# 1000 (number)

(Redirected from 1011 (number))

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.

 ← 999 1000 1001 →
Cardinalone thousand
Ordinal1000th
(one thousandth)
Factorization23 × 53
Divisors1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Greek numeral,Α´
Roman numeralM
Unicode symbol(s)
Greek prefixchilia
Latin prefixmilli
Binary11111010002
Ternary11010013
Octal17508
Duodecimal6B412
Tamil
Chinese
Punjabi੧੦੦੦

It may also be described as the short thousand in historical discussion of medieval contexts where it might be confused with the Germanic concept of the "long thousand" (1200).

A period of 1,000 years is sometimes termed, after the Greek root, a chiliad. A chiliad of other objects means 1,000 of them.

## Notation

• The decimal representation for one thousand is
• The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilometre or "km" is a thousand metres.
• 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": 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 of America this is sometimes abbreviated with a "G" suffix.
• The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.

## Properties

• 1000 is a Harshad number in base 10.
• The sum of Euler's totient function over the first 57 integers is 1000.
• Prime Curios! mentions that 1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers (1 000 999, 1 000 999 998 997, and 1 000 999 998 997 996 995 994 993 are prime). The criterion excludes counting the number itself.

## Selected numbers in the range 1001–1999

### 1001 to 1099

1001 = sphenic number (7 × 11 × 13), pentagonal number, pentatope number
1002 = sphenic number, Mertens function zero, abundant number, number of partitions of 22
1003 = the product of some prime p and the pth prime, namely p = 17.
1004 = heptanacci number
1005 = Mertens function zero, decagonal pyramidal number
1006 = number that is the sum of 7 positive 5th powers
1007 = number that is the sum of 8 positive 5th powers
1008 = divisible by the number of primes below it
1009 = smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (83811, 47415, 2F219, 1I124, 18128). It is also a Lucky prime.
1010 = 103 + 10, Mertens function zero
1011 = the largest n such that 2n contains 101 and doesn't contain 11011; also a Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction
1012 = ternary number, (3210) quadruple triangular number (triangular number is 253), number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction
1013 = Sophie Germain prime, centered square number, Mertens function zero
1014 = 210-10, Mertens function zero
1015 = square pyramidal number
1016 = member of the Mian–Chowla sequence, stella octangula number
1017 = generalized triacontagonal number
1018 = Mertens function zero, 101816 + 1 is prime
1019 = Sophie Germain prime, safe prime
1020 = polydivisible number
1021 = twin prime with 1019. It is also a Lucky prime.
1022 = Friedman number
1023 = the highest number one can count to on one's fingers using binary; also the magic number used in Global Positioning System signals.
1024 = 322 = 45 = 210, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number.
1025 = Proth number 210 + 1; member of Moser–de Bruijn sequence, because its base-4 representation (1000014) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (45 + 40); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle
1026 = sum of two distinct powers of 2 (1024 + 2)
1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.
1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9.
1029 = can be written from base 2 to base 18 using only the digits 0 to 9.
1030 = generalized heptagonal number
1031 = exponent and number of ones for the largest proven base-10 repunit prime, Sophie Germain prime, super-prime
1032 = sum of two distinct powers of 2 (1024 + 8)
1033 = emirp, twin prime with 1031
1034 = sum of 12 positive 9th powers
1035 = triangular number, hexagonal number
1036 = central polygonal number
1037 = number in E-toothpick sequence
1038 = even integer that is an unordered sum of two primes in exactly n ways
1039 = prime of the form 8n+7
1040 = sum of distinct powers of 4
1041 = sum of 11 positive 5th powers
1042 = sum of 12 positive 5th powers
1043 = number whose sum of even digits and sum of odd digits are even
1044 = sum of distinct powers of 4
1045 = octagonal number
1046 = coefficient of f(q) (3rd order mock theta function)
1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum
1048 = number of partitions of n into squarefree parts
1049 = Sophie Germain prime, highly cototient number
1050 = 10508 to decimal becomes a pronic number (55210)
1051 = centered pentagonal number, centered decagonal number
1052 = number that is the sum of 9 positive 6th powers
1053 = triangular matchstick number
1054 = centered triangular number
1055 = number that is the sum of 12 positive 6th powers
1056 = pronic number
1057 = central polygonal number
1058 = number that is the sum of 4 positive 5th powers
1059 = number n such that n4 is written in the form of a sum of four positive 4th powers
1060 = sum of the first 25 primes
1061 = emirp, twin prime with 1063
1062 = number that is not the sum of two palindromes
1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime
1064 = sum of two positive cubes
1065 = generalized duodecagonal 
1066 = number whose sum of their divisors is a square
1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones
1068 = number that is the sum of 7 positive 5th powers
1069 = emirp
1070 = number that is the sum of 9 positive 5th powers
1071 = heptagonal number
1072 = centered heptagonal number
1073 = number that is the sum of 12 positive 5th powers
1074 = number that is not the sum of two palindromes
1075 = number non-sum of two palindromes
1076 = number of strict trees weight n
1077 = number where 7 outnumbers every other digit in the number
1078 = Euler transform of negative integers
1079 = every positive integer is the sum of at most 1079 tenth powers.
1080 = pentagonal number
1081 = triangular number, member of Padovan sequence
1082 = central polygonal number
1083 = three-quarter square
1084 = third spoke of a hexagonal spiral
1085 = number of partitions of n into distinct parts > or = 2
1086 = Smith number, sum of totient function for first 59 integers
1087 = super-prime, cousin prime, lucky prime
1088 = octo-triangular number, (triangular number result being 136) sum of two distinct powers of 2, (1024 + 64) number that is divisible by exactly seven primes with the inclusion of multiplicity
1089 = 332, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.
1090 = sum of 5 positive 5th powers
1091 = cousin prime and twin prime with 1093
1092 = divisible by the number of primes below it
1093 = the smallest Wieferich prime (the only other known Wieferich prime is 3511), twin prime with 1091 and star number
1094 = sum of 9 positive 5th powers
1095 = sum of 10 positive 5th powers, number that is not the sum of two palindromes
1096 = hendecagonal number
1097 = emirp
1098 = multiple of 9 containing digit 9 in its base-10 representation
1099 = number where 9 outnumbers every other digit

