Number

821

821 is a prime, odd, a calendar year.

Arithmetic Number Chen Prime Deficient Number Descending Digits Evil Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Squarefree Twin Prime Year

Historical context — 821 AD

Calendar year

Year 821 (DCCCXXI) was a common year starting on Tuesday of the Julian calendar.

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Historical context — 821 BC

Decade

This article concerns the period 829 BC – 820 BC.

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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: Friday
January 1, 821
Ended on: Friday
December 31, 821
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 820s
820–829
Century: 9th century
801–900
Millennium: 1st millennium
1–1000
Years ago: 1,205
1205 years before 2026.

In other calendars

Hebrew: 4581 / 4582 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 205 / 206 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Ox
Sexagenary cycle position 38 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1364 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 199 / 200 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 813 / 814 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 743 / 742 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 3
Digit sum: 11
Digit product: 16
Digital root: 2
Palindrome: No
Bit width: 10 bits
Reversed: 128
Recamán's sequence: a(2,106) = 821
Square (n²): 674,041
Cube (n³): 553,387,661
Divisor count: 2
σ(n) — sum of divisors: 822
φ(n) — Euler's totient: 820

Primality

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

Divisors & multiples

All divisors (2)

1 · 821

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 821)

1 × 821

First multiples

821 · 1,642 (double) · 2,463 · 3,284 · 4,105 · 4,926 · 5,747 · 6,568 · 7,389 · 8,210

Sums & aliquot sequence

As a sum of two squares: 14² + 25²

As consecutive integers: 410 + 411

Representations

In words: eight hundred twenty-one
Ordinal: 821st
Roman numeral: DCCCXXI
Binary: 1100110101
Octal: 1465
Hexadecimal: 0x335
Base64: AzU=
One's complement: 64,714 (16-bit)

In other bases

ternary (3) 1010102

quaternary (4) 30311

quinary (5) 11241

senary (6) 3445

septenary (7) 2252

nonary (9) 1112

undecimal (11) 687

duodecimal (12) 585

tridecimal (13) 4b2

tetradecimal (14) 429

pentadecimal (15) 39b

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺
Greek (Milesian): ωκαʹ
Mayan (base 20): 𝋢·𝋡·𝋡
Chinese: 八百二十一
Chinese (financial): 捌佰貳拾壹

In other modern scripts

Eastern Arabic ٨٢١ Devanagari ८२१ Bengali ৮২১ Tamil ௮௨௧ Thai ๘๒๑ Tibetan ༨༢༡ Khmer ៨២១ Lao ໘໒໑ Burmese ၈၂၁

Digit at this position in famous constants

π — Pi (π): Digit 821 = 6
e — Euler's number (e): Digit 821 = 9
φ — Golden ratio (φ): Digit 821 = 3
√2 — Pythagoras's (√2): Digit 821 = 9
ln 2 — Natural log of 2: Digit 821 = 9
γ — Euler-Mascheroni (γ): Digit 821 = 2

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 811 (gap of 10)
Next prime: 823 (gap of 2)

Pair status: twin with 823.

Unicode codepoint

Combining Short Stroke Overlay

U+0335

Non-spacing mark (Mn)

UTF-8 encoding: CC B5 (2 bytes).

Lookup U+0335 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000335

RGB(0, 3, 53)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.53.

Address: 0.0.3.53
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.53

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