Number

1,056

1,056 is a composite number, even, a calendar year.

1,056 (one thousand fifty-six) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2⁵ × 3 × 11. Its proper divisors sum to 1,968, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MLVI and in binary, 10000100000.

Abundant Number Arithmetic Number Evil Number Gapful Number Harshad / Niven Pernicious Number Practical Number Pronic / Oblong Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

1,044 1,045 1,046 1,047 1,048 1,049 1,050 1,051 1,052 1,053 1,054 1,055 1,056 1,057 1,058 1,059 1,060 1,061 1,062 1,063 1,064 1,065 1,066 1,067 1,068

less more

Historical context — 1056 AD

Calendar year

Year 1056 (MLVI) was a leap year starting on Monday 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: Tuesday
January 1, 1056
Ended on: Wednesday
December 31, 1056
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 1050s
1050–1059
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 970
970 years before 2026.

In other calendars

Hebrew: 4816 / 4817 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 447 / 448 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Fire zodiac:Monkey
Sexagenary cycle position 33 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1599 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 434 / 435 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1048 / 1049 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 978 / 977 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 11 bits
Reversed: 6,501
Recamán's sequence: a(4,307) = 1,056
Square (n²): 1,115,136
Cube (n³): 1,177,583,616
Divisor count: 24
σ(n) — sum of divisors: 3,024
φ(n) — Euler's totient: 320
Sum of prime factors: 24

Primality

Prime factorization: 2 ⁵ × 3 × 11

Nearest primes: 1,051 (−5) · 1,061 (+5)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 6 · 8 · 11 · 12 · 16 · 22 · 24 · 32 · 33 · 44 · 48 · 66 · 88 · 96 · 132 · 176 · 264 · 352 · 528 (half) · 1056

Aliquot sum (sum of proper divisors): 1,968

Factor pairs (a × b = 1,056)

1 × 1056

2 × 528

3 × 352

4 × 264

6 × 176

8 × 132

11 × 96

12 × 88

16 × 66

22 × 48

24 × 44

32 × 33

First multiples

1,056 · 2,112 (double) · 3,168 · 4,224 · 5,280 · 6,336 · 7,392 · 8,448 · 9,504 · 10,560

Sums & aliquot sequence

As consecutive integers: 351 + 352 + 353 91 + 92 + … + 101 16 + 17 + … + 48

Aliquot sequence: 1,056 → 1,968 → 3,240 → 7,650 → 14,112 → 32,571 → 27,333 → 12,161 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,056 = [32; (2, 64)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: one thousand fifty-six
Ordinal: 1056th
Roman numeral: MLVI
Binary: 10000100000
Octal: 2040
Hexadecimal: 0x420
Base64: BCA=
One's complement: 64,479 (16-bit)
Scientific notation: 1.056 × 10³
As a duration: 1,056 s = 17 minutes, 36 seconds

In other bases

ternary (3) 1110010

quaternary (4) 100200

quinary (5) 13211

senary (6) 4520

septenary (7) 3036

nonary (9) 1403

undecimal (11) 880

duodecimal (12) 740

tridecimal (13) 633

tetradecimal (14) 556

pentadecimal (15) 4a6

As an angle

1,056° = 2 × 360° + 336°

336° ≈ 5.864 rad

Compass bearing: NNW (north-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵ανϛʹ
Mayan (base 20): 𝋢·𝋬·𝋰
Chinese: 一千零五十六
Chinese (financial): 壹仟零伍拾陸

In other modern scripts

Eastern Arabic ١٠٥٦ Devanagari १०५६ Bengali ১০৫৬ Tamil ௧௦௫௬ Thai ๑๐๕๖ Tibetan ༡༠༥༦ Khmer ១០៥៦ Lao ໑໐໕໖ Burmese ၁၀၅၆

Digit at this position in famous constants

π — Pi (π): Digit 1,056 = 0
e — Euler's number (e): Digit 1,056 = 1
φ — Golden ratio (φ): Digit 1,056 = 9
√2 — Pythagoras's (√2): Digit 1,056 = 2
ln 2 — Natural log of 2: Digit 1,056 = 4
γ — Euler-Mascheroni (γ): Digit 1,056 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1056, here are decompositions:

5 + 1051 = 1056
7 + 1049 = 1056
17 + 1039 = 1056
23 + 1033 = 1056
37 + 1019 = 1056
43 + 1013 = 1056
47 + 1009 = 1056
59 + 997 = 1056

Showing the first eight; more decompositions exist.

Unicode codepoint

Cyrillic Capital Letter Er

U+0420

Uppercase letter (Lu)

UTF-8 encoding: D0 A0 (2 bytes).

Lookup U+0420 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000420

RGB(0, 4, 32)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.32.

Address: 0.0.4.32
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.4.32

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

Musical pitch

Heard as a frequency, 1,056 Hz is closest to:

Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, +16¢)
Scientific pitch (C4 = 256 Hz): C♯6 (1084.9 Hz, -47¢ — about midway to C6)
Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, +17¢)

Position in π

The digit sequence 1056 first appears in π at position 25,547 of the decimal expansion (the 25,547ordinal-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 1056 on Pi Search ↗