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Number

1,013

1,013 is a prime, odd, a calendar year.

Arithmetic Number Cousin Prime Deficient Number Evil Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Sophie Germain Prime Squarefree Year

Historical context — 1013 AD

Calendar year

Year 1013 (MXIII) was a common year starting on Thursday 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
Friday
January 1, 1013
Ended on
Friday
December 31, 1013
Friday the 13ths
1
One Friday the 13th this year.
Decade
1010s
1010–1019
Century
11th century
1001–1100
Millennium
2nd millennium
1001–2000
Years ago
1,013
1013 years before 2026.

In other calendars

Hebrew
4773 / 4774 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
403 / 404 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Water zodiac:Ox
Sexagenary cycle position 50 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
1556 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
391 / 392 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1005 / 1006 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
935 / 934 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
10 bits
Reversed
3,101
Recamán's sequence
a(4,393) = 1,013
Square (n²)
1,026,169
Cube (n³)
1,039,509,197
Divisor count
2
σ(n) — sum of divisors
1,014
φ(n) — Euler's totient
1,012

Primality

1,013 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 1013
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 1,013)
1 × 1013
First multiples
1,013 · 2,026 (double) · 3,039 · 4,052 · 5,065 · 6,078 · 7,091 · 8,104 · 9,117 · 10,130

Sums & aliquot sequence

As a sum of two squares: 22² + 23²
As consecutive integers: 506 + 507

Representations

In words
one thousand thirteen
Ordinal
1013th
Roman numeral
MXIII
Binary
1111110101
Octal
1765
Hexadecimal
0x3F5
Base64
A/U=
One's complement
64,522 (16-bit)
In other bases
ternary (3) 1101112
quaternary (4) 33311
quinary (5) 13023
senary (6) 4405
septenary (7) 2645
nonary (9) 1345
undecimal (11) 841
duodecimal (12) 705
tridecimal (13) 5cc
tetradecimal (14) 525
pentadecimal (15) 478

Historical numeral systems

Babylonian (base 60)
𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹𒁹
Egyptian hieroglyphic
𓆼𓎆𓏺𓏺𓏺
Greek (Milesian)
͵αιγʹ
Mayan (base 20)
𝋢·𝋪·𝋭
Chinese
一千零一十三
Chinese (financial)
壹仟零壹拾參
In other modern scripts
Eastern Arabic ١٠١٣ Devanagari १०१३ Bengali ১০১৩ Tamil ௧௦௧௩ Thai ๑๐๑๓ Tibetan ༡༠༡༣ Khmer ១០១៣ Lao ໑໐໑໓ Burmese ၁၀၁၃

Digit at this position in famous constants

π — Pi (π)
Digit 1,013 = 0
e — Euler's number (e)
Digit 1,013 = 8
φ — Golden ratio (φ)
Digit 1,013 = 4
√2 — Pythagoras's (√2)
Digit 1,013 = 2
ln 2 — Natural log of 2
Digit 1,013 = 4
γ — Euler-Mascheroni (γ)
Digit 1,013 = 0

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 1,009 (gap of 4)
  • Next prime: 1,019 (gap of 6)

Pair status: cousin with 1009, sexy with 1019.

Unicode codepoint
ϵ
Greek Lunate Epsilon Symbol
U+03F5
Lowercase letter (Ll)

UTF-8 encoding: CF B5 (2 bytes).

Hex color
#0003F5
RGB(0, 3, 245)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.245.

Address
0.0.3.245
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.3.245

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

Position in π

The digit sequence 1013 first appears in π at position 8,270 of the decimal expansion (the 8,270ordinal-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.