# ⓘ 1000 (number)

## ⓘ 1000 (number)

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it is often written with a comma separating the thousands unit: 1.000.

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.

## 1. Notation

• 1 × 10 3 exactly - in scientific normalized exponential notation ;
• The decimal representation for one thousand is
• 1000 - a one followed by three zeros, in the general notation ;
• 1 E+3 exactly - in scientific E notation.
• 1 × 10 3 - in engineering notation, which for this number coincides with
• The SI prefix for a thousand units is "kilo-", abbreviated to "k" - for instance, a kilometre or "km" is a thousand metres.
• 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, which can be abbreviated with a "G" suffix.
• 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 1 000.

## 2. Properties

• 1000 is a Harshad number in base 10.
• The sum of Eulers 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 1000999, 1000999998997, and 1000999998997996995994993 are prime. The criterion excludes counting the number itself.

### 3.1. 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 1004 – heptanacci number 1005 – Mertens function zero 1008 – divisible by the number of primes below it 1009 – smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: 1010 – Mertens function zero 1011 – The largest number that 2 n contains 101 and doesnt contain 11011, and it is a Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 and 202 other bases. 1013 – Sophie Germain prime, centered square number, Mertens function zero 1014 – Mertens function zero 1015 – square pyramidal number 1016 – member of the Mian–Chowla sequence, stella octangula number 1018 – Mertens function zero 1019 – Sophie Germain prime, safe prime 1020 – polydivisible number 1022 – Friedman number 1023 – the highest number one can count to on ones fingers using binary; also the magic number used in Global Positioning System signals. 1024 – 2 10, the number of bytes in a kilobyte. 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. 1031 – exponent and number of ones for the largest proven base-10 repunit prime, Sophie Germain prime, super-prime 1033 – locale ID of English United States in some version of Windows. 1035 – triangular number, hexagonal number 1049 – Sophie Germain prime, highly cototient number 1051 – centered pentagonal number, centered decagonal number 1056 – pronic number 1060 – sum of the first 25 primes 1063 – super-prime, sum of seven consecutive primes 137 + 139 + 149 + 151 + 157 + 163 + 167 1071 – heptagonal number 1072 – centered heptagonal number 1079 – every positive integer is the sum of at most 1079 tenth powers. 1080 – pentagonal number 1081 – triangular number, member of Padovan sequence 1086 – Smith number, sum of totient function for first 59 integers 1087 – super-prime, cousin prime, lucky prime, Kynea number 1089 – 33 2, nonagonal number, centered octagonal number, first natural integer which digits in its decimal expression get reversed when multiplied by 9. 1091 – cousin prime and twin prime 1092 – divisible by the number of primes below it 1093 – the smallest Wieferich prime the only other known Wieferich prime is 3511, twin prime and star number

### 3.2. Selected numbers in the range 1001–1999 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 = 33 2 + 4 2 = 32 2 + 9 2 = 31 2 + 12 2 = 23 2 + 24 2 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 1153 – super-prime, Proth prime 1156 – 34 2, 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

### 3.3. Selected numbers in the range 1001–1999 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 – 35 2, triangular number, 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 – 12 2 + 33 2 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, this number 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 1288 – heptagonal number 1289 – Sophie Germain prime, Mertens function zero 1291 – Mertens function zero 1292 – Mertens function zero 1296 – 6 4, 36 2, 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

### 3.4. Selected numbers in the range 1001–1999 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 = 1 + 3 2 + 0 3 + 6 4. 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 – 11 3, centered heptagonal number, forms a Ruth–Aaron pair with 1330 under second definition. This is the only cube of the form x 2 + 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, 1369 – 37 2, 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

### 3.5. Selected numbers in the range 1001–1999 1400 to 1499

1404 – heptagonal number 1405 – 26 2 + 27 2, 7 2 + 8 2 + … + 16 2, 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 8½" 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 WXGAII computer displays 1441 – star number 1444 – 38 2, smallest pandigital number in Roman numerals 1447 – super-prime, happy number 1451 – Sophie Germain prime 1458 – maximum determinant of an 11 by 11 matrix of zeroes 1459 – Sexy prime with 1453, sum of nine consecutive primes 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181, pierpont prime 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

### 3.6. Selected numbers in the range 1001–1999 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 – 39 2, 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 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 number, Markov number, super-prime, emirp

### 3.7. Selected numbers in the range 1001–1999 1600 to 1699

1600 – 40 2, repdigit in base 7 4444 7, 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 – 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 – 41 2, smallest number yielded by the formula n 2 + n + 41 that is not a prime; centered octagonal number 1682 – member of a Ruth–Aaron pair first definition 1683 – 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

### 3.8. Selected numbers in the range 1001–1999 1700 to 1799

1701 – decagonal number, hull number of the U.S.S. Enterprise on Star Trek 1702 – palindromic in 3 consecutive bases: 898 14, 787 15, 6A6 16 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 1331 11 and 23 363 23 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 – 42 2 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. 1794 – nonagonal number

### 3.9. Selected numbers in the range 1001–1999 1800 to 1899

1800 – pentagonal pyramidal number, Achilles number, also, in da Pontes Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporellos 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 Sylvesters sequence, primary pseudoperfect number, only number for which n equals the denominator of the n th Bernoulli 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 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 – 43 2, palindromic in base 6 = 12321 6, 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

### 3.10. Selected numbers in the range 1001–1999 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 – 44 2, 18-gonal number, 324-gonal number. 1938 – Mertens function zero 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 1980 – pronic number 1984 – 11111000000 in binary, see also: 1984 disambiguation 1985 – centered square number 1987 – 300th prime number 1988 – sum of the first 33 primes