4,004
4,004 is a composite number, even.
4,004 (four thousand four) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2² × 7 × 11 × 13. Its proper divisors sum to 5,404, more than the number itself, making it an abundant number. Its digits read the same forwards and backwards, so it is a palindromic number. Written other ways, in binary, 111110100100.
Interestingness
Properties
- Parity
- Even
- Digit count
- 4
- Digit sum
- 8
- Digit product
- 0
- Digital root
- 8
- Palindrome
- Yes
- Bit width
- 12 bits
- Recamán's sequence
- a(14,383) = 4,004
- Square (n²)
- 16,032,016
- Cube (n³)
- 64,192,192,064
- Divisor count
- 24
- σ(n) — sum of divisors
- 9,408
- φ(n) — Euler's totient
- 1,440
- Sum of prime factors
- 35
Primality
Prime factorization: 2 2 × 7 × 11 × 13
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√4,004 = [63; (3, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 1, 3, 126)]
Period length 14 — the block in parentheses repeats forever.
Representations
- In words
- four thousand four
- Ordinal
- 4004th
- Binary
- 111110100100
- Octal
- 7644
- Hexadecimal
- 0xFA4
- Base64
- D6Q=
- One's complement
- 61,531 (16-bit)
- Scientific notation
- 4.004 × 10³
- As a duration
- 4,004 s = 1 hour, 6 minutes, 44 seconds
As an angle
Historical numeral systems
- Babylonian (base 60)
- 𒁹 𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹
- Egyptian hieroglyphic
- 𓆼𓆼𓆼𓆼𓏺𓏺𓏺𓏺
- Greek (Milesian)
- ͵δδʹ
- Mayan (base 20)
- 𝋪·𝋠·𝋤
- Chinese
- 四千零四
- Chinese (financial)
- 肆仟零肆
Digit at this position in famous constants
- π — Pi (π)
- Digit 4,004 = 5
- e — Euler's number (e)
- Digit 4,004 = 1
- φ — Golden ratio (φ)
- Digit 4,004 = 8
- √2 — Pythagoras's (√2)
- Digit 4,004 = 3
- ln 2 — Natural log of 2
- Digit 4,004 = 9
- γ — Euler-Mascheroni (γ)
- Digit 4,004 = 3
Also seen as
Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 4004, here are decompositions:
- 3 + 4001 = 4004
- 37 + 3967 = 4004
- 61 + 3943 = 4004
- 73 + 3931 = 4004
- 97 + 3907 = 4004
- 127 + 3877 = 4004
- 151 + 3853 = 4004
- 157 + 3847 = 4004
Showing the first eight; more decompositions exist.
UTF-8 encoding: E0 BE A4 (3 bytes).
As an unsigned 32-bit integer, this is the IPv4 address 0.0.15.164.
- Address
- 0.0.15.164
- Class
- reserved
- IPv4-mapped IPv6
- ::ffff:0.0.15.164
Unspecified address (0.0.0.0/8) — "this network" placeholder.
Heard as a frequency, 4,004 Hz is closest to:
- Concert pitch (A4 = 440 Hz): B7 (3951.1 Hz, +23¢)
- Scientific pitch (C4 = 256 Hz): C8 (4096 Hz, -39¢)
- Baroque pitch (A4 = 415 Hz): C8 (3948.2 Hz, +24¢)
The digit sequence 4004 first appears in π at position 5,092 of the decimal expansion (the 5,092ordinal-suffix:nd 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
- Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.