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Number

17

17 — Seventeen

17 is a prime, odd, a calendar year.

Seventeen is the seventh prime, and is famously the favorite ‘random’ number people pick when asked. It is the only prime that is the sum of four consecutive primes (2 + 3 + 5 + 7).

Sources https://en.wikipedia.org/wiki/17_(number)
Arithmetic Number Binary Palindrome Chen Prime Circular Prime Cousin Prime Cube-Free Curated Deficient Number Emirp Evil Number Fermat Number Left-Truncatable Prime Leyland Number Pernicious Number Perrin Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Squarefree Twin Prime Unlucky Number

Interestingness

18 notable facts · grade A
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Historical context — 17 AD

Calendar year

AD 17 (XVII) 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 →

Historical context — 17 BC

Calendar year

Year 17 BC was either a common year starting on Sunday or Monday or a leap year starting on Saturday, Sunday or Monday of the Julian calendar and a leap year starting on Friday of the Proleptic 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, 17
Ended on
Sunday
December 31, 17
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
2,009
2009 years before 2026.

In other calendars

Hebrew
3777 / 3778 AM
Rosh Hashanah falls in September/October.
Chinese
Year of the zodiac:Fire zodiac:Ox
Sexagenary cycle position 14 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
560 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian
9 / 10 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
-61 / -62 Saka
Indian national calendar; year starts in March.

Cultural significance

Italian unlucky

Avoided — many Italian airlines skip row 17.

The Roman numeral XVII is an anagram of VIXI — Latin for "I have lived," implying death.

Wikipedia ↗

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

Properties

Parity
Odd
Digit count
2
Digit sum
8
Digit product
7
Digital root
8
Palindrome
No
Bit width
5 bits
Reversed
71
Recamán's sequence
a(25) = 17
Square (n²)
289
Cube (n³)
4,913
Divisor count
2
σ(n) — sum of divisors
18
φ(n) — Euler's totient
16

Primality

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

Divisors & multiples

All divisors (2)
1 · 17
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 17)
1 × 17
First multiples
17 · 34 (double) · 51 · 68 · 85 · 102 · 119 · 136 · 153 · 170

Sums & aliquot sequence

As a sum of two squares: 1² + 4²
As consecutive integers: 8 + 9

Continued fraction of √n

√17 = [4; (8)]

Period length 1 — the block in parentheses repeats forever.

Representations

In words
seventeen
Ordinal
17th
Roman numeral
XVII
Binary
10001
Octal
21
Hexadecimal
0x11
Base64
EQ==
One's complement
238 (8-bit)
Scientific notation
1.7 × 10¹
In other bases
ternary (3) 122
quaternary (4) 101
quinary (5) 32
senary (6) 25
septenary (7) 23
nonary (9) 18
undecimal (11) 16
duodecimal (12) 15
tridecimal (13) 14
tetradecimal (14) 13
pentadecimal (15) 12
Palindromic in base 2, base 4

Historical numeral systems

Babylonian (base 60)
𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian)
ιζʹ
Mayan (base 20)
𝋱
Chinese
一十七
Chinese (financial)
壹拾柒
In other modern scripts
Eastern Arabic ١٧ Devanagari १७ Bengali ১৭ Tamil ௧௭ Thai ๑๗ Tibetan ༡༧ Khmer ១៧ Lao ໑໗ Burmese ၁၇

Digit at this position in famous constants

π — Pi (π)
Digit 17 = 2
e — Euler's number (e)
Digit 17 = 2
φ — Golden ratio (φ)
Digit 17 = 8
√2 — Pythagoras's (√2)
Digit 17 = 0
ln 2 — Natural log of 2
Digit 17 = 3
γ — Euler-Mascheroni (γ)
Digit 17 = 8

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 13 (gap of 4)
  • Next prime: 19 (gap of 2)

Pair status: twin with 19, cousin with 13.

ASCII character

As an ASCII codepoint, 17 is control character (0x11). ASCII control character.

Hex color
#000011
RGB(0, 0, 17)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.17.

Address
0.0.0.17
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.0.17

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

US numbered highway

Matches numbered highway designation:

  • I-17 — Phoenix to Flagstaff, AZ.
Musical pitch

Heard as a frequency, 17 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): C♯0 (17.3 Hz, -33¢)
  • Scientific pitch (C4 = 256 Hz): C♯0 (17 Hz, +5¢)
  • Baroque pitch (A4 = 415 Hz): D0 (17.3 Hz, -31¢)
(below the ~20 Hz floor of human hearing — likely inaudible)

As a MIDI note number, 17 is F0 (21.8 Hz at concert pitch). (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 17 is Chlorine (Cl) — period 3.

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.