634 → 320 → 442 — unresolved within range

Representations

In words: six hundred sixty-six
Ordinal: 666th
Roman numeral: DCLXVI
Binary: 1010011010
Octal: 1232
Hexadecimal: 0x29A
Base64: Apo=
One's complement: 64,869 (16-bit)

In other bases

ternary (3) 220200

quaternary (4) 22122

quinary (5) 10131

senary (6) 3030

septenary (7) 1641

nonary (9) 820

undecimal (11) 556

duodecimal (12) 476

tridecimal (13) 3c3

tetradecimal (14) 358

pentadecimal (15) 2e6

Historical numeral systems

Babylonian (base 60): 𒌋𒁹 𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): χξϛʹ
Mayan (base 20): 𝋡·𝋭·𝋦
Chinese: 六百六十六
Chinese (financial): 陸佰陸拾陸

In other modern scripts

Eastern Arabic ٦٦٦ Devanagari ६६६ Bengali ৬৬৬ Tamil ௬௬௬ Thai ๖๖๖ Tibetan ༦༦༦ Khmer ៦៦៦ Lao ໖໖໖ Burmese ၆၆၆

Digit at this position in famous constants

π — Pi (π): Digit 666 = 5
e — Euler's number (e): Digit 666 = 0
φ — Golden ratio (φ): Digit 666 = 0
√2 — Pythagoras's (√2): Digit 666 = 4
ln 2 — Natural log of 2: Digit 666 = 9
γ — Euler-Mascheroni (γ): Digit 666 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 666, here are decompositions:

5 + 661 = 666
7 + 659 = 666
13 + 653 = 666
19 + 647 = 666
23 + 643 = 666
47 + 619 = 666
53 + 613 = 666
59 + 607 = 666

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter Closed Open E

U+029A

Lowercase letter (Ll)

UTF-8 encoding: CA 9A (2 bytes).

Lookup U+029A on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00029A

RGB(0, 2, 154)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.154.

Address: 0.0.2.154
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.154

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