number.wiki
Number

1,688

1,688 is a composite number, even, a calendar year.

Deficient Number Flippable Odious Number Pernicious Number Recamán's Sequence Year

Notable events — 1688 AD

  1. Nov 5 William of Orange lands at Torbay, beginning the Glorious Revolution.
  2. Dec 11 James II flees England.
  3. Sep 24 Louis XIV invades the Palatinate, starting the Nine Years' War.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type
Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year
366
ISO weeks
53
Long year: contains 53 ISO weeks.
Started on
Thursday
January 1, 1688
Ended on
Friday
December 31, 1688
Friday the 13ths
2
2 Friday the 13ths this year.
Easter Sunday
April 18
Sunday, April 18, 1688
Decade
1680s
1680–1689
Century
17th century
1601–1700
Millennium
2nd millennium
1001–2000
Years ago
338
338 years before 2026.

In other calendars

Hebrew
5448 / 5449 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
1099 / 1100 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Earth zodiac:Dragon
Sexagenary cycle position 5 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
2231 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
1066 / 1067 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1680 / 1681 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
1610 / 1609 Saka
Indian national calendar; year starts in March.

Properties

Parity
Even
Digit count
4
Digit sum
23
Digit product
384
Digital root
5
Palindrome
No
Bit width
11 bits
Reversed
8,861
Flips to (rotate 180°)
8,891
Recamán's sequence
a(844) = 1,688
Square (n²)
2,849,344
Cube (n³)
4,809,692,672
Divisor count
8
σ(n) — sum of divisors
3,180
φ(n) — Euler's totient
840
Sum of prime factors
217

Primality

Prime factorization: 2 3 × 211

Nearest primes: 1,669 (−19) · 1,693 (+5)

Divisors & multiples

All divisors (8)
1 · 2 · 4 · 8 · 211 · 422 · 844 (half) · 1688
Aliquot sum (sum of proper divisors): 1,492
Factor pairs (a × b = 1,688)
1 × 1688
2 × 844
4 × 422
8 × 211
First multiples
1,688 · 3,376 (double) · 5,064 · 6,752 · 8,440 · 10,128 · 11,816 · 13,504 · 15,192 · 16,880

Sums & aliquot sequence

As consecutive integers: 98 + 99 + … + 113
Aliquot sequence: 1,688 1,492 1,126 566 286 218 112 136 134 70 74 40 50 43 1 0 — terminates at zero

Representations

In words
one thousand six hundred eighty-eight
Ordinal
1688th
Roman numeral
MDCLXXXVIII
Binary
11010011000
Octal
3230
Hexadecimal
0x698
Base64
Bpg=
One's complement
63,847 (16-bit)
In other bases
ternary (3) 2022112
quaternary (4) 122120
quinary (5) 23223
senary (6) 11452
septenary (7) 4631
nonary (9) 2275
undecimal (11) 12a5
duodecimal (12) b88
tridecimal (13) 9cb
tetradecimal (14) 888
pentadecimal (15) 778

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian)
͵αχπηʹ
Mayan (base 20)
𝋤·𝋤·𝋨
Chinese
一千六百八十八
Chinese (financial)
壹仟陸佰捌拾捌
In other modern scripts
Eastern Arabic ١٦٨٨ Devanagari १६८८ Bengali ১৬৮৮ Tamil ௧௬௮௮ Thai ๑๖๘๘ Tibetan ༡༦༨༨ Khmer ១៦៨៨ Lao ໑໖໘໘ Burmese ၁၆၈၈

Digit at this position in famous constants

π — Pi (π)
Digit 1,688 = 3
e — Euler's number (e)
Digit 1,688 = 2
φ — Golden ratio (φ)
Digit 1,688 = 9
√2 — Pythagoras's (√2)
Digit 1,688 = 5
ln 2 — Natural log of 2
Digit 1,688 = 7
γ — Euler-Mascheroni (γ)
Digit 1,688 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1688, here are decompositions:

  • 19 + 1669 = 1688
  • 31 + 1657 = 1688
  • 61 + 1627 = 1688
  • 67 + 1621 = 1688
  • 79 + 1609 = 1688
  • 109 + 1579 = 1688
  • 139 + 1549 = 1688
  • 157 + 1531 = 1688

Showing the first eight; more decompositions exist.

Unicode codepoint
ژ
Arabic Letter Jeh
U+0698
Other letter (Lo)

UTF-8 encoding: DA 98 (2 bytes).

Hex color
#000698
RGB(0, 6, 152)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.152.

Address
0.0.6.152
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.6.152

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

Position in π

The digit sequence 1688 first appears in π at position 5,152 of the decimal expansion (the 5,152ordinal-suffix:nd 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.