Number

1,001

1,001 is a composite number, odd, a calendar year.

1,001 (one thousand one) is an odd 4-digit number. It is a composite number with 8 divisors, and factors as 7 × 11 × 13. Its digits read the same forwards and backwards, so it is a palindromic number. Written other ways, in Roman numerals it is MI and in binary, 1111101001.

Arithmetic Number Cube-Free Deficient Number Flippable Gapful Number Odious Number Palindrome Pentagonal Pentatope Number Pernicious Number Recamán's Sequence Sphenic Number Squarefree Strobogrammatic Year

Interestingness

★ ★ ★ ★ ★

11 notable facts · grade A

989 990 991 992 993 994 995 996 997 998 999 1,000 1,001 1,002 1,003 1,004 1,005 1,006 1,007 1,008 1,009 1,010 1,011 1,012 1,013

less more

Historical context — 1001 AD

Calendar year

1001 (MI) was a common year starting on Wednesday of the Julian calendar, the 1001st year of the Common Era (CE) and Anno Domini (AD) designations, the 1st year of the 2nd millennium and the 11th century, and the 2nd year of the 1000s decade.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 1001
Ended on: Thursday
December 31, 1001
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 1000s
1000–1009
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 1,025
1025 years before 2026.

In other calendars

Hebrew: 4761 / 4762 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 391 / 392 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Ox
Sexagenary cycle position 38 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1544 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 379 / 380 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 993 / 994 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 923 / 922 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 4
Digit sum: 2
Digit product: 0
Digital root: 2
Palindrome: Yes
Bit width: 10 bits
Recamán's sequence: a(4,417) = 1,001
Square (n²): 1,002,001
Cube (n³): 1,003,003,001
Divisor count: 8
σ(n) — sum of divisors: 1,344
φ(n) — Euler's totient: 720
Sum of prime factors: 31

Primality

Prime factorization: 7 × 11 × 13

Nearest primes: 997 (−4) · 1,009 (+8)

Divisors & multiples

All divisors (8)

1 · 7 · 11 · 13 · 77 · 91 · 143 · 1001

Aliquot sum (sum of proper divisors): 343

Factor pairs (a × b = 1,001)

1 × 1001

7 × 143

11 × 91

13 × 77

First multiples

1,001 · 2,002 (double) · 3,003 · 4,004 · 5,005 · 6,006 · 7,007 · 8,008 · 9,009 · 10,010

Sums & aliquot sequence

As a sum of two cubes: 1³ + 10³

As consecutive integers: 500 + 501 140 + 141 + … + 146 86 + 87 + … + 96 71 + 72 + … + 83

Aliquot sequence: 1,001 → 343 → 57 → 23 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,001 = [31; (1, 1, 1, 3, 3, 2, 4, 2, 3, 3, 1, 1, 1, 62)]

Period length 14 — the block in parentheses repeats forever.

Representations

In words: one thousand one
Ordinal: 1001st
Roman numeral: MI
Binary: 1111101001
Octal: 1751
Hexadecimal: 0x3E9
Base64: A+k=
One's complement: 64,534 (16-bit)
Scientific notation: 1.001 × 10³
As a duration: 1,001 s = 16 minutes, 41 seconds

In other bases

ternary (3) 1101002

quaternary (4) 33221

quinary (5) 13001

senary (6) 4345

septenary (7) 2630

nonary (9) 1332

undecimal (11) 830

duodecimal (12) 6b5

tridecimal (13) 5c0

tetradecimal (14) 517

pentadecimal (15) 46b

As an angle

1,001° = 2 × 360° + 281°

281° ≈ 4.904 rad

Compass bearing: W (west)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓆼𓏺
Greek (Milesian): ͵ααʹ
Mayan (base 20): 𝋢·𝋪·𝋡
Chinese: 一千零一
Chinese (financial): 壹仟零壹

In other modern scripts

Eastern Arabic ١٠٠١ Devanagari १००१ Bengali ১০০১ Tamil ௧௦௦௧ Thai ๑๐๐๑ Tibetan ༡༠༠༡ Khmer ១០០១ Lao ໑໐໐໑ Burmese ၁၀၀၁

Digit at this position in famous constants

π — Pi (π): Digit 1,001 = 9
e — Euler's number (e): Digit 1,001 = 4
φ — Golden ratio (φ): Digit 1,001 = 2
√2 — Pythagoras's (√2): Digit 1,001 = 2
ln 2 — Natural log of 2: Digit 1,001 = 7
γ — Euler-Mascheroni (γ): Digit 1,001 = 2

Also seen as

Unicode codepoint

Coptic Small Letter Hori

U+03E9

Lowercase letter (Ll)

UTF-8 encoding: CF A9 (2 bytes).

Lookup U+03E9 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0003E9

RGB(0, 3, 233)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.233.

Address: 0.0.3.233
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.233

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

Musical pitch

Heard as a frequency, 1,001 Hz is closest to:

Concert pitch (A4 = 440 Hz): B5 (987.8 Hz, +23¢)
Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, -39¢)
Baroque pitch (A4 = 415 Hz): C6 (987 Hz, +24¢)

Position in π

The digit sequence 1001 first appears in π at position 15,761 of the decimal expansion (the 15,761ordinal-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 1001 on Pi Search ↗