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. 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. It is the first 4-digit integer.

Notation

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. 1000 is the element of multiplicity in a toroidal board in the n-Queens problem, with respective indicator of 25 and count of 51. 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, of order 2000 in its regular form.

Totient values

1000 has a reduced totient value \lambda(n) of 100, and Euler totient \varphi(n) of 400. 11 integers have a totient value of 1000 (1111, 1255, ..., 3750). One thousand is also equal to the sum of Euler's totient summatory function \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. 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, where is the number of integer partitions of 23.

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: all represent prime numbers. Adding the prime 853 with its prime index of 147 yields 1000.

Sporadic groups

The one-thousandth prime number is 7919. It is a difference of 1 from the order of the smallest sporadic group:.

Numbers in the range 1001–1999

1001 to 1099

1100 to 1199

1200 to 1299

1300 to 1399

1400 to 1499

1500 to 1599

1600 to 1699

1700 to 1799

1800 to 1899

367 + 373 + 379 + 383 + 389 ) hexagonal number, centered pentagonal number, centered triangular number

1900 to 1999

Prime numbers

There are 135 prime numbers between 1000 and 2000: