Number

1,020

1,020 is a composite number, even, a calendar year.

1,020 (one thousand twenty) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2² × 3 × 5 × 17. Its proper divisors sum to 2,004, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MXX and in binary, 1111111100.

Abundant Number Arithmetic Number Cube-Free Evil Number Gapful Number Harshad / Niven Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

1,008 1,009 1,010 1,011 1,012 1,013 1,014 1,015 1,016 1,017 1,018 1,019 1,020 1,021 1,022 1,023 1,024 1,025 1,026 1,027 1,028 1,029 1,030 1,031 1,032

less more

Historical context — 1020 AD

Calendar year

Year 1020 (MXX) was a leap year starting on Friday of the Julian calendar.

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

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Saturday
January 1, 1020
Ended on: Sunday
December 31, 1020
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 1020s
1020–1029
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 1,006
1006 years before 2026.

In other calendars

Hebrew: 4780 / 4781 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 410 / 411 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1563 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 398 / 399 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1012 / 1013 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 942 / 941 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: 201
Recamán's sequence: a(4,379) = 1,020
Square (n²): 1,040,400
Cube (n³): 1,061,208,000
Divisor count: 24
σ(n) — sum of divisors: 3,024
φ(n) — Euler's totient: 256
Sum of prime factors: 29

Primality

Prime factorization: 2 ² × 3 × 5 × 17

Nearest primes: 1,019 (−1) · 1,021 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 10 · 12 · 15 · 17 · 20 · 30 · 34 · 51 · 60 · 68 · 85 · 102 · 170 · 204 · 255 · 340 · 510 (half) · 1020

Aliquot sum (sum of proper divisors): 2,004

Factor pairs (a × b = 1,020)

1 × 1020

2 × 510

3 × 340

4 × 255

5 × 204

6 × 170

10 × 102

12 × 85

15 × 68

17 × 60

20 × 51

30 × 34

First multiples

1,020 · 2,040 (double) · 3,060 · 4,080 · 5,100 · 6,120 · 7,140 · 8,160 · 9,180 · 10,200

Sums & aliquot sequence

As consecutive integers: 339 + 340 + 341 202 + 203 + 204 + 205 + 206 124 + 125 + … + 131 61 + 62 + … + 75

Aliquot sequence: 1,020 → 2,004 → 2,700 → 5,980 → 8,132 → 6,988 → 5,248 → 5,462 → 2,734 → 1,370 → 1,114 → 560 → 928 → 962 → 634 → 320 → 442 — unresolved within range

Continued fraction of √n

√1,020 = [31; (1, 14, 1, 62)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: one thousand twenty
Ordinal: 1020th
Roman numeral: MXX
Binary: 1111111100
Octal: 1774
Hexadecimal: 0x3FC
Base64: A/w=
One's complement: 64,515 (16-bit)
Scientific notation: 1.02 × 10³
As a duration: 1,020 s = 17 minutes

In other bases

ternary (3) 1101210

quaternary (4) 33330

quinary (5) 13040

senary (6) 4420

septenary (7) 2655

nonary (9) 1353

undecimal (11) 848

duodecimal (12) 710

tridecimal (13) 606

tetradecimal (14) 52c

pentadecimal (15) 480

Palindromic in base 11, base 13

As an angle

1,020° = 2 × 360° + 300°

300° ≈ 5.236 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓎆𓎆
Greek (Milesian): ͵ακʹ
Mayan (base 20): 𝋢·𝋫·𝋠
Chinese: 一千零二十
Chinese (financial): 壹仟零貳拾

In other modern scripts

Eastern Arabic ١٠٢٠ Devanagari १०२० Bengali ১০২০ Tamil ௧௦௨௦ Thai ๑๐๒๐ Tibetan ༡༠༢༠ Khmer ១០២០ Lao ໑໐໒໐ Burmese ၁၀၂၀

Digit at this position in famous constants

π — Pi (π): Digit 1,020 = 6
e — Euler's number (e): Digit 1,020 = 2
φ — Golden ratio (φ): Digit 1,020 = 6
√2 — Pythagoras's (√2): Digit 1,020 = 8
ln 2 — Natural log of 2: Digit 1,020 = 6
γ — Euler-Mascheroni (γ): Digit 1,020 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1020, here are decompositions:

7 + 1013 = 1020
11 + 1009 = 1020
23 + 997 = 1020
29 + 991 = 1020
37 + 983 = 1020
43 + 977 = 1020
53 + 967 = 1020
67 + 953 = 1020

Showing the first eight; more decompositions exist.

Unicode codepoint

Greek Rho With Stroke Symbol

U+03FC

Lowercase letter (Ll)

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

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

Hex color

#0003FC

RGB(0, 3, 252)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.252.

Address: 0.0.3.252
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.252

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

Musical pitch

Heard as a frequency, 1,020 Hz is closest to:

Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, -44¢)
Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, -7¢)
Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, -43¢)

Position in π

The digit sequence 1020 first appears in π at position 9,807 of the decimal expansion (the 9,807ordinal-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 1020 on Pi Search ↗