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Number

13,721

13,721 is a prime, odd.

13,721 (thirteen thousand seven hundred twenty-one) is an odd 5-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x3599.

Arithmetic Number Chen Prime Cube-Free Deficient Number Evil Number Prime Pythagorean Prime Recamán's Sequence Squarefree Twin Prime

Interestingness

Properties

Parity
Odd
Digit count
5
Digit sum
14
Digit product
42
Digital root
5
Palindrome
No
Bit width
14 bits
Reversed
12,731
Recamán's sequence
a(4,146) = 13,721
Square (n²)
188,265,841
Cube (n³)
2,583,195,604,361
Divisor count
2
σ(n) — sum of divisors
13,722
φ(n) — Euler's totient
13,720

Primality

13,721 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 13721
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 13,721)
1 × 13721
First multiples
13,721 · 27,442 (double) · 41,163 · 54,884 · 68,605 · 82,326 · 96,047 · 109,768 · 123,489 · 137,210

Sums & aliquot sequence

As a sum of two squares: 61² + 100²
As consecutive integers: 6,860 + 6,861

Continued fraction of √n

√13,721 = [117; (7, 3, 6, 2, 1, 1, 1, 46, 4, 2, 1, 1, 32, 1, 7, 9, 4, 13, 1, 1, 6, 5, 1, 2, …)]

Representations

In words
thirteen thousand seven hundred twenty-one
Ordinal
13721st
Binary
11010110011001
Octal
32631
Hexadecimal
0x3599
Base64
NZk=
One's complement
51,814 (16-bit)
Scientific notation
1.3721 × 10⁴
As a duration
13,721 s = 3 hours, 48 minutes, 41 seconds
In other bases
ternary (3) 200211012
quaternary (4) 3112121
quinary (5) 414341
senary (6) 143305
septenary (7) 55001
nonary (9) 20735
undecimal (11) a344
duodecimal (12) 7b35
tridecimal (13) 6326
tetradecimal (14) 5001
pentadecimal (15) 40eb

As an angle

13,721° = 38 × 360° + 41°
41° ≈ 0.716 rad
Compass bearing: NE (northeast)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic
𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺
Greek (Milesian)
͵ιγψκαʹ
Mayan (base 20)
𝋡·𝋮·𝋦·𝋡
Chinese
一萬三千七百二十一
Chinese (financial)
壹萬參仟柒佰貳拾壹
In other modern scripts
Eastern Arabic ١٣٧٢١ Devanagari १३७२१ Bengali ১৩৭২১ Tamil ௧௩௭௨௧ Thai ๑๓๗๒๑ Tibetan ༡༣༧༢༡ Khmer ១៣៧២១ Lao ໑໓໗໒໑ Burmese ၁၃၇၂၁

Digit at this position in famous constants

π — Pi (π)
Digit 13,721 = 7
e — Euler's number (e)
Digit 13,721 = 2
φ — Golden ratio (φ)
Digit 13,721 = 7
√2 — Pythagoras's (√2)
Digit 13,721 = 4
ln 2 — Natural log of 2
Digit 13,721 = 4
γ — Euler-Mascheroni (γ)
Digit 13,721 = 7

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 13,711 (gap of 10)
  • Next prime: 13,723 (gap of 2)

Pair status: twin with 13723.

Unicode codepoint
CJK Unified Ideograph-3599
U+3599
Other letter (Lo)

UTF-8 encoding: E3 96 99 (3 bytes).

Hex color
#003599
RGB(0, 53, 153)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.53.153.

Address
0.0.53.153
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.53.153

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

Musical pitch

Heard as a frequency, 13,721 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -45¢ — about midway to G♯9)
  • Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, -7¢)
  • Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -43¢)
Position in π

The digit sequence 13721 first appears in π at position 134,643 of the decimal expansion (the 134,643ordinal-suffix:rd 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.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.