# 1000 (number)

(Redirected from 1789 (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.[1]

## 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.[2]

## 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.[3]

## 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[4]
1005 = Mertens function zero, decagonal pyramidal number[5]
1006 = number that is the sum of 7 positive 5th powers[6]
1007 = number that is the sum of 8 positive 5th powers[7]
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,[8] 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[9]
1012 = ternary number, (3210) quadruple triangular number (triangular number is 253),[10] number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction[9]
1013 = Sophie Germain prime,[11] centered square number,[12] Mertens function zero
1014 = 210-10,[13] Mertens function zero, sum of the nontriangular numbers between successive triangular numbers
1015 = square pyramidal number[14]
1016 = member of the Mian–Chowla sequence,[15] stella octangula number, number of cubes of edge length 1 required to make a hollow cube of edge length 14
1017 = generalized triacontagonal number[16]
1018 = Mertens function zero, 101816 + 1 is prime[17]
1019 = Sophie Germain prime,[11] safe prime[18]
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; number of compositions of 12 whose run-lengths are either weakly increasing or weakly decreasing;[19] 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; number of primes <= 213.[20]
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,[21] Sophie Germain prime,[11] 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[22]
1035 = triangular number,[23] hexagonal number[24]
1036 = central polygonal number[25]
1037 = number in E-toothpick sequence[26]
1038 = even integer that is an unordered sum of two primes in exactly n ways[27]
1039 = prime of the form 8n+7,[28] number of partitions of 30 that do not contain 1 as a part[29]
1040 = sum of distinct powers of 4[30]
1041 = sum of 11 positive 5th powers[31]
1042 = sum of 12 positive 5th powers[32]
1043 = number whose sum of even digits and sum of odd digits are even[33]
1044 = sum of distinct powers of 4[30]
1045 = octagonal number[34]
1046 = coefficient of f(q) (3rd order mock theta function)[35]
1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum[36]
1048 = number of partitions of n into squarefree parts[37]
1049 = Sophie Germain prime,[11] highly cototient number[38]
1050 = 10508 to decimal becomes a pronic number (55210)[39]
1051 = centered pentagonal number,[40] centered decagonal number
1052 = number that is the sum of 9 positive 6th powers[41]
1053 = triangular matchstick number[42]
1054 = centered triangular number[43]
1055 = number that is the sum of 12 positive 6th powers[44]
1056 = pronic number[45]
1057 = central polygonal number[46]
1058 = number that is the sum of 4 positive 5th powers,[47] area of a square with diagonal 46[48]
1059 = number n such that n4 is written in the form of a sum of four positive 4th powers[49]
1060 = sum of the first 25 primes
1061 = emirp, twin prime with 1063
1062 = number that is not the sum of two palindromes[50]
1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[51]
1064 = sum of two positive cubes[52]
1065 = generalized duodecagonal[53]
1066 = number whose sum of their divisors is a square[54]
1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones[55]
1068 = number that is the sum of 7 positive 5th powers[6]
1069 = emirp[56]
1070 = number that is the sum of 9 positive 5th powers[57]
1071 = heptagonal number[58]
1072 = centered heptagonal number[59]
1073 = number that is the sum of 12 positive 5th powers[32]
1074 = number that is not the sum of two palindromes[50]
1075 = number non-sum of two palindromes[50]
1076 = number of strict trees weight n[60]
1077 = number where 7 outnumbers every other digit in the number[61]
1078 = Euler transform of negative integers[62]
1079 = every positive integer is the sum of at most 1079 tenth powers.
1080 = pentagonal number[63]
1081 = triangular number,[23] member of Padovan sequence[64]
1082 = central polygonal number[25]
1083 = three-quarter square[65]
1084 = third spoke of a hexagonal spiral,[66] 108464 + 1 is prime
1085 = number of partitions of n into distinct parts > or = 2[67]
1086 = Smith number,[68] sum of totient function for first 59 integers
1087 = super-prime, cousin prime, lucky prime[69]
1088 = octo-triangular number, (triangular number result being 136)[70] sum of two distinct powers of 2, (1024 + 64)[71] number that is divisible by exactly seven primes with the inclusion of multiplicity[72]
1089 = 332, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.[73]
1090 = sum of 5 positive 5th powers[74]
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[75]), twin prime with 1091 and star number[76]
1094 = sum of 9 positive 5th powers,[57] 109464 + 1 is prime
1095 = sum of 10 positive 5th powers,[77] number that is not the sum of two palindromes
1096 = hendecagonal number[78]
1097 = emirp[56]
1098 = multiple of 9 containing digit 9 in its base-10 representation[79]
1099 = number where 9 outnumbers every other digit[80]

