1,021
1,021 is a prime, odd, a calendar year.
1,021 (one thousand twenty-one) is an odd 4-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in Roman numerals it is MXXI and in binary, 1111111101.
Interestingness
Historical context — 1021 AD
Calendar year
Year 1021 (MXXI) was a common year starting on Sunday of the Julian calendar.
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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
Primality
1,021 is prime. It has exactly two divisors: 1 and itself.
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√1,021 = [31; (1, 20, 3, 6, 1, 3, 2, 1, 1, 12, 5, 4, 15, 1, 2, 1, 4, 1, 1, 2, 1, 1, 1, 5, …)]
Period length 49 — the block in parentheses repeats forever.
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)
- Scientific notation
- 1.021 × 10³
- As a duration
- 1,021 s = 17 minutes, 1 second
As an angle
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
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
UTF-8 encoding: CF BD (2 bytes).
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.
Heard as a frequency, 1,021 Hz is closest to:
- Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, -43¢)
- Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, -5¢)
- Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, -41¢)
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.
Related reading
- Prime numbers — The building blocks of arithmetic: what primes are, why they matter, and how we find them.
- Egyptian hieroglyphic numerals — Seven hieroglyphs for every power of ten, from a single stroke to a million.