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Number

2,113

2,113 is a prime, odd.

2,113 (two thousand one hundred thirteen) is an odd 4-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in Roman numerals it is MMCXIII and in binary, 100001000001.

Arithmetic Number Centered Square Cube-Free Deficient Number Left-Truncatable Prime Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Squarefree Twin Prime

Interestingness

Properties

Parity
Odd
Digit count
4
Digit sum
7
Digit product
6
Digital root
7
Palindrome
No
Bit width
12 bits
Reversed
3,112
Recamán's sequence
a(3,525) = 2,113
Square (n²)
4,464,769
Cube (n³)
9,434,056,897
Divisor count
2
σ(n) — sum of divisors
2,114
φ(n) — Euler's totient
2,112

Primality

2,113 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 2113
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 2,113)
1 × 2113
First multiples
2,113 · 4,226 (double) · 6,339 · 8,452 · 10,565 · 12,678 · 14,791 · 16,904 · 19,017 · 21,130

Sums & aliquot sequence

As a sum of two squares: 32² + 33²
As consecutive integers: 1,056 + 1,057

Continued fraction of √n

√2,113 = [45; (1, 29, 1, 1, 1, 9, 1, 1, 4, 3, 5, 2, 3, 2, 1, 2, 11, 8, 3, 1, 2, 2, 2, 2, …)]

Period length 45 — the block in parentheses repeats forever.

Representations

In words
two thousand one hundred thirteen
Ordinal
2113th
Roman numeral
MMCXIII
Binary
100001000001
Octal
4101
Hexadecimal
0x841
Base64
CEE=
One's complement
63,422 (16-bit)
Scientific notation
2.113 × 10³
As a duration
2,113 s = 35 minutes, 13 seconds
In other bases
ternary (3) 2220021
quaternary (4) 201001
quinary (5) 31423
senary (6) 13441
septenary (7) 6106
nonary (9) 2807
undecimal (11) 1651
duodecimal (12) 1281
tridecimal (13) c67
tetradecimal (14) aad
pentadecimal (15) 95d

As an angle

2,113° = 5 × 360° + 313°
313° ≈ 5.463 rad
Compass bearing: NW (northwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹
Egyptian hieroglyphic
𓆼𓆼𓍢𓎆𓏺𓏺𓏺
Greek (Milesian)
͵βριγʹ
Mayan (base 20)
𝋥·𝋥·𝋭
Chinese
二千一百一十三
Chinese (financial)
貳仟壹佰壹拾參
In other modern scripts
Eastern Arabic ٢١١٣ Devanagari २११३ Bengali ২১১৩ Tamil ௨௧௧௩ Thai ๒๑๑๓ Tibetan ༢༡༡༣ Khmer ២១១៣ Lao ໒໑໑໓ Burmese ၂၁၁၃

Digit at this position in famous constants

π — Pi (π)
Digit 2,113 = 9
e — Euler's number (e)
Digit 2,113 = 6
φ — Golden ratio (φ)
Digit 2,113 = 2
√2 — Pythagoras's (√2)
Digit 2,113 = 4
ln 2 — Natural log of 2
Digit 2,113 = 1
γ — Euler-Mascheroni (γ)
Digit 2,113 = 6

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 2,111 (gap of 2)
  • Next prime: 2,129 (gap of 16)

Pair status: twin with 2111.

Unicode codepoint
Mandaic Letter Ab
U+0841
Other letter (Lo)

UTF-8 encoding: E0 A1 81 (3 bytes).

Hex color
#000841
RGB(0, 8, 65)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.8.65.

Address
0.0.8.65
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.8.65

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

Musical pitch

Heard as a frequency, 2,113 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): C7 (2093 Hz, +16¢)
  • Scientific pitch (C4 = 256 Hz): C♯7 (2169.8 Hz, -46¢ — about midway to C7)
  • Baroque pitch (A4 = 415 Hz): C♯7 (2091.5 Hz, +18¢)
Position in π

The digit sequence 2113 first appears in π at position 757 of the decimal expansion (the 757ordinal-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.

Related reading

  • Prime numbers — The building blocks of arithmetic: what primes are, why they matter, and how we find them.
  • Egyptian hieroglyphic numerals — Seven hieroglyphs for every power of ten, from a single stroke to a million.