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Number

1,021

1,021 is a prime, odd, a calendar year.

Arithmetic Number Deficient Number Emirp Odious Number Prime Pythagorean Prime Recamán's Sequence Self Number Squarefree Twin Prime Year

Historical context — 1021 AD

Calendar year

Year 1021 (MXXI) was a common year starting on Sunday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback 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
Monday
January 1, 1021
Ended on
Monday
December 31, 1021
Friday the 13ths
2
2 Friday the 13ths this year.
Decade
1020s
1020–1029
Century
11th century
1001–1100
Millennium
2nd millennium
1001–2000
Years ago
1,005
1005 years before 2026.

In other calendars

Hebrew
4781 / 4782 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
411 / 412 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Metal zodiac:Rooster
Sexagenary cycle position 58 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
1564 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
399 / 400 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1013 / 1014 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
943 / 942 Saka
Indian national calendar; year starts in March.

Properties

Parity
Odd
Digit count
4
Digit sum
4
Digit product
0
Digital root
4
Palindrome
No
Bit width
10 bits
Reversed
1,201
Recamán's sequence
a(4,377) = 1,021
Square (n²)
1,042,441
Cube (n³)
1,064,332,261
Divisor count
2
σ(n) — sum of divisors
1,022
φ(n) — Euler's totient
1,020

Primality

1,021 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 1021
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 1,021)
1 × 1021
First multiples
1,021 · 2,042 (double) · 3,063 · 4,084 · 5,105 · 6,126 · 7,147 · 8,168 · 9,189 · 10,210

Sums & aliquot sequence

As a sum of two squares: 11² + 30²
As consecutive integers: 510 + 511

Representations

In words
one thousand twenty-one
Ordinal
1021st
Roman numeral
MXXI
Binary
1111111101
Octal
1775
Hexadecimal
0x3FD
Base64
A/0=
One's complement
64,514 (16-bit)
In other bases
ternary (3) 1101211
quaternary (4) 33331
quinary (5) 13041
senary (6) 4421
septenary (7) 2656
nonary (9) 1354
undecimal (11) 849
duodecimal (12) 711
tridecimal (13) 607
tetradecimal (14) 52d
pentadecimal (15) 481

Historical numeral systems

Babylonian (base 60)
𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒁹
Egyptian hieroglyphic
𓆼𓎆𓎆𓏺
Greek (Milesian)
͵ακαʹ
Mayan (base 20)
𝋢·𝋫·𝋡
Chinese
一千零二十一
Chinese (financial)
壹仟零貳拾壹
In other modern scripts
Eastern Arabic ١٠٢١ Devanagari १०२१ Bengali ১০২১ Tamil ௧௦௨௧ Thai ๑๐๒๑ Tibetan ༡༠༢༡ Khmer ១០២១ Lao ໑໐໒໑ Burmese ၁၀၂၁

Digit at this position in famous constants

π — Pi (π)
Digit 1,021 = 3
e — Euler's number (e)
Digit 1,021 = 1
φ — Golden ratio (φ)
Digit 1,021 = 0
√2 — Pythagoras's (√2)
Digit 1,021 = 8
ln 2 — Natural log of 2
Digit 1,021 = 7
γ — Euler-Mascheroni (γ)
Digit 1,021 = 1

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 1,019 (gap of 2)
  • Next prime: 1,031 (gap of 10)

Pair status: twin with 1019.

Unicode codepoint
Ͻ
Greek Capital Reversed Lunate Sigma Symbol
U+03FD
Uppercase letter (Lu)

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

Hex color
#0003FD
RGB(0, 3, 253)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.253.

Address
0.0.3.253
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.3.253

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

Position in π

The digit sequence 1021 first appears in π at position 2,749 of the decimal expansion (the 2,749ordinal-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.