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Number

13,121

13,121 is a prime, odd.

13,121 (thirteen thousand one 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, 0x3341.

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

Interestingness

Properties

Parity
Odd
Digit count
5
Digit sum
8
Digit product
6
Digital root
8
Palindrome
No
Bit width
14 bits
Reversed
12,131
Recamán's sequence
a(48,033) = 13,121
Square (n²)
172,160,641
Cube (n³)
2,258,919,770,561
Divisor count
2
σ(n) — sum of divisors
13,122
φ(n) — Euler's totient
13,120

Primality

13,121 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 13121
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 13,121)
1 × 13121
First multiples
13,121 · 26,242 (double) · 39,363 · 52,484 · 65,605 · 78,726 · 91,847 · 104,968 · 118,089 · 131,210

Sums & aliquot sequence

As a sum of two squares: 64² + 95²
As consecutive integers: 6,560 + 6,561

Continued fraction of √n

√13,121 = [114; (1, 1, 4, 1, 4, 1, 3, 2, 1, 27, 1, 16, 1, 1, 1, 11, 2, 1, 1, 13, 1, 2, 1, 1, …)]

Representations

In words
thirteen thousand one hundred twenty-one
Ordinal
13121st
Binary
11001101000001
Octal
31501
Hexadecimal
0x3341
Base64
M0E=
One's complement
52,414 (16-bit)
Scientific notation
1.3121 × 10⁴
As a duration
13,121 s = 3 hours, 38 minutes, 41 seconds
In other bases
ternary (3) 122222222
quaternary (4) 3031001
quinary (5) 404441
senary (6) 140425
septenary (7) 53153
nonary (9) 18888
undecimal (11) 9949
duodecimal (12) 7715
tridecimal (13) 5c84
tetradecimal (14) 4ad3
pentadecimal (15) 3d4b

As an angle

13,121° = 36 × 360° + 161°
161° ≈ 2.81 rad
Compass bearing: SSE (south-southeast)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic
𓂍𓆼𓆼𓆼𓍢𓎆𓎆𓏺
Greek (Milesian)
͵ιγρκαʹ
Mayan (base 20)
𝋡·𝋬·𝋰·𝋡
Chinese
一萬三千一百二十一
Chinese (financial)
壹萬參仟壹佰貳拾壹
In other modern scripts
Eastern Arabic ١٣١٢١ Devanagari १३१२१ Bengali ১৩১২১ Tamil ௧௩௧௨௧ Thai ๑๓๑๒๑ Tibetan ༡༣༡༢༡ Khmer ១៣១២១ Lao ໑໓໑໒໑ Burmese ၁၃၁၂၁

Digit at this position in famous constants

π — Pi (π)
Digit 13,121 = 4
e — Euler's number (e)
Digit 13,121 = 3
φ — Golden ratio (φ)
Digit 13,121 = 9
√2 — Pythagoras's (√2)
Digit 13,121 = 4
ln 2 — Natural log of 2
Digit 13,121 = 3
γ — Euler-Mascheroni (γ)
Digit 13,121 = 7

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 13,109 (gap of 12)
  • Next prime: 13,127 (gap of 6)

Pair status: sexy with 13127.

Unicode codepoint
Square Hooru
U+3341
Other symbol (So)

UTF-8 encoding: E3 8D 81 (3 bytes).

Hex color
#003341
RGB(0, 51, 65)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.51.65.

Address
0.0.51.65
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.51.65

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

Musical pitch

Heard as a frequency, 13,121 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, -22¢)
  • Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, +16¢)
  • Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, -21¢)
Position in π

The digit sequence 13121 first appears in π at position 89,023 of the decimal expansion (the 89,023ordinal-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.