Number

1,313

1,313 is a composite number, odd, a calendar year.

1,313 (one thousand three hundred thirteen) is an odd 4-digit number. It is a composite number with 4 divisors, and factors as 13 × 101. Written other ways, in Roman numerals it is MCCCXIII and in binary, 10100100001.

Arithmetic Number Cube-Free Deficient Number Evil Number Gapful Number Recamán's Sequence Self Number Semiprime Squarefree Undulating Number Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

1,301 1,302 1,303 1,304 1,305 1,306 1,307 1,308 1,309 1,310 1,311 1,312 1,313 1,314 1,315 1,316 1,317 1,318 1,319 1,320 1,321 1,322 1,323 1,324 1,325

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Historical context — 1313 AD

Calendar year

Year 1313 (MCCCXIII) was a common 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: 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: Sunday
January 1, 1313
Ended on: Sunday
December 31, 1313
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1310s
1310–1319
Century: 14th century
1301–1400
Millennium: 2nd millennium
1001–2000
Years ago: 713
713 years before 2026.

In other calendars

Hebrew: 5073 / 5074 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 712 / 713 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: 1856 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 691 / 692 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1305 / 1306 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1235 / 1234 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 4
Digit sum: 8
Digit product: 9
Digital root: 8
Palindrome: No
Bit width: 11 bits
Reversed: 3,131
Recamán's sequence: a(418) = 1,313
Square (n²): 1,723,969
Cube (n³): 2,263,571,297
Divisor count: 4
σ(n) — sum of divisors: 1,428
φ(n) — Euler's totient: 1,200
Sum of prime factors: 114

Primality

Prime factorization: 13 × 101

Nearest primes: 1,307 (−6) · 1,319 (+6)

Divisors & multiples

All divisors (4)

1 · 13 · 101 · 1313

Aliquot sum (sum of proper divisors): 115

Factor pairs (a × b = 1,313)

1 × 1313

13 × 101

First multiples

1,313 · 2,626 (double) · 3,939 · 5,252 · 6,565 · 7,878 · 9,191 · 10,504 · 11,817 · 13,130

Sums & aliquot sequence

As a sum of two squares: 17² + 32² = 23² + 28²

As consecutive integers: 656 + 657 95 + 96 + … + 107 38 + 39 + … + 63

Aliquot sequence: 1,313 → 115 → 29 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,313 = [36; (4, 4, 72)]

Period length 3 — the block in parentheses repeats forever.

Representations

In words: one thousand three hundred thirteen
Ordinal: 1313th
Roman numeral: MCCCXIII
Binary: 10100100001
Octal: 2441
Hexadecimal: 0x521
Base64: BSE=
One's complement: 64,222 (16-bit)
Scientific notation: 1.313 × 10³
As a duration: 1,313 s = 21 minutes, 53 seconds

In other bases

ternary (3) 1210122

quaternary (4) 110201

quinary (5) 20223

senary (6) 10025

septenary (7) 3554

nonary (9) 1718

undecimal (11) a94

duodecimal (12) 915

tridecimal (13) 7a0

tetradecimal (14) 69b

pentadecimal (15) 5c8

As an angle

1,313° = 3 × 360° + 233°

233° ≈ 4.067 rad

Compass bearing: SW (southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓎆𓏺𓏺𓏺
Greek (Milesian): ͵ατιγʹ
Mayan (base 20): 𝋣·𝋥·𝋭
Chinese: 一千三百一十三
Chinese (financial): 壹仟參佰壹拾參

In other modern scripts

Eastern Arabic ١٣١٣ Devanagari १३१३ Bengali ১৩১৩ Tamil ௧௩௧௩ Thai ๑๓๑๓ Tibetan ༡༣༡༣ Khmer ១៣១៣ Lao ໑໓໑໓ Burmese ၁၃၁၃

Digit at this position in famous constants

π — Pi (π): Digit 1,313 = 9
e — Euler's number (e): Digit 1,313 = 4
φ — Golden ratio (φ): Digit 1,313 = 8
√2 — Pythagoras's (√2): Digit 1,313 = 9
ln 2 — Natural log of 2: Digit 1,313 = 6
γ — Euler-Mascheroni (γ): Digit 1,313 = 8

Also seen as

Unicode codepoint

Cyrillic Small Letter El With Middle Hook

U+0521

Lowercase letter (Ll)

UTF-8 encoding: D4 A1 (2 bytes).

Lookup U+0521 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000521

RGB(0, 5, 33)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.5.33.

Address: 0.0.5.33
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.5.33

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

Musical pitch

Heard as a frequency, 1,313 Hz is closest to:

Concert pitch (A4 = 440 Hz): E6 (1318.5 Hz, -7¢)
Scientific pitch (C4 = 256 Hz): E6 (1290.2 Hz, +30¢)
Baroque pitch (A4 = 415 Hz): F6 (1317.5 Hz, -6¢)

Position in π

The digit sequence 1313 first appears in π at position 14,956 of the decimal expansion (the 14,956ordinal-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 1313 on Pi Search ↗