### 1100 to 1199

1102 = sum of totient function for first 60 integers
1103 = Sophie Germain prime,[11] balanced prime[81]
1104 = Keith number[82]
1105 = Carmichael number,[83] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,[84] centered square number,[12] 1105 = 332 + 42 = 322 + 92 = 312 + 122 = 232 + 242
1108 = number k such that k^64 + 1 is prime
1111 = repdigit
1116 = divisible by the number of primes below it
1120 = number k such that k^64 + 1 is prime
1122 = pronic number,[45] divisible by the number of primes below it
1123 = balanced prime[81]
1124 = Leyland number[85]
1128 = triangular number,[23] hexagonal number,[24] divisible by the number of primes below it
1134 = divisible by the number of primes below it, triangular matchstick number[86]
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.
1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph[87]
1140 = tetrahedral number[88]
1151 = first prime following a prime gap of 22.[89]
1152 = highly totient number,[90] 3-smooth number (27×32), area of a square with diagonal 48[48]
1153 = super-prime, Proth prime[91]
1156 = 342, octahedral number,[92] centered pentagonal number,[40] centered hendecagonal number.[93]
1159 = member of the Mian–Chowla sequence,[15] a centered octahedral number[94]
1161 = sum of the first 26 primes
1162 = pentagonal number,[63] sum of totient function for first 61 integers
1169 = highly cototient number[38]
1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match
1171 = super-prime
1176 = triangular number[23]
1177 = heptagonal number[58]
1178 = number of cubes of edge length 1 required to make a hollow cube of edge length 15
1184 = amicable number with 1210[95]
1187 = safe prime,[18] Stern prime,[96] balanced prime[81]
1190 = pronic number[45]
1192 = sum of totient function for first 62 integers
1193 = a number such that 41193 - 31193 is prime
1198 = centered heptagonal number[59]

### 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,[97] number k such that k^64 + 1 is prime
1201 = centered square number,[12] super-prime, centered decagonal number
1210 = amicable number with 1184[98]
1213 = emirp
1216 = nonagonal number[99]
1217 = super-prime, Proth prime[91]
1218 = triangular matchstick number[86]
1219 = Mertens function zero
1220 = Mertens function zero
1223 = Sophie Germain prime,[11] balanced prime, 200th prime number[81]
1225 = 352, square triangular number,[100] hexagonal number,[24] centered octagonal number[101]
1228 = sum of totient function for first 63 integers
1229 = Sophie Germain prime,[11] number of primes between 0 and 10000
1233 = 122 + 332
1237 = prime of the form 2p-1
1238 = number of partitions of 31 that do not contain 1 as a part[29]
1240 = square pyramidal number[14]
1241 = centered cube number[102]
1242 = decagonal number[84]
1247 = pentagonal number[63]
1249 = emirp, trimorphic number[103]
1250 = area of a square with diagonal 50[48]
1255 = Mertens function zero
1256 = Mertens function zero
1258 = Mertens function zero
1259 = highly cototient number[38]
1260 = highly composite number,[104] pronic number,[45] the smallest vampire number,[105] sum of totient function for first 64 integers, and appears twice in the Book of Revelation
1261 = star number,[76] Mertens function zero
1264 = sum of the first 27 primes
1266 = centered pentagonal number,[40] Mertens function zero
1270 = Mertens function zero
1274 = sum of the nontriangular numbers between successive triangular numbers
1275 = triangular number,[23] sum of the first 50 natural numbers
1279 = Mertens function zero, Mersenne prime exponent
1280 = Mertens function zero, number of parts in all compositions of 9.[106]
1282 = Mertens function zero
1283 = safe prime[18]
1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.[107]
1288 = heptagonal number[58]
1289 = Sophie Germain prime,[11] 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[12]
1302 = Mertens function zero
1305 = triangular matchstick number[86]
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[18]
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;[15] code for "ACAB" itself an acronym for "all cops are bastards"[108]
1318 = Mertens function zero
1319 = safe prime[18]
1325 = Markov number[109]
1326 = triangular number,[23] hexagonal number,[24] 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,[85] forms a Ruth–Aaron pair with 1331 under second definition
1331 = 113, centered heptagonal number,[59] 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[45]
1335 = pentagonal number,[63] 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[99]
1352 = number of cubes of edge length 1 required to make a hollow cube of edge length 16
1361 = first prime following a prime gap of 34,[89] centered decagonal number
1365 = pentatope number[110]
1367 = safe prime,[18] 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),[81]
1369 = 372, centered octagonal number[101]
1371 = sum of the first 28 primes
1378 = triangular number[23]
1379 = magic constant of n × n normal magic square and n-queens problem for n = 14.
1381 = centered pentagonal number[40]
1387 = 5th Fermat pseudoprime of base 2,[111] 22nd centered hexagonal number and the 19th decagonal number,[84] second Super-Poulet number.[112]
1394 = sum of totient function for first 67 integers
1395 = vampire number,[105] member of the Mian–Chowla sequence[15] triangular matchstick number[86]

