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Number

1,031

1,031 is a prime, odd, a calendar year.

1,031 (one thousand thirty-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 MXXXI and in binary, 10000000111.

Arithmetic Number Chen Prime Cube-Free Deficient Number Emirp Evil Number Prime Recamán's Sequence Sophie Germain Prime Squarefree Twin Prime Year

Interestingness

Historical context — 1031 AD

Calendar year

Year 1031 (MXXXI) was a common 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
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
Saturday
January 1, 1031
Ended on
Saturday
December 31, 1031
Friday the 13ths
1
One Friday the 13th this year.
Decade
1030s
1030–1039
Century
11th century
1001–1100
Millennium
2nd millennium
1001–2000
Years ago
995
995 years before 2026.

In other calendars

Hebrew
4791 / 4792 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
421 / 423 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Metal zodiac:Goat
Sexagenary cycle position 8 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
1574 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
409 / 410 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1023 / 1024 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
953 / 952 Saka
Indian national calendar; year starts in March.

Properties

Parity
Odd
Digit count
4
Digit sum
5
Digit product
0
Digital root
5
Palindrome
No
Bit width
11 bits
Reversed
1,301
Recamán's sequence
a(4,357) = 1,031
Square (n²)
1,062,961
Cube (n³)
1,095,912,791
Divisor count
2
σ(n) — sum of divisors
1,032
φ(n) — Euler's totient
1,030

Primality

1,031 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 1031
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 1,031)
1 × 1031
First multiples
1,031 · 2,062 (double) · 3,093 · 4,124 · 5,155 · 6,186 · 7,217 · 8,248 · 9,279 · 10,310

Sums & aliquot sequence

As consecutive integers: 515 + 516

Continued fraction of √n

√1,031 = [32; (9, 6, 3, 4, 1, 1, 1, 1, 1, 12, 4, 1, 1, 31, 1, 1, 4, 12, 1, 1, 1, 1, 1, 4, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words
one thousand thirty-one
Ordinal
1031st
Roman numeral
MXXXI
Binary
10000000111
Octal
2007
Hexadecimal
0x407
Base64
BAc=
One's complement
64,504 (16-bit)
Scientific notation
1.031 × 10³
As a duration
1,031 s = 17 minutes, 11 seconds
In other bases
ternary (3) 1102012
quaternary (4) 100013
quinary (5) 13111
senary (6) 4435
septenary (7) 3002
nonary (9) 1365
undecimal (11) 858
duodecimal (12) 71b
tridecimal (13) 614
tetradecimal (14) 539
pentadecimal (15) 48b
Palindromic in base 11

As an angle

1,031° = 2 × 360° + 311°
311° ≈ 5.428 rad
Compass bearing: NW (northwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹
Egyptian hieroglyphic
𓆼𓎆𓎆𓎆𓏺
Greek (Milesian)
͵αλαʹ
Mayan (base 20)
𝋢·𝋫·𝋫
Chinese
一千零三十一
Chinese (financial)
壹仟零參拾壹
In other modern scripts
Eastern Arabic ١٠٣١ Devanagari १०३१ Bengali ১০৩১ Tamil ௧௦௩௧ Thai ๑๐๓๑ Tibetan ༡༠༣༡ Khmer ១០៣១ Lao ໑໐໓໑ Burmese ၁၀၃၁

Digit at this position in famous constants

π — Pi (π)
Digit 1,031 = 1
e — Euler's number (e)
Digit 1,031 = 0
φ — Golden ratio (φ)
Digit 1,031 = 6
√2 — Pythagoras's (√2)
Digit 1,031 = 5
ln 2 — Natural log of 2
Digit 1,031 = 6
γ — Euler-Mascheroni (γ)
Digit 1,031 = 7

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 1,021 (gap of 10)
  • Next prime: 1,033 (gap of 2)

Pair status: twin with 1033.

Unicode codepoint
Ї
Cyrillic Capital Letter Yi
U+0407
Uppercase letter (Lu)

UTF-8 encoding: D0 87 (2 bytes).

Hex color
#000407
RGB(0, 4, 7)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.7.

Address
0.0.4.7
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.4.7

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

Musical pitch

Heard as a frequency, 1,031 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, -26¢)
  • Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, +12¢)
  • Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, -25¢)
Position in π

The digit sequence 1031 first appears in π at position 3,494 of the decimal expansion (the 3,494ordinal-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.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.