Number

13,709

13,709 is a prime, odd.

13,709 (thirteen thousand seven hundred nine) is an odd 5-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x358D.

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

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

13,697 13,698 13,699 13,700 13,701 13,702 13,703 13,704 13,705 13,706 13,707 13,708 13,709 13,710 13,711 13,712 13,713 13,714 13,715 13,716 13,717 13,718 13,719 13,720 13,721

less more

Properties

Parity: Odd
Digit count: 5
Digit sum: 20
Digit product: 0
Digital root: 2
Palindrome: No
Bit width: 14 bits
Reversed: 90,731
Recamán's sequence: a(91,226) = 13,709
Square (n²): 187,936,681
Cube (n³): 2,576,423,959,829
Divisor count: 2
σ(n) — sum of divisors: 13,710
φ(n) — Euler's totient: 13,708

Primality

13,709 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 13709

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 13,709)

1 × 13709

First multiples

13,709 · 27,418 (double) · 41,127 · 54,836 · 68,545 · 82,254 · 95,963 · 109,672 · 123,381 · 137,090

Sums & aliquot sequence

As a sum of two squares: 22² + 115²

As consecutive integers: 6,854 + 6,855

Continued fraction of √n

√13,709 = [117; (11, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 21, 10, 7, 2, 4, 1, 46, 58, 1, …)]

Representations

In words: thirteen thousand seven hundred nine
Ordinal: 13709th
Binary: 11010110001101
Octal: 32615
Hexadecimal: 0x358D
Base64: NY0=
One's complement: 51,826 (16-bit)
Scientific notation: 1.3709 × 10⁴
As a duration: 13,709 s = 3 hours, 48 minutes, 29 seconds

In other bases

ternary (3) 200210202

quaternary (4) 3112031

quinary (5) 414314

senary (6) 143245

septenary (7) 54653

nonary (9) 20722

undecimal (11) a333

duodecimal (12) 7b25

tridecimal (13) 6317

tetradecimal (14) 4dd3

pentadecimal (15) 40de

As an angle

13,709° = 38 × 360° + 29°

29° ≈ 0.506 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵ιγψθʹ
Mayan (base 20): 𝋡·𝋮·𝋥·𝋩
Chinese: 一萬三千七百零九
Chinese (financial): 壹萬參仟柒佰零玖

In other modern scripts

Eastern Arabic ١٣٧٠٩ Devanagari १३७०९ Bengali ১৩৭০৯ Tamil ௧௩௭௦௯ Thai ๑๓๗๐๙ Tibetan ༡༣༧༠༩ Khmer ១៣៧០៩ Lao ໑໓໗໐໙ Burmese ၁၃၇၀၉

Digit at this position in famous constants

π — Pi (π): Digit 13,709 = 3
e — Euler's number (e): Digit 13,709 = 1
φ — Golden ratio (φ): Digit 13,709 = 9
√2 — Pythagoras's (√2): Digit 13,709 = 9
ln 2 — Natural log of 2: Digit 13,709 = 2
γ — Euler-Mascheroni (γ): Digit 13,709 = 1

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 13,697 (gap of 12)
Next prime: 13,711 (gap of 2)

Pair status: twin with 13711.

Unicode codepoint

㖍

CJK Unified Ideograph-358D

U+358D

Other letter (Lo)

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

Lookup U+358D on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00358D

RGB(0, 53, 141)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.53.141.

Address: 0.0.53.141
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.53.141

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

Musical pitch

Heard as a frequency, 13,709 Hz is closest to:

Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -46¢ — about midway to G♯9)
Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, -9¢)
Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -45¢ — about midway to A9)

Position in π

The digit sequence 13709 first appears in π at position 16,051 of the decimal expansion (the 16,051ordinal-suffix:st 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 13709 on Pi Search ↗