Number

1,311

1,311 is a composite number, odd, a calendar year.

1,311 (one thousand three hundred eleven) is an odd 4-digit number. It is a composite number with 8 divisors, and factors as 3 × 19 × 23. Written other ways, in Roman numerals it is MCCCXI and in binary, 10100011111.

Arithmetic Number Cube-Free Deficient Number Odious Number Pernicious Number Recamán's Sequence Self Number Sphenic Number Squarefree Year Zuckerman Number

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

1,299 1,300 1,301 1,302 1,303 1,304 1,305 1,306 1,307 1,308 1,309 1,310 1,311 1,312 1,313 1,314 1,315 1,316 1,317 1,318 1,319 1,320 1,321 1,322 1,323

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Historical context — 1311 AD

Calendar year

Year 1311 (MCCCXI) 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 →

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: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 1311
Ended on: Thursday
December 31, 1311
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 1310s
1310–1319
Century: 14th century
1301–1400
Millennium: 2nd millennium
1001–2000
Years ago: 715
715 years before 2026.

In other calendars

Hebrew: 5071 / 5072 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 710 / 711 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Pig
Sexagenary cycle position 48 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1854 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 689 / 690 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1303 / 1304 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1233 / 1232 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 4
Digit sum: 6
Digit product: 3
Digital root: 6
Palindrome: No
Bit width: 11 bits
Reversed: 1,131
Recamán's sequence: a(414) = 1,311
Square (n²): 1,718,721
Cube (n³): 2,253,243,231
Divisor count: 8
σ(n) — sum of divisors: 1,920
φ(n) — Euler's totient: 792
Sum of prime factors: 45

Primality

Prime factorization: 3 × 19 × 23

Nearest primes: 1,307 (−4) · 1,319 (+8)

Divisors & multiples

All divisors (8)

1 · 3 · 19 · 23 · 57 · 69 · 437 · 1311

Aliquot sum (sum of proper divisors): 609

Factor pairs (a × b = 1,311)

1 × 1311

3 × 437

19 × 69

23 × 57

First multiples

1,311 · 2,622 (double) · 3,933 · 5,244 · 6,555 · 7,866 · 9,177 · 10,488 · 11,799 · 13,110

Sums & aliquot sequence

As consecutive integers: 655 + 656 436 + 437 + 438 216 + 217 + 218 + 219 + 220 + 221 60 + 61 + … + 78

Aliquot sequence: 1,311 → 609 → 351 → 209 → 31 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,311 = [36; (4, 1, 4, 2, 1, 2, 4, 1, 4, 72)]

Period length 10 — the block in parentheses repeats forever.

Representations

In words: one thousand three hundred eleven
Ordinal: 1311th
Roman numeral: MCCCXI
Binary: 10100011111
Octal: 2437
Hexadecimal: 0x51F
Base64: BR8=
One's complement: 64,224 (16-bit)
Scientific notation: 1.311 × 10³
As a duration: 1,311 s = 21 minutes, 51 seconds

In other bases

ternary (3) 1210120

quaternary (4) 110133

quinary (5) 20221

senary (6) 10023

septenary (7) 3552

nonary (9) 1716

undecimal (11) a92

duodecimal (12) 913

tridecimal (13) 79b

tetradecimal (14) 699

pentadecimal (15) 5c6

As an angle

1,311° = 3 × 360° + 231°

231° ≈ 4.032 rad

Compass bearing: SW (southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹 𒌋𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓎆𓏺
Greek (Milesian): ͵ατιαʹ
Mayan (base 20): 𝋣·𝋥·𝋫
Chinese: 一千三百一十一
Chinese (financial): 壹仟參佰壹拾壹

In other modern scripts

Eastern Arabic ١٣١١ Devanagari १३११ Bengali ১৩১১ Tamil ௧௩௧௧ Thai ๑๓๑๑ Tibetan ༡༣༡༡ Khmer ១៣១១ Lao ໑໓໑໑ Burmese ၁၃၁၁

Digit at this position in famous constants

π — Pi (π): Digit 1,311 = 2
e — Euler's number (e): Digit 1,311 = 9
φ — Golden ratio (φ): Digit 1,311 = 5
√2 — Pythagoras's (√2): Digit 1,311 = 5
ln 2 — Natural log of 2: Digit 1,311 = 0
γ — Euler-Mascheroni (γ): Digit 1,311 = 2

Also seen as

Unicode codepoint

Cyrillic Small Letter Aleut Ka

U+051F

Lowercase letter (Ll)

UTF-8 encoding: D4 9F (2 bytes).

Lookup U+051F on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00051F

RGB(0, 5, 31)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.5.31.

Address: 0.0.5.31
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.5.31

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

Musical pitch

Heard as a frequency, 1,311 Hz is closest to:

Concert pitch (A4 = 440 Hz): E6 (1318.5 Hz, -10¢)
Scientific pitch (C4 = 256 Hz): E6 (1290.2 Hz, +28¢)
Baroque pitch (A4 = 415 Hz): F6 (1317.5 Hz, -9¢)

Position in π

The digit sequence 1311 first appears in π at position 4,506 of the decimal expansion (the 4,506ordinal-suffix:th digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 1311 on Pi Search ↗