Number

8,191

8,191 is a prime, odd.

8,191 (eight thousand one hundred ninety-one) is an odd 4-digit number. It is a prime number — divisible only by 1 and itself. It is a Mersenne prime. Written other ways, in hexadecimal, 0x1FFF.

Arithmetic Number Binary Palindrome Chen Prime Cube-Free Deficient Number Flippable Mersenne Prime Odious Number Pernicious Number Prime Recamán's Sequence Squarefree

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

8,179 8,180 8,181 8,182 8,183 8,184 8,185 8,186 8,187 8,188 8,189 8,190 8,191 8,192 8,193 8,194 8,195 8,196 8,197 8,198 8,199 8,200 8,201 8,202 8,203

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Properties

Parity: Odd
Digit count: 4
Digit sum: 19
Digit product: 72
Digital root: 1
Palindrome: No
Bit width: 13 bits
Reversed: 1,918
Flips to (rotate 180°): 1,618
Recamán's sequence: a(10,385) = 8,191
Square (n²): 67,092,481
Cube (n³): 549,554,511,871
Divisor count: 2
σ(n) — sum of divisors: 8,192
φ(n) — Euler's totient: 8,190

Primality

8,191 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 8191

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 8,191)

1 × 8191

First multiples

8,191 · 16,382 (double) · 24,573 · 32,764 · 40,955 · 49,146 · 57,337 · 65,528 · 73,719 · 81,910

Sums & aliquot sequence

As consecutive integers: 4,095 + 4,096

Continued fraction of √n

√8,191 = [90; (1, 1, 59, 1, 5, 19, 1, 17, 6, 1, 1, 1, 5, 2, 1, 1, 1, 1, 4, 1, 1, 3, 1, 6, …)]

Representations

In words: eight thousand one hundred ninety-one
Ordinal: 8191st
Binary: 1111111111111
Octal: 17777
Hexadecimal: 0x1FFF
Base64: H/8=
One's complement: 57,344 (16-bit)
Scientific notation: 8.191 × 10³
As a duration: 8,191 s = 2 hours, 16 minutes, 31 seconds

In other bases

ternary (3) 102020101

quaternary (4) 1333333

quinary (5) 230231

senary (6) 101531

septenary (7) 32611

nonary (9) 12211

undecimal (11) 6177

duodecimal (12) 48a7

tridecimal (13) 3961

tetradecimal (14) 2db1

pentadecimal (15) 2661

Palindromic in base 2

As an angle

8,191° = 22 × 360° + 271°

271° ≈ 4.73 rad

Compass bearing: W (west)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺
Greek (Milesian): ͵ηρϟαʹ
Mayan (base 20): 𝋡·𝋠·𝋩·𝋫
Chinese: 八千一百九十一
Chinese (financial): 捌仟壹佰玖拾壹

In other modern scripts

Eastern Arabic ٨١٩١ Devanagari ८१९१ Bengali ৮১৯১ Tamil ௮௧௯௧ Thai ๘๑๙๑ Tibetan ༨༡༩༡ Khmer ៨១៩១ Lao ໘໑໙໑ Burmese ၈၁၉၁

Digit at this position in famous constants

π — Pi (π): Digit 8,191 = 9
e — Euler's number (e): Digit 8,191 = 5
φ — Golden ratio (φ): Digit 8,191 = 5
√2 — Pythagoras's (√2): Digit 8,191 = 0
ln 2 — Natural log of 2: Digit 8,191 = 5
γ — Euler-Mascheroni (γ): Digit 8,191 = 2

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 8,179 (gap of 12)
Next prime: 8,209 (gap of 18)

Hex color

#001FFF

RGB(0, 31, 255)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.31.255.

Address: 0.0.31.255
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.31.255

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

Musical pitch

Heard as a frequency, 8,191 Hz is closest to:

Concert pitch (A4 = 440 Hz): C9 (8372 Hz, -38¢)
Scientific pitch (C4 = 256 Hz): C9 (8192 Hz, exact)
Baroque pitch (A4 = 415 Hz): C♯9 (8365.9 Hz, -37¢)

Position in π

The digit sequence 8191 first appears in π at position 2,901 of the decimal expansion (the 2,901ordinal-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 8191 on Pi Search ↗