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Number

311

311 is a prime, odd, a calendar year.

311 (three hundred eleven) is an odd 3-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in Roman numerals it is CCCXI and in binary, 100110111.

Arithmetic Number Chen Prime Circular Prime Cousin Prime Cube-Free Deficient Number Emirp Evil Number Prime Recamán's Sequence Right-Truncatable Prime Sexy Prime Squarefree Twin Prime Year

Interestingness

12 notable facts · grade A
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Historical context — 311 AD

Calendar year

Year 311 (CCCXI) was a common year starting on Monday of the Julian calendar.

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

Historical context — 311 BC

Calendar year

Year 311 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
Sunday
January 1, 311
Ended on
Sunday
December 31, 311
Friday the 13ths
2
2 Friday the 13ths this year.
Decade
310s
310–319
Century
4th century
301–400
Millennium
1st millennium
1–1000
Years ago
1,715
1715 years before 2026.

In other calendars

Hebrew
4071 / 4072 AM
Rosh Hashanah falls in September/October.
Chinese
Year of the zodiac:Metal zodiac:Goat
Sexagenary cycle position 8 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
854 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian
303 / 304 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
233 / 232 Saka
Indian national calendar; year starts in March.

Properties

Parity
Odd
Digit count
3
Digit sum
5
Digit product
3
Digital root
5
Palindrome
No
Bit width
9 bits
Reversed
113
Recamán's sequence
a(626) = 311
Square (n²)
96,721
Cube (n³)
30,080,231
Divisor count
2
σ(n) — sum of divisors
312
φ(n) — Euler's totient
310

Primality

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

Divisors & multiples

All divisors (2)
1 · 311
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 311)
1 × 311
First multiples
311 · 622 (double) · 933 · 1,244 · 1,555 · 1,866 · 2,177 · 2,488 · 2,799 · 3,110

Sums & aliquot sequence

As consecutive integers: 155 + 156

Continued fraction of √n

√311 = [17; (1, 1, 1, 2, 1, 6, 3, 17, 3, 6, 1, 2, 1, 1, 1, 34)]

Period length 16 — the block in parentheses repeats forever.

Representations

In words
three hundred eleven
Ordinal
311th
Roman numeral
CCCXI
Binary
100110111
Octal
467
Hexadecimal
0x137
Base64
ATc=
One's complement
65,224 (16-bit)
Scientific notation
3.11 × 10²
As a duration
311 s = 5 minutes, 11 seconds
In other bases
ternary (3) 102112
quaternary (4) 10313
quinary (5) 2221
senary (6) 1235
septenary (7) 623
nonary (9) 375
undecimal (11) 263
duodecimal (12) 21b
tridecimal (13) 1ac
tetradecimal (14) 183
pentadecimal (15) 15b

As an angle

311°
311° ≈ 5.428 rad
Compass bearing: NW (northwest)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹𒁹𒁹𒁹 𒌋𒁹
Egyptian hieroglyphic
𓍢𓍢𓍢𓎆𓏺
Greek (Milesian)
τιαʹ
Mayan (base 20)
𝋯·𝋫
Chinese
三百一十一
Chinese (financial)
參佰壹拾壹
In other modern scripts
Eastern Arabic ٣١١ Devanagari ३११ Bengali ৩১১ Tamil ௩௧௧ Thai ๓๑๑ Tibetan ༣༡༡ Khmer ៣១១ Lao ໓໑໑ Burmese ၃၁၁

Digit at this position in famous constants

π — Pi (π)
Digit 311 = 6
e — Euler's number (e)
Digit 311 = 8
φ — Golden ratio (φ)
Digit 311 = 0
√2 — Pythagoras's (√2)
Digit 311 = 5
ln 2 — Natural log of 2
Digit 311 = 8
γ — Euler-Mascheroni (γ)
Digit 311 = 2

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 307 (gap of 4)
  • Next prime: 313 (gap of 2)

Pair status: twin with 313, cousin with 307.

Unicode codepoint
ķ
Latin Small Letter K With Cedilla
U+0137
Lowercase letter (Ll)

UTF-8 encoding: C4 B7 (2 bytes).

Hex color
#000137
RGB(0, 1, 55)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.55.

Address
0.0.1.55
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.1.55

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

Musical pitch

Heard as a frequency, 311 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): D♯4 (311.1 Hz, -1¢)
  • Scientific pitch (C4 = 256 Hz): D♯4 (304.4 Hz, +37¢)
  • Baroque pitch (A4 = 415 Hz): E4 (310.9 Hz, +1¢)

Related reading

  • Prime numbers — The building blocks of arithmetic: what primes are, why they matter, and how we find them.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.