Number

13,001

13,001 is a prime, odd.

13,001 (thirteen thousand one) is an odd 5-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x32C9.

Arithmetic Number Chen Prime Cube-Free Deficient Number Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Sophie Germain Prime Squarefree Twin Prime

Interestingness

★ ★ ★ ★ ★

10 notable facts · grade A

12,989 12,990 12,991 12,992 12,993 12,994 12,995 12,996 12,997 12,998 12,999 13,000 13,001 13,002 13,003 13,004 13,005 13,006 13,007 13,008 13,009 13,010 13,011 13,012 13,013

less more

Properties

Parity: Odd
Digit count: 5
Digit sum: 5
Digit product: 0
Digital root: 5
Palindrome: No
Bit width: 14 bits
Reversed: 10,031
Recamán's sequence: a(48,273) = 13,001
Square (n²): 169,026,001
Cube (n³): 2,197,507,039,001
Divisor count: 2
σ(n) — sum of divisors: 13,002
φ(n) — Euler's totient: 13,000

Primality

13,001 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 13001

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 13,001)

1 × 13001

First multiples

13,001 · 26,002 (double) · 39,003 · 52,004 · 65,005 · 78,006 · 91,007 · 104,008 · 117,009 · 130,010

Sums & aliquot sequence

As a sum of two squares: 76² + 85²

As consecutive integers: 6,500 + 6,501

Continued fraction of √n

√13,001 = [114; (45, 1, 1, 1, 1, 8, 1, 1, 11, 2, 9, 2, 3, 2, 1, 1, 3, 2, 13, 1, 4, 2, 1, 2, …)]

Representations

In words: thirteen thousand one
Ordinal: 13001st
Binary: 11001011001001
Octal: 31311
Hexadecimal: 0x32C9
Base64: Msk=
One's complement: 52,534 (16-bit)
Scientific notation: 1.3001 × 10⁴
As a duration: 13,001 s = 3 hours, 36 minutes, 41 seconds

In other bases

ternary (3) 122211112

quaternary (4) 3023021

quinary (5) 404001

senary (6) 140105

septenary (7) 52622

nonary (9) 18745

undecimal (11) 984a

duodecimal (12) 7635

tridecimal (13) 5bc1

tetradecimal (14) 4a49

pentadecimal (15) 3cbb

As an angle

13,001° = 36 × 360° + 41°

41° ≈ 0.716 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓏺
Greek (Milesian): ͵ιγαʹ
Mayan (base 20): 𝋡·𝋬·𝋪·𝋡
Chinese: 一萬三千零一
Chinese (financial): 壹萬參仟零壹

In other modern scripts

Eastern Arabic ١٣٠٠١ Devanagari १३००१ Bengali ১৩০০১ Tamil ௧௩௦௦௧ Thai ๑๓๐๐๑ Tibetan ༡༣༠༠༡ Khmer ១៣០០១ Lao ໑໓໐໐໑ Burmese ၁၃၀၀၁

Digit at this position in famous constants

π — Pi (π): Digit 13,001 = 9
e — Euler's number (e): Digit 13,001 = 4
φ — Golden ratio (φ): Digit 13,001 = 6
√2 — Pythagoras's (√2): Digit 13,001 = 8
ln 2 — Natural log of 2: Digit 13,001 = 2
γ — Euler-Mascheroni (γ): Digit 13,001 = 5

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 12,983 (gap of 18)
Next prime: 13,003 (gap of 2)

Pair status: twin with 13003.

Unicode codepoint

㋉

Ideographic Telegraph Symbol For October

U+32C9

Other symbol (So)

UTF-8 encoding: E3 8B 89 (3 bytes).

Lookup U+32C9 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0032C9

RGB(0, 50, 201)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.50.201.

Address: 0.0.50.201
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.50.201

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

Musical pitch

Heard as a frequency, 13,001 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, -38¢)
Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, exact)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, -37¢)

Position in π

The digit sequence 13001 first appears in π at position 971 of the decimal expansion (the 971ordinal-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 13001 on Pi Search ↗