Live analysis

4,000

4,000 is a composite number, even.

This number doesn't have a permanent NumberWiki page yet — what you see below is computed live. Pages get added to the permanent index when they're notable (years, primes, curated, etc.).

4,000 (four thousand) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2⁵ × 5³. Its proper divisors sum to 5,828, more than the number itself, making it an abundant number. Written other ways, in binary, 111110100000.

Abundant Number Achilles Number Decagonal Evil Number Gapful Number Harshad / Niven Powerful Number Practical Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

3,988 3,989 3,990 3,991 3,992 3,993 3,994 3,995 3,996 3,997 3,998 3,999 4,000 4,001 4,002 4,003 4,004 4,005 4,006 4,007 4,008 4,009 4,010 4,011 4,012

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 4
Digit product: 0
Digital root: 4
Palindrome: No
Bit width: 12 bits
Reversed: 4
Recamán's sequence: a(14,391) = 4,000
Square (n²): 16,000,000
Cube (n³): 64,000,000,000
Divisor count: 24
σ(n) — sum of divisors: 9,828
φ(n) — Euler's totient: 1,600
Sum of prime factors: 25

Primality

Prime factorization: 2 ⁵ × 5 ³

Nearest primes: 3,989 (−11) · 4,001 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 4 · 5 · 8 · 10 · 16 · 20 · 25 · 32 · 40 · 50 · 80 · 100 · 125 · 160 · 200 · 250 · 400 · 500 · 800 · 1000 · 2000 (half) · 4000

Aliquot sum (sum of proper divisors): 5,828

Factor pairs (a × b = 4,000)

1 × 4000

2 × 2000

4 × 1000

5 × 800

8 × 500

10 × 400

16 × 250

20 × 200

25 × 160

32 × 125

40 × 100

50 × 80

First multiples

4,000 · 8,000 (double) · 12,000 · 16,000 · 20,000 · 24,000 · 28,000 · 32,000 · 36,000 · 40,000

Sums & aliquot sequence

As a sum of two squares: 20² + 60² = 36² + 52²

As consecutive integers: 798 + 799 + 800 + 801 + 802 148 + 149 + … + 172 31 + 32 + … + 94

Aliquot sequence: 4,000 → 5,828 → 4,924 → 3,700 → 4,546 → 2,276 → 1,714 → 860 → 988 → 972 → 1,576 → 1,394 → 874 → 566 → 286 → 218 → 112 — unresolved within range

Continued fraction of √n

√4,000 = [63; (4, 13, 1, 4, 7, 1, 2, 2, 1, 2, 1, 4, 3, 31, 3, 4, 1, 2, 1, 2, 2, 1, 7, 4, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words: four thousand
Ordinal: 4000th
Binary: 111110100000
Octal: 7640
Hexadecimal: 0xFA0
Base64: D6A=
One's complement: 61,535 (16-bit)
Scientific notation: 4 × 10³
As a duration: 4,000 s = 1 hour, 6 minutes, 40 seconds

In other bases

ternary (3) 12111011

quaternary (4) 332200

quinary (5) 112000

senary (6) 30304

septenary (7) 14443

nonary (9) 5434

undecimal (11) 3007

duodecimal (12) 2394

tridecimal (13) 1a89

tetradecimal (14) 165a

pentadecimal (15) 12ba

As an angle

4,000° = 11 × 360° + 40°

40° ≈ 0.698 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓆼𓆼𓆼𓆼
Greek (Milesian): ͵δ
Mayan (base 20): 𝋪·𝋠·𝋠
Chinese: 四千
Chinese (financial): 肆仟

In other modern scripts

Eastern Arabic ٤٠٠٠ Devanagari ४००० Bengali ৪০০০ Tamil ௪௦௦௦ Thai ๔๐๐๐ Tibetan ༤༠༠༠ Khmer ៤០០០ Lao ໔໐໐໐ Burmese ၄၀၀၀

Digit at this position in famous constants

π — Pi (π): Digit 4,000 = 9
e — Euler's number (e): Digit 4,000 = 9
φ — Golden ratio (φ): Digit 4,000 = 6
√2 — Pythagoras's (√2): Digit 4,000 = 8
ln 2 — Natural log of 2: Digit 4,000 = 1
γ — Euler-Mascheroni (γ): Digit 4,000 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 4000, here are decompositions:

11 + 3989 = 4000
53 + 3947 = 4000
71 + 3929 = 4000
83 + 3917 = 4000
89 + 3911 = 4000
137 + 3863 = 4000
149 + 3851 = 4000
167 + 3833 = 4000

Showing the first eight; more decompositions exist.

Unicode codepoint

ྠ

Tibetan Subjoined Letter Tha

U+0FA0

Non-spacing mark (Mn)

UTF-8 encoding: E0 BE A0 (3 bytes).

Lookup U+0FA0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000FA0

RGB(0, 15, 160)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.15.160.

Address: 0.0.15.160
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.15.160

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

Musical pitch

Heard as a frequency, 4,000 Hz is closest to:

Concert pitch (A4 = 440 Hz): B7 (3951.1 Hz, +21¢)
Scientific pitch (C4 = 256 Hz): C8 (4096 Hz, -41¢)
Baroque pitch (A4 = 415 Hz): C8 (3948.2 Hz, +23¢)

Position in π

The digit sequence 4000 first appears in π at position 14,636 of the decimal expansion (the 14,636ordinal-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.

Look up 4000 on Pi Search ↗