Number

13

13 — Thirteen

13 is a prime, odd, a calendar year.

Thirteen is the sixth prime and is widely considered unlucky in many Western cultures (a phenomenon called triskaidekaphobia). It is also the smallest emirp — a prime whose digit reversal (31) is a different prime.

Sources https://en.wikipedia.org/wiki/13_(number)

Arithmetic Number Chen Prime Cousin Prime Curated Deficient Number Emirp Fibonacci Happy Number Lucky Number Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Squarefree Tribonacci Number Twin Prime Unlucky Number

Historical context — 13 AD

Calendar year

AD 13 (XIII) was a common year starting on Sunday of the Julian calendar.

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Historical context — 13 BC

Calendar year

Year 13 BC was either a common year starting on Friday, Saturday or Sunday or a leap year starting on Friday or Saturday of the Julian calendar and a leap year starting on Wednesday of the Proleptic 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: Tuesday
January 1, 13
Ended on: Tuesday
December 31, 13
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 10s
10–19
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,013
2013 years before 2026.

In other calendars

Hebrew: 3773 / 3774 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Water zodiac:Rooster
Sexagenary cycle position 10 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 556 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 5 / 6 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -65 / -66 Saka
Indian national calendar; year starts in March.

Cultural significance

Western unlucky

Triskaidekaphobia — buildings often skip the 13th floor; Friday the 13th is feared.

Traced variously to the Last Supper (13 at the table), Norse myth (Loki the 13th guest), and the arrest of the Knights Templar on Friday October 13, 1307.

Wikipedia ↗

Italian lucky

Considered lucky — "fare tredici" means "to hit the jackpot."

Associated with Saint Anthony of Padua.

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Odd
Digit count: 2
Digit sum: 4
Digit product: 3
Digital root: 4
Palindrome: No
Bit width: 4 bits
Reversed: 31
Recamán's sequence: a(6) = 13
Square (n²): 169
Cube (n³): 2,197
Divisor count: 2
σ(n) — sum of divisors: 14
φ(n) — Euler's totient: 12

Primality

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

Divisors & multiples

All divisors (2)

1 · 13

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 13)

1 × 13

First multiples

13 · 26 (double) · 39 · 52 · 65 · 78 · 91 · 104 · 117 · 130

Sums & aliquot sequence

As a sum of two squares: 2² + 3²

As consecutive integers: 6 + 7

Representations

In words: thirteen
Ordinal: 13th
Roman numeral: XIII
Binary: 1101
Octal: 15
Hexadecimal: 0xD
Base64: DQ==
One's complement: 242 (8-bit)

In other bases

ternary (3) 111

quaternary (4) 31

quinary (5) 23

senary (6) 21

septenary (7) 16

nonary (9) 14

undecimal (11) 12

duodecimal (12) 11

tridecimal (13) 10

tetradecimal (14) d

pentadecimal (15) d

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹
Egyptian hieroglyphic: 𓎆𓏺𓏺𓏺
Greek (Milesian): ιγʹ
Mayan (base 20): 𝋭
Chinese: 一十三
Chinese (financial): 壹拾參

In other modern scripts

Eastern Arabic ١٣ Devanagari १३ Bengali ১৩ Tamil ௧௩ Thai ๑๓ Tibetan ༡༣ Khmer ១៣ Lao ໑໓ Burmese ၁၃

Digit at this position in famous constants

π — Pi (π): Digit 13 = 9
e — Euler's number (e): Digit 13 = 9
φ — Golden ratio (φ): Digit 13 = 9
√2 — Pythagoras's (√2): Digit 13 = 3
ln 2 — Natural log of 2: Digit 13 = 9
γ — Euler-Mascheroni (γ): Digit 13 = 1

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 11 (gap of 2)
Next prime: 17 (gap of 4)

Pair status: twin with 11, cousin with 17.

ASCII character

As an ASCII codepoint, 13 is CR (carriage return). ASCII control character.

Hex color

#00000D

RGB(0, 0, 13)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.13.

Address: 0.0.0.13
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.13

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

Possible US bank routing number

This passes the ABA routing number checksum and matches the Federal Reserve numbering scheme.

Routing number

000000013

Federal Reserve

United States Government

Banks operate many routing numbers per state and division; an unmatched checksum-valid number can still be a real RTN at a smaller institution.

Look up on FedACH (official) ↗ Search Google for routing number 000000013 ↗