Number

521

521 is a prime, odd, a calendar year.

521 (five hundred twenty-one) is an odd 3-digit number. It is a prime number — divisible only by 1 and itself. It is a Lucas number. Written other ways, in Roman numerals it is DXXI and in binary, 1000001001.

Arithmetic Number Chen Prime Cube-Free Deficient Number Descending Digits Lucas Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Squarefree Twin Prime Year

Interestingness

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10 notable facts · grade A

509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533

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Historical context — 521 AD

Calendar year

Year 521 (DXXI) was a common year starting on Friday of the Julian calendar.

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

Historical context — 521 BC

Calendar year

The year 521 BC was a year of the pre-Julian Roman 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, 521
Ended on: Wednesday
December 31, 521
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 520s
520–529
Century: 6th century
501–600
Millennium: 1st millennium
1–1000
Years ago: 1,505
1505 years before 2026.

In other calendars

Hebrew: 4281 / 4282 AM
Rosh Hashanah falls in September/October.
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: 1064 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 513 / 514 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 443 / 442 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese slang

"I love you too" — partner of 520.

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

Properties

Parity: Odd
Digit count: 3
Digit sum: 8
Digit product: 10
Digital root: 8
Palindrome: No
Bit width: 10 bits
Reversed: 125
Recamán's sequence: a(1,217) = 521
Square (n²): 271,441
Cube (n³): 141,420,761
Divisor count: 2
σ(n) — sum of divisors: 522
φ(n) — Euler's totient: 520

Primality

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

Divisors & multiples

All divisors (2)

1 · 521

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 521)

1 × 521

First multiples

521 · 1,042 (double) · 1,563 · 2,084 · 2,605 · 3,126 · 3,647 · 4,168 · 4,689 · 5,210

Sums & aliquot sequence

As a sum of two squares: 11² + 20²

As consecutive integers: 260 + 261

Continued fraction of √n

√521 = [22; (1, 4, 1, 2, 1, 2, 8, 1, 3, 3, 1, 8, 2, 1, 2, 1, 4, 1, 44)]

Period length 19 — the block in parentheses repeats forever.

Representations

In words: five hundred twenty-one
Ordinal: 521st
Roman numeral: DXXI
Binary: 1000001001
Octal: 1011
Hexadecimal: 0x209
Base64: Agk=
One's complement: 65,014 (16-bit)
Scientific notation: 5.21 × 10²
As a duration: 521 s = 8 minutes, 41 seconds

In other bases

ternary (3) 201022

quaternary (4) 20021

quinary (5) 4041

senary (6) 2225

septenary (7) 1343

nonary (9) 638

undecimal (11) 434

duodecimal (12) 375

tridecimal (13) 311

tetradecimal (14) 293

pentadecimal (15) 24b

Palindromic in base 11

As an angle

521° = 1 × 360° + 161°

161° ≈ 2.81 rad

Compass bearing: SSE (south-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺
Greek (Milesian): φκαʹ
Mayan (base 20): 𝋡·𝋦·𝋡
Chinese: 五百二十一
Chinese (financial): 伍佰貳拾壹

In other modern scripts

Eastern Arabic ٥٢١ Devanagari ५२१ Bengali ৫২১ Tamil ௫௨௧ Thai ๕๒๑ Tibetan ༥༢༡ Khmer ៥២១ Lao ໕໒໑ Burmese ၅၂၁

Digit at this position in famous constants

π — Pi (π): Digit 521 = 0
e — Euler's number (e): Digit 521 = 5
φ — Golden ratio (φ): Digit 521 = 8
√2 — Pythagoras's (√2): Digit 521 = 7
ln 2 — Natural log of 2: Digit 521 = 2
γ — Euler-Mascheroni (γ): Digit 521 = 1

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 509 (gap of 12)
Next prime: 523 (gap of 2)

Pair status: twin with 523.

Unicode codepoint

Latin Small Letter I With Double Grave

U+0209

Lowercase letter (Ll)

UTF-8 encoding: C8 89 (2 bytes).

Lookup U+0209 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000209

RGB(0, 2, 9)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.9.

Address: 0.0.2.9
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.9

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

Musical pitch

Heard as a frequency, 521 Hz is closest to:

Concert pitch (A4 = 440 Hz): C5 (523.3 Hz, -7¢)
Scientific pitch (C4 = 256 Hz): C5 (512 Hz, +30¢)
Baroque pitch (A4 = 415 Hz): C♯5 (522.9 Hz, -6¢)