### 1100 to 1199

1102 = sum of totient function for first 60 integers
1103 = Sophie Germain prime, balanced prime
1104 = Keith number
1105 = Carmichael number, magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number, centered square number, 1105 = 332 + 42 = 322 + 92 = 312 + 122 = 232 + 242
1111 = repdigit
1116 = divisible by the number of primes below it
1122 = pronic number, divisible by the number of primes below it
1123 = balanced prime
1124 = Leyland number
1128 = triangular number, hexagonal number, divisible by the number of primes below it
1134 = divisible by the number of primes below it
1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138; particularly, a special code for Easter eggs on Star Wars DVDs.
1140 = tetrahedral number
1151 = first prime following a prime gap of 22.
1152 = highly totient number, 3-smooth number (27×32)
1153 = super-prime, Proth prime
1156 = 342, octahedral number, centered pentagonal number, centered hendecagonal number.
1159 = member of the Mian–Chowla sequence
1161 = sum of the first 26 primes
1162 = pentagonal number, sum of totient function for first 61 integers
1169 = highly cototient number
1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match
1171 = super-prime
1176 = triangular number
1177 = heptagonal number
1184 = amicable number with 1210
1187 = safe prime, Stern prime, balanced prime
1190 = pronic number
1192 = sum of totient function for first 62 integers
1198 = centered heptagonal number

### 1200 to 1299

1200 = the long thousand, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages, the number of households the Nielsen ratings sample
1201 = centered square number, super-prime, centered decagonal number
1210 = amicable number with 1184
1213 = emirp
1216 = nonagonal number
1217 = super-prime, Proth prime
1219 = Mertens function zero
1220 = Mertens function zero
1223 = Sophie Germain prime, balanced prime, 200th prime number
1225 = 352, square triangular number, hexagonal number, centered octagonal number
1228 = sum of totient function for first 63 integers
1229 = Sophie Germain prime, number of primes between 0 and 10000
1233 = 122 + 332
1237 = prime of the form 2p-1
1240 = square pyramidal number
1241 = centered cube number
1242 = decagonal number
1247 = pentagonal number
1249 = emirp, trimorphic number
1255 = Mertens function zero
1256 = Mertens function zero
1258 = Mertens function zero
1259 = highly cototient number
1260 = highly composite number, pronic number, the smallest vampire number, sum of totient function for first 64 integers, and appears twice in the Book of Revelation
1261 = star number, Mertens function zero
1264 = sum of the first 27 primes
1266 = centered pentagonal number, Mertens function zero
1270 = Mertens function zero
1275 = triangular number, sum of the first 50 natural numbers
1279 = Mertens function zero, Mersenne prime exponent
1280 = Mertens function zero
1282 = Mertens function zero
1283 = safe prime
1285 = Mertens function zero, number of free nonominoes
1288 = heptagonal number
1289 = Sophie Germain prime, Mertens function zero
1291 = Mertens function zero
1292 = Mertens function zero
1296 = 362 = 64, sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard, also the maximum font size allowed in Adobe InDesign
1297 = super-prime, Mertens function zero
1299 = Mertens function zero