### 1400 to 1499

1404 = heptagonal number[58]
1405 = 262 + 272, 72 + 82 + ... + 162, centered square number[12]
1406 = pronic number,[45] semi-meandric number[113]
1409 = super-prime, Sophie Germain prime,[11] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime[91]
1419 = Zeisel number[114]
1425 = self-descriptive number in base 5
1426 = sum of totient function for first 68 integers, pentagonal number[63]
1430 = Catalan number[115]
1431 = triangular number,[23] hexagonal number[24]
1432 = member of Padovan sequence[64]
1433 = super-prime, Typical port used for remote connections to Microsoft SQL Server databases
1435 = vampire number;[105] the standard railway gauge in millimetres, equivalent to 4 feet 8+12 inches (1.435 m)
1439 = Sophie Germain prime,[11] safe prime[18]
1440 = a highly totient number[90] 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[76]
1444 = 382, smallest pandigital number in Roman numerals
1447 = super-prime, happy number
1451 = Sophie Germain prime[11]
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,[92] highly cototient number[38]
1470 = pentagonal pyramidal number,[116] sum of totient function for first 69 integers
1471 = super-prime, centered heptagonal number[59]
1479 = number of planar partitions of 12[117]
1480 = sum of the first 29 primes
1481 = Sophie Germain prime[11]
1482 = pronic number,[45] number of unimodal compositions of 15 where the maximal part appears once[118]
1485 = triangular number
1487 = safe prime[18]
1488 = triangular matchstick number[86]
1490 = tetranacci number[119]
1491 = nonagonal number,[99] Mertens function zero
1492 = Mertens function zero
1493 = Stern prime[96]
1494 = sum of totient function for first 70 integers
1496 = square pyramidal number[14]
1499 = Sophie Germain prime,[11] super-prime

### 1500 to 1599

1501 = centered pentagonal number[40]
1507 = number of partitions of 32 that do not contain 1 as a part[29]
1510 = deficient number, odious number
1511 = Sophie Germain prime,[11] balanced prime[81]
1513 = centered square number[12]
1518 = Mertens function zero
1519 = Mertens function zero
1520 = pentagonal number,[63] Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition
1521 = 392, Mertens function zero, centered octagonal number,[101] forms a Ruth–Aaron pair with 1520 under second definition
1523 = super-prime, Mertens function zero, safe prime,[18] member of the Mian–Chowla sequence[15]
1524 = Mertens function zero
1525 = heptagonal number,[58] Mertens function zero
1527 = Mertens function zero
1528 = Mertens function zero
1530 = vampire number[105]
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,[82] Mertens function zero
1540 = triangular number, hexagonal number,[24] decagonal number,[84] tetrahedral number[85]
1543 = Mertens function zero
1544 = Mertens function zero
1546 = Mertens function zero
1556 = sum of the squares of the first nine primes
1558 = number k such that k^64 + 1 is prime
1559 = Sophie Germain prime[11]
1560 = pronic number[45]
1561 = a centered octahedral number,[94] number of series-reduced trees with 19 nodes[120]
1564 = sum of totient function for first 71 integers
1566 = number k such that k^64 + 1 is prime
1572 = member of the Mian–Chowla sequence[15]
1575 = odd abundant number,[121] sum of the nontriangular numbers between successive triangular numbers
1583 = Sophie