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Number

13,691

13,691 is a prime, odd.

13,691 (thirteen thousand six hundred ninety-one) is an odd 5-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x357B.

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

Interestingness

Properties

Parity
Odd
Digit count
5
Digit sum
20
Digit product
162
Digital root
2
Palindrome
No
Bit width
14 bits
Reversed
19,631
Recamán's sequence
a(91,262) = 13,691
Square (n²)
187,443,481
Cube (n³)
2,566,288,698,371
Divisor count
2
σ(n) — sum of divisors
13,692
φ(n) — Euler's totient
13,690

Primality

13,691 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 13691
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 13,691)
1 × 13691
First multiples
13,691 · 27,382 (double) · 41,073 · 54,764 · 68,455 · 82,146 · 95,837 · 109,528 · 123,219 · 136,910

Sums & aliquot sequence

As consecutive integers: 6,845 + 6,846

Continued fraction of √n

√13,691 = [117; (117, 234)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words
thirteen thousand six hundred ninety-one
Ordinal
13691st
Binary
11010101111011
Octal
32573
Hexadecimal
0x357B
Base64
NXs=
One's complement
51,844 (16-bit)
Scientific notation
1.3691 × 10⁴
As a duration
13,691 s = 3 hours, 48 minutes, 11 seconds
In other bases
ternary (3) 200210002
quaternary (4) 3111323
quinary (5) 414231
senary (6) 143215
septenary (7) 54626
nonary (9) 20702
undecimal (11) a317
duodecimal (12) 7b0b
tridecimal (13) 6302
tetradecimal (14) 4dbd
pentadecimal (15) 40cb
Palindromic in base 9

As an angle

13,691° = 38 × 360° + 11°
11° ≈ 0.192 rad
Compass bearing: N (north)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹
Egyptian hieroglyphic
𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺
Greek (Milesian)
͵ιγχϟαʹ
Mayan (base 20)
𝋡·𝋮·𝋤·𝋫
Chinese
一萬三千六百九十一
Chinese (financial)
壹萬參仟陸佰玖拾壹
In other modern scripts
Eastern Arabic ١٣٦٩١ Devanagari १३६९१ Bengali ১৩৬৯১ Tamil ௧௩௬௯௧ Thai ๑๓๖๙๑ Tibetan ༡༣༦༩༡ Khmer ១៣៦៩១ Lao ໑໓໖໙໑ Burmese ၁၃၆၉၁

Digit at this position in famous constants

π — Pi (π)
Digit 13,691 = 7
e — Euler's number (e)
Digit 13,691 = 0
φ — Golden ratio (φ)
Digit 13,691 = 1
√2 — Pythagoras's (√2)
Digit 13,691 = 8
ln 2 — Natural log of 2
Digit 13,691 = 5
γ — Euler-Mascheroni (γ)
Digit 13,691 = 5

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 13,687 (gap of 4)
  • Next prime: 13,693 (gap of 2)

Pair status: twin with 13693, cousin with 13687.

Unicode codepoint
CJK Unified Ideograph-357B
U+357B
Other letter (Lo)

UTF-8 encoding: E3 95 BB (3 bytes).

Hex color
#00357B
RGB(0, 53, 123)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.53.123.

Address
0.0.53.123
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.53.123

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

Musical pitch

Heard as a frequency, 13,691 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -49¢ — about midway to G♯9)
  • Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, -11¢)
  • Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -47¢ — about midway to A9)
Position in π

The digit sequence 13691 first appears in π at position 16,235 of the decimal expansion (the 16,235ordinal-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.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.