### 1300 to 1399

1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match
1301 = centered square number
1302 = Mertens function zero
1306 = Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 11 + 32 + 03 + 64. 135, 175, 518, and 598 also have this property.
1307 = safe prime
1308 = sum of totient function for first 65 integers
1309 = the first sphenic number followed by two consecutive such number
1312 = member of the Mian-Chowla sequence; code for "ACAB" itself an acronym for "all cops are bastards"
1318 = Mertens function zero
1319 = safe prime
1325 = Markov number
1326 = triangular number, hexagonal number, Mertens function zero
1327 = first prime followed by 33 consecutive composite numbers
1328 = sum of totient function for first 66 integers
1329 = Mertens function zero
1330 = tetrahedral number, forms a Ruth–Aaron pair with 1331 under second definition
1331 = 113, centered heptagonal number, forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form x2 + x − 1, for x = 36.
1332 = pronic number
1335 = pentagonal number, Mertens function zero
1336 = Mertens function zero
1337 = Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.
1338 = Mertens function zero
1342 = Mertens function zero
1350 = nonagonal number
1361 = first prime following a prime gap of 34, centered decagonal number
1365 = pentatope number
1367 = safe prime, balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),
1369 = 372, centered octagonal number
1371 = sum of the first 28 primes
1378 = triangular number
1379 = magic constant of n × n normal magic square and n-queens problem for n = 14.
1381 = centered pentagonal number
1387 = 5th Fermat pseudoprime of base 2, 22nd centered hexagonal number and the 19th decagonal number, second Super-Poulet number.
1394 = sum of totient function for first 67 integers
1395 = vampire number, member of the Mian–Chowla sequence

### 1400 to 1499

1404 = heptagonal number
1405 = 262 + 272, 72 + 82 + ... + 162, centered square number
1406 = pronic number, semi-meandric number
1409 = super-prime, Sophie Germain prime, smallest number whose eighth power is the sum of 8 eighth powers, Proth prime
1419 = Zeisel number
1425 = self-descriptive number in base 5
1426 = sum of totient function for first 68 integers, pentagonal number
1430 = Catalan number
1431 = triangular number, hexagonal number
1432 = member of Padovan sequence
1433 = super-prime, Typical port used for remote connections to Microsoft SQL Server databases
1435 = vampire number; the standard railway gauge in millimetres, equivalent to 4 feet 8+12 inches (1.435 m)
1439 = Sophie Germain prime, safe prime
1440 = a highly totient number and a 481-gonal number. Also, the number of minutes in one day, the blocksize of a standard 3+1/2 floppy disk, and the horizontal resolution of WXGA(II) computer displays
1441 = star number
1444 = 382, smallest pandigital number in Roman numerals
1447 = super-prime, happy number
1451 = Sophie Germain prime
1453 = Sexy prime with 1459
1458 = maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×36)
1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime
1460 = Nickname of the original "Doc Marten's" boots, released 1 April 1960
1469 = octahedral number, highly cototient number
1470 = pentagonal pyramidal number, sum of totient function for first 69 integers
1471 = super-prime, centered heptagonal number
1480 = sum of the first 29 primes
1481 = Sophie Germain prime
1482 = pronic number
1485 = triangular number
1487 = safe prime
1490 = tetranacci number
1491 = nonagonal number, Mertens function zero
1492 = Mertens function zero
1493 = Stern prime
1494 = sum of totient function for first 70 integers
1496 = square pyramidal number
1499 = Sophie Germain prime, super-prime

### 1500 to 1599

1501 = centered pentagonal number
1510 = deficient number, odious number
1511 = Sophie Germain prime, balanced prime
1513 = centered square number
1518 = Mertens function zero
1519 = Mertens function zero
1520 = pentagonal number, Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition
1521 = 392, Mertens function zero, centered octagonal number, forms a Ruth–Aaron pair with 1520 under second definition
1523 = super-prime, Mertens function zero, safe prime, member of the Mian–Chowla sequence
1524 = Mertens function zero
1525 = heptagonal number, Mertens function zero
1527 = Mertens function zero
1528 = Mertens function zero
1530 = vampire number
1531 = centered decagonal number, Mertens function zero
1532 = Mertens function zero
1535 = Thabit number
1536 = a common size of microplate, 3-smooth number (29×3)
1537 = Keith number, Mertens function zero
1540 = triangular number, hexagonal number, decagonal number, tetrahedral number
1543 = Mertens function zero
1544 = Mertens function zero
1546 = Mertens function zero
1556 = sum of the squares of the first nine primes
1559 = Sophie Germain prime
1560 = pronic number
1564 = sum of totient function for first 71 integers
1572 = member of the Mian–Chowla sequence
1575 = odd abundant number
1583 = Sophie Germain prime
1588 = sum of totient function for first 72 integers
1593 = sum of the first 30 primes
1596 = triangular number
1597 = Fibonacci prime, Markov prime, super-prime, emirp

