1000 (number) explained

Number:	1000
Divisor:	1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Roman Unicode:	M, m, ↀ
Unicode:	ↀ
Greek Prefix:	chilia
Latin Prefix:	milli
Lang1:	Tamil
Lang1 Symbol:	௲
Lang2:	Chinese
Lang2 Symbol:	千
Lang3:	Punjabi
Lang3 Symbol:	੧੦੦੦
Lang4:	Devanagari
Lang4 Symbol:	१०००
Lang5:	Armenian
Lang5 Symbol:	Ռ
Lang6:	Egyptian hieroglyph
Lang6 Symbol:

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

A group of one thousand things is sometimes known, from Ancient Greek, as a chiliad.^[1] A period of one thousand years may be known as a chiliad or, more often from Latin, as a millennium. The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand.

Notation

• The decimal representation for one thousand is
  • 1000—a one followed by three zeros, in the general notation;
  • 1 × 10³—in engineering notation, which for this number coincides with:
  • 1 × 10³ exactly—in scientific normalized exponential notation;
  • 1 E+3 exactly—in scientific E notation.
• The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
• In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
• Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
• A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States, this is sometimes abbreviated with a "G" suffix.

Properties

1000 is the 10th icositetragonal number, or 24-gonal number. It is also the 16th generalized 30-gonal number.

1000 is the Wiener index of cycle length 20, also the sum of labeled boxes arranged as a pyramid with base 1 – 20.^{[2] [3]}

1000 is the element of multiplicity in a

24 x 24 toroidal board in the n-Queens problem, with respective indicator of 25 and count of 51.^[4]

1000 is the number of strict partitions of 50 containing the sum of no subset of the parts.

A chiliagon is a 1000-sided polygon,^[5] of order 2000 in its regular form.

Totient values

1000 has a reduced totient value

λ (n) of 100, and Euler totient \varphi(n) of 400.^[6]

11 integers have a totient value of 1000 (1111, 1255, ..., 3750).

\Phi(n) over the first 57 integers.

Repdigits

In decimal, multiples of one thousand are totient values of four-digit repdigits:

In the list of composite numbers, 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number.^[7] Also,

1600 = 40² is the totient value of 4000, as well as 6000, whose collective sum is 10000, where 6000 is the totient of 9999, one less than 10⁴.

The sum of the first nine prime numbers up to 23 is 100, with

\varphi(p( 23 )) = 1000 , where p( 23 ) = 1255 is the number of integer partitions of 23.^[8]

Prime values

Using decimal representation as well,

On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973.

1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:^[9] all represent prime numbers.

Notes and References

1. Web site: chiliad. . https://archive.today/20220325170822/https://www.merriam-webster.com/dictionary/chiliad. March 25, 2022. live.
2. Web site: Ngaokrajang, Kival . Sloane, N. J. A. . Neil Sloane . Illustration for n equal to 1..10 [A034828]. ]. . OEIS Foundation .
3. Janjic . M. . Petkovic . B. . A Counting Function . 2013 . 14,15 . 1301.4550 . math.CO .
4. I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639.
5. Aṣiru . Muniru A. . All square chiliagonal numbers . International Journal of Mathematical Education in Science and Technology . 47 . 7 . . Oxfordshire . 2016 . 1123–1134 . 10.1080/0020739X.2016.1164346 . 2016IJMES..47.1123A . 3528540 . 1396.97005 . 123953958 .
6. Euler totient function phi(n): count numbers <= n and prime to n.
7. 2023-12-18 .
8. a(n) = phi(p(n)), where phi is Euler's totient function (A000010) and p(n) is the number of partitions of n (A000041).
9. Web site: 1000. Prime Curious!. https://archive.today/20220325171202/https://www.gcflcm.com/factors-of-1000. March 25, 2022. live.