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Number

2,013

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

Arithmetic Number Deficient Number Odious Number Recamán's Sequence Sphenic Number Squarefree Year

Notable events — 2013 AD

  1. Feb 15 A meteor explodes over Chelyabinsk, Russia, injuring nearly 1,500.
  2. Feb 28 Pope Benedict XVI resigns, the first papal resignation in nearly 600 years.
  3. Mar 13 Cardinal Jorge Mario Bergoglio is elected Pope Francis, the first Jesuit and first pope from the Americas.
  4. Apr 15 Two bombs explode at the Boston Marathon, killing three and injuring hundreds.
  5. 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

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)
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

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
ߝ
Nko Letter Fa
U+07DD
Other letter (Lo)

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

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.

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.