### 1600 to 1699

1600 = 402, repdigit in base 7 (44447), street number on Pennsylvania Avenue of the White House, length in meters of a common High School Track Event, perfect score on SAT (except from 2005-2015)
1601 = Sophie Germain prime, Proth prime, the novel 1601 (Mark Twain)
1617 = pentagonal number
1618 = centered heptagonal number
1619 = palindromic prime in binary, safe prime
1621 = super-prime
1625 = centered square number
1626 = centered pentagonal number
1633 = star number
1634 = Narcissistic number in base 10
1638 = harmonic divisor number
1639 = nonagonal number
1640 = pronic number
1649 = highly cototient number, Leyland number
1651 = heptagonal number
1653 = triangular number, hexagonal number
1657 = cuban prime, prime of the form 2p-1
1660 = sum of totient function for first 73 integers
1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)
1669 = super-prime
1679 = highly cototient number, semiprime (23 × 73, see also Arecibo message)
1680 = highly composite number
1681 = 412, smallest number yielded by the formula n2 + n + 41 that is not a prime; centered octagonal number
1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)
1695 = magic constant of n × n normal magic square and n-queens problem for n = 15.
1696 = sum of totient function for first 74 integers

### 1700 to 1799

1701 = decagonal number, hull number of the U.S.S. Enterprise on Star Trek
1702 = palindromic in 3 consecutive bases: 89814, 78715, 6A616
1705 = tribonacci number
1709 = first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773
1711 = triangular number, centered decagonal number
1717 = pentagonal number
1720 = sum of the first 31 primes
1722 = Giuga number, pronic number
1723 = super-prime
1728 = the quantity expressed as 1000 in duodecimal, that is, the cube of twelve (called a great gross), and so, the number of cubic inches in a cubic foot, palindromic in base 11 (133111) and 23 (36323)
1729 = taxicab number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical Hair closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.
1733 = Sophie Germain prime, palindromic in bases 3, 18, 19.
1736 = sum of totient function for first 75 integers
1741 = super-prime, centered square number
1747 = balanced prime
1753 = balanced prime
1756 = centered pentagonal number
1760 = the number of yards in a mile
1764 = 422
1770 = triangular number, hexagonal number, Town of Seventeen Seventy in Australia
1771 = tetrahedral number
1772 = centered heptagonal number, sum of totient function for first 76 integers
1782 = heptagonal number
1785 = square pyramidal number
1787 = super-prime, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)
1791 = largest natural number that cannot be expressed as a sum of at most four hexagonal numbers.
1792 = Granville number
1794 = nonagonal number

### 1800 to 1899

1800 = pentagonal pyramidal number, Achilles number, also, in da Ponte's Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally
1801 = cuban prime, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)
1806 = pronic number, product of first four terms of Sylvester's sequence, primary pseudoperfect number, only number for which n equals the denominator of the nth Bernoulli number, Schröder number
1807 = fifth term of Sylvester's sequence
1811 = Sophie Germain prime
1820 = pentagonal number, pentatope number
1821 = member of the Mian–Chowla sequence
1823 = super-prime, safe prime
1827 = vampire number
1828 = meandric number, open meandric number, appears twice in the first 10 decimal digits of e
1830 = triangular number
1832 = sum of totient function for first 77 integers
1834 = octahedral number, sum of the cubes of the first five primes
1836 = factor by which a proton is more massive than an electron
1837 = star number
1841 = Mertens function zero
1843 = Mertens function zero
1844 = Mertens function zero
1845 = Mertens function zero
1847 = super-prime
1849 = 432, palindromic in base 6 (= 123216), centered octagonal number
1851 = sum of the first 32 primes
1853 = Mertens function zero
1854 = Mertens function zero
1856 = sum of totient function for first 78 integers
1857 = Mertens function zero
1861 = centered square number, Mertens function zero
1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition
1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition
1864 = Mertens function zero
1866 = Mertens function zero
1870 = decagonal number
1885 = Zeisel number
1889 = Sophie Germain prime, highly cototient number
1891 = triangular number, hexagonal number, centered pentagonal number
1892 = pronic number
1896 = member of the Mian-Chowla sequence
1897 = member of Padovan sequence

### 1900 to 1999

1900 = 1900 (film) or Novecento, 1976 movie
1901 = Sophie Germain prime, centered decagonal number
1907 = safe prime, balanced prime
1909 = hyperperfect number
1913 = super-prime
1918 = heptagonal number
1926 = pentagonal number
1929 = Mertens function zero
1931 = Sophie Germain prime
1933 = centered heptagonal number, prime number
1934 = sum of totient function for first 79 integers
1936 = 442, 18-gonal number, 324-gonal number.
1938 = Mertens function zero
1944 = 3-smooth number (23×35)
1951 = cuban prime
1953 = triangular number
1956 = nonagonal number
1966 = sum of totient function for first 80 integers
1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize
1973 = Sophie Germain prime, Leonardo prime
1980 = pronic number