513
513 is a composite number, odd, a calendar year.
513 (five hundred thirteen) is an odd 3-digit number. It is a composite number with 8 divisors, and factors as 3³ × 19. Written other ways, in Roman numerals it is DXIII and in binary, 1000000001.
Interestingness
Historical context — 513 AD
Calendar year
Year 513 (DXIII) was a common year starting on Tuesday of the Julian calendar.
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Historical context — 513 BC
Calendar year
The year 513 BC was a year of the pre-Julian Roman 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
-
Sunday
January 1, 513
- Ended on
-
Sunday
December 31, 513
- Friday the 13ths
-
2
2 Friday the 13ths this year.
- Decade
-
510s
510–519
- Century
-
6th century
501–600
- Millennium
-
1st millennium
1–1000
- Years ago
-
1,513
1513 years before 2026.
In other calendars
- Hebrew
-
4273 / 4274 AM
Rosh Hashanah falls in September/October.
- Chinese
-
Year of the zodiac:Water zodiac:Snake
Sexagenary cycle position 30 of 60. Lunar new year falls in late January / mid-February.
- Buddhist Era
-
1056 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
- Ethiopian
-
505 / 506 ET
Year boundary at Enkutatash (September 11/12).
- Indian National (Saka)
-
435 / 434 Saka
Indian national calendar; year starts in March.
Properties
Primality
Prime factorization: 3 3 × 19
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√513 = [22; (1, 1, 1, 5, 1, 4, 5, 2, 5, 4, 1, 5, 1, 1, 1, 44)]
Period length 16 — the block in parentheses repeats forever.
Representations
- In words
- five hundred thirteen
- Ordinal
- 513th
- Roman numeral
- DXIII
- Binary
- 1000000001
- Octal
- 1001
- Hexadecimal
- 0x201
- Base64
- AgE=
- One's complement
- 65,022 (16-bit)
- Scientific notation
- 5.13 × 10²
- As a duration
- 513 s = 8 minutes, 33 seconds
As an angle
Historical numeral systems
- Babylonian (base 60)
- 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹
- Egyptian hieroglyphic
- 𓍢𓍢𓍢𓍢𓍢𓎆𓏺𓏺𓏺
- Greek (Milesian)
- φιγʹ
- Mayan (base 20)
- 𝋡·𝋥·𝋭
- Chinese
- 五百一十三
- Chinese (financial)
- 伍佰壹拾參
Digit at this position in famous constants
- π — Pi (π)
- Digit 513 = 4
- e — Euler's number (e)
- Digit 513 = 2
- φ — Golden ratio (φ)
- Digit 513 = 4
- √2 — Pythagoras's (√2)
- Digit 513 = 6
- ln 2 — Natural log of 2
- Digit 513 = 8
- γ — Euler-Mascheroni (γ)
- Digit 513 = 7
Also seen as
UTF-8 encoding: C8 81 (2 bytes).
As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.1.
- Address
- 0.0.2.1
- Class
- reserved
- IPv4-mapped IPv6
- ::ffff:0.0.2.1
Unspecified address (0.0.0.0/8) — "this network" placeholder.
The number 513 is an active NANP area code (North American Numbering Plan).
- Primary area
- Cincinnati
- Region
- Ohio
- Country
- United States
Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.
Heard as a frequency, 513 Hz is closest to:
- Concert pitch (A4 = 440 Hz): C5 (523.3 Hz, -34¢)
- Scientific pitch (C4 = 256 Hz): C5 (512 Hz, +3¢)
- Baroque pitch (A4 = 415 Hz): C♯5 (522.9 Hz, -33¢)
Related reading
- Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.