Number

2,013

2,013 is a composite number, odd, a calendar year.

2,013 (two thousand thirteen) is an odd 4-digit number. It is a composite number with 8 divisors, and factors as 3 × 11 × 61. Written other ways, in Roman numerals it is MMXIII and in binary, 11111011101.

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

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

2,001 2,002 2,003 2,004 2,005 2,006 2,007 2,008 2,009 2,010 2,011 2,012 2,013 2,014 2,015 2,016 2,017 2,018 2,019 2,020 2,021 2,022 2,023 2,024 2,025

less more

Notable events — 2013 AD

Feb 15 A meteor explodes over Chelyabinsk, Russia, injuring nearly 1,500.
Feb 28 Pope Benedict XVI resigns, the first papal resignation in nearly 600 years.
Mar 13 Cardinal Jorge Mario Bergoglio is elected Pope Francis, the first Jesuit and first pope from the Americas.
Apr 15 Two bombs explode at the Boston Marathon, killing three and injuring hundreds.
Jun 6 Edward Snowden leaks classified details of NSA mass-surveillance programs.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

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: Tuesday
January 1, 2013
Ended on: Tuesday
December 31, 2013
Friday the 13ths: 2
2 Friday the 13ths this year.
Easter Sunday: March 31
Sunday, March 31, 2013
Decade: 2010s
2010–2019
Century: 21st century
2001–2100
Millennium: 3rd millennium
2001–3000
Years ago: 13
13 years before 2026.

In other calendars

Hebrew: 5773 / 5774 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1434 / 1435 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Water zodiac:Snake
Sexagenary cycle position 30 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 2556 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1391 / 1392 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 2005 / 2006 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1935 / 1934 Saka
Indian national calendar; year starts in March.
Japanese: Heisei 25
Reign-era counting from the start of each emperor's reign.

Properties

Parity: Odd
Digit count: 4
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 11 bits
Reversed: 3,102
Recamán's sequence: a(3,725) = 2,013
Square (n²): 4,052,169
Cube (n³): 8,157,016,197
Divisor count: 8
σ(n) — sum of divisors: 2,976
φ(n) — Euler's totient: 1,200
Sum of prime factors: 75

Primality

Prime factorization: 3 × 11 × 61

Nearest primes: 2,011 (−2) · 2,017 (+4)

Divisors & multiples

All divisors (8)

1 · 3 · 11 · 33 · 61 · 183 · 671 · 2013

Aliquot sum (sum of proper divisors): 963

Factor pairs (a × b = 2,013)

1 × 2013

3 × 671

11 × 183

33 × 61

First multiples

2,013 · 4,026 (double) · 6,039 · 8,052 · 10,065 · 12,078 · 14,091 · 16,104 · 18,117 · 20,130

Sums & aliquot sequence

As consecutive integers: 1,006 + 1,007 670 + 671 + 672 333 + 334 + 335 + 336 + 337 + 338 178 + 179 + … + 188

Aliquot sequence: 2,013 → 963 → 441 → 300 → 568 → 512 → 511 → 81 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√2,013 = [44; (1, 6, 2, 21, 1, 28, 1, 21, 2, 6, 1, 88)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: two thousand thirteen
Ordinal: 2013th
Roman numeral: MMXIII
Binary: 11111011101
Octal: 3735
Hexadecimal: 0x7DD
Base64: B90=
One's complement: 63,522 (16-bit)
Scientific notation: 2.013 × 10³
As a duration: 2,013 s = 33 minutes, 33 seconds

In other bases

ternary (3) 2202120

quaternary (4) 133131

quinary (5) 31023

senary (6) 13153

septenary (7) 5604

nonary (9) 2676

undecimal (11) 1570

duodecimal (12) 11b9

tridecimal (13) bbb

tetradecimal (14) a3b

pentadecimal (15) 8e3

Palindromic in base 13

As an angle

2,013° = 5 × 360° + 213°

213° ≈ 3.718 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓆼𓎆𓏺𓏺𓏺
Greek (Milesian): ͵βιγʹ
Mayan (base 20): 𝋥·𝋠·𝋭
Chinese: 二千零一十三
Chinese (financial): 貳仟零壹拾參

In other modern scripts

Eastern Arabic ٢٠١٣ Devanagari २०१३ Bengali ২০১৩ Tamil ௨௦௧௩ Thai ๒๐๑๓ Tibetan ༢༠༡༣ Khmer ២០១៣ Lao ໒໐໑໓ Burmese ၂၀၁၃

Digit at this position in famous constants

π — Pi (π): Digit 2,013 = 5
e — Euler's number (e): Digit 2,013 = 4
φ — Golden ratio (φ): Digit 2,013 = 1
√2 — Pythagoras's (√2): Digit 2,013 = 5
ln 2 — Natural log of 2: Digit 2,013 = 8
γ — Euler-Mascheroni (γ): Digit 2,013 = 0

Also seen as

Unicode codepoint

Nko Letter Fa

U+07DD

Other letter (Lo)

UTF-8 encoding: DF 9D (2 bytes).

Lookup U+07DD on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0007DD

RGB(0, 7, 221)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.7.221.

Address: 0.0.7.221
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.7.221

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

Musical pitch

Heard as a frequency, 2,013 Hz is closest to:

Concert pitch (A4 = 440 Hz): B6 (1975.5 Hz, +33¢)
Scientific pitch (C4 = 256 Hz): C7 (2048 Hz, -30¢)
Baroque pitch (A4 = 415 Hz): C7 (1974.1 Hz, +34¢)

Position in π

The digit sequence 2013 first appears in π at position 6,276 of the decimal expansion (the 6,276ordinal-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 2013 on Pi Search ↗