Number

1,002

1,002 is a composite number, even, a calendar year.

1,002 (one thousand two) is an even 4-digit number. It is a composite number with 8 divisors, and factors as 2 × 3 × 167. Its proper divisors sum to 1,014, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MII and in binary, 1111101010.

Abundant Number Arithmetic Number Cube-Free Harshad / Niven Odious Number Partition Number Pernicious Number Recamán's Sequence Semiperfect Number Sphenic Number Squarefree Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

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 1,014

less more

Historical context — 1002 AD

Calendar year

Year 1002 (MII) was a common year starting on Thursday of the Julian calendar.

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: 52
Started on: Friday
January 1, 1002
Ended on: Friday
December 31, 1002
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 1000s
1000–1009
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 1,024
1024 years before 2026.

In other calendars

Hebrew: 4762 / 4763 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 392 / 393 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Water zodiac:Tiger
Sexagenary cycle position 39 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1545 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 380 / 381 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 994 / 995 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 924 / 923 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 3
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 10 bits
Reversed: 2,001
Recamán's sequence: a(4,415) = 1,002
Square (n²): 1,004,004
Cube (n³): 1,006,012,008
Divisor count: 8
σ(n) — sum of divisors: 2,016
φ(n) — Euler's totient: 332
Sum of prime factors: 172

Primality

Prime factorization: 2 × 3 × 167

Nearest primes: 997 (−5) · 1,009 (+7)

Divisors & multiples

All divisors (8)

1 · 2 · 3 · 6 · 167 · 334 · 501 (half) · 1002

Aliquot sum (sum of proper divisors): 1,014

Factor pairs (a × b = 1,002)

1 × 1002

2 × 501

3 × 334

6 × 167

First multiples

1,002 · 2,004 (double) · 3,006 · 4,008 · 5,010 · 6,012 · 7,014 · 8,016 · 9,018 · 10,020

Sums & aliquot sequence

As consecutive integers: 333 + 334 + 335 249 + 250 + 251 + 252 78 + 79 + … + 89

Aliquot sequence: 1,002 → 1,014 → 1,182 → 1,194 → 1,206 → 1,446 → 1,458 → 1,821 → 611 → 61 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,002 = [31; (1, 1, 1, 8, 2, 1, 1, 1, 3, 10, 3, 1, 1, 1, 2, 8, 1, 1, 1, 62)]

Period length 20 — the block in parentheses repeats forever.

Representations

In words: one thousand two
Ordinal: 1002nd
Roman numeral: MII
Binary: 1111101010
Octal: 1752
Hexadecimal: 0x3EA
Base64: A+o=
One's complement: 64,533 (16-bit)
Scientific notation: 1.002 × 10³
As a duration: 1,002 s = 16 minutes, 42 seconds

In other bases

ternary (3) 1101010

quaternary (4) 33222

quinary (5) 13002

senary (6) 4350

septenary (7) 2631

nonary (9) 1333

undecimal (11) 831

duodecimal (12) 6b6

tridecimal (13) 5c1

tetradecimal (14) 518

pentadecimal (15) 46c

Palindromic in base 12

As an angle

1,002° = 2 × 360° + 282°

282° ≈ 4.922 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹
Egyptian hieroglyphic: 𓆼𓏺𓏺
Greek (Milesian): ͵αβʹ
Mayan (base 20): 𝋢·𝋪·𝋢
Chinese: 一千零二
Chinese (financial): 壹仟零貳

In other modern scripts

Eastern Arabic ١٠٠٢ Devanagari १००२ Bengali ১০০২ Tamil ௧௦௦௨ Thai ๑๐๐๒ Tibetan ༡༠༠༢ Khmer ១០០២ Lao ໑໐໐໒ Burmese ၁၀၀၂

Digit at this position in famous constants

π — Pi (π): Digit 1,002 = 3
e — Euler's number (e): Digit 1,002 = 0
φ — Golden ratio (φ): Digit 1,002 = 1
√2 — Pythagoras's (√2): Digit 1,002 = 0
ln 2 — Natural log of 2: Digit 1,002 = 6
γ — Euler-Mascheroni (γ): Digit 1,002 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1002, here are decompositions:

5 + 997 = 1002
11 + 991 = 1002
19 + 983 = 1002
31 + 971 = 1002
61 + 941 = 1002
73 + 929 = 1002
83 + 919 = 1002
139 + 863 = 1002

Showing the first eight; more decompositions exist.

Unicode codepoint

Coptic Capital Letter Gangia

U+03EA

Uppercase letter (Lu)

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

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

Hex color

#0003EA

RGB(0, 3, 234)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.234.

Address: 0.0.3.234
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.234

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

Musical pitch

Heard as a frequency, 1,002 Hz is closest to:

Concert pitch (A4 = 440 Hz): B5 (987.8 Hz, +25¢)
Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, -38¢)
Baroque pitch (A4 = 415 Hz): C6 (987 Hz, +26¢)

Position in π

The digit sequence 1002 first appears in π at position 6,739 of the decimal expansion (the 6,739ordinal-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 1002 on Pi Search ↗