Number

4,001

4,001 is a prime, odd.

4,001 (four thousand one) is an odd 4-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in binary, 111110100001.

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

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

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 4,013

less more

Properties

Parity: Odd
Digit count: 4
Digit sum: 5
Digit product: 0
Digital root: 5
Palindrome: No
Bit width: 12 bits
Reversed: 1,004
Recamán's sequence: a(14,389) = 4,001
Square (n²): 16,008,001
Cube (n³): 64,048,012,001
Divisor count: 2
σ(n) — sum of divisors: 4,002
φ(n) — Euler's totient: 4,000

Primality

4,001 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 4001

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 4,001)

1 × 4001

First multiples

4,001 · 8,002 (double) · 12,003 · 16,004 · 20,005 · 24,006 · 28,007 · 32,008 · 36,009 · 40,010

Sums & aliquot sequence

As a sum of two squares: 40² + 49²

As consecutive integers: 2,000 + 2,001

Continued fraction of √n

√4,001 = [63; (3, 1, 17, 3, 9, 2, 2, 9, 3, 17, 1, 3, 126)]

Period length 13 — the block in parentheses repeats forever.

Representations

In words: four thousand one
Ordinal: 4001st
Binary: 111110100001
Octal: 7641
Hexadecimal: 0xFA1
Base64: D6E=
One's complement: 61,534 (16-bit)
Scientific notation: 4.001 × 10³
As a duration: 4,001 s = 1 hour, 6 minutes, 41 seconds

In other bases

ternary (3) 12111012

quaternary (4) 332201

quinary (5) 112001

senary (6) 30305

septenary (7) 14444

nonary (9) 5435

undecimal (11) 3008

duodecimal (12) 2395

tridecimal (13) 1a8a

tetradecimal (14) 165b

pentadecimal (15) 12bb

As an angle

4,001° = 11 × 360° + 41°

41° ≈ 0.716 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓆼𓆼𓆼𓆼𓏺
Greek (Milesian): ͵δαʹ
Mayan (base 20): 𝋪·𝋠·𝋡
Chinese: 四千零一
Chinese (financial): 肆仟零壹

In other modern scripts

Eastern Arabic ٤٠٠١ Devanagari ४००१ Bengali ৪০০১ Tamil ௪௦௦௧ Thai ๔๐๐๑ Tibetan ༤༠༠༡ Khmer ៤០០១ Lao ໔໐໐໑ Burmese ၄၀၀၁

Digit at this position in famous constants

π — Pi (π): Digit 4,001 = 6
e — Euler's number (e): Digit 4,001 = 7
φ — Golden ratio (φ): Digit 4,001 = 1
√2 — Pythagoras's (√2): Digit 4,001 = 8
ln 2 — Natural log of 2: Digit 4,001 = 1
γ — Euler-Mascheroni (γ): Digit 4,001 = 5

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 3,989 (gap of 12)
Next prime: 4,003 (gap of 2)

Pair status: twin with 4003.

Unicode codepoint

ྡ

Tibetan Subjoined Letter Da

U+0FA1

Non-spacing mark (Mn)

UTF-8 encoding: E0 BE A1 (3 bytes).

Lookup U+0FA1 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000FA1

RGB(0, 15, 161)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.15.161.

Address: 0.0.15.161
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.15.161

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

Musical pitch

Heard as a frequency, 4,001 Hz is closest to:

Concert pitch (A4 = 440 Hz): B7 (3951.1 Hz, +22¢)
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 4001 first appears in π at position 22,056 of the decimal expansion (the 22,056ordinal-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 4001 on Pi Search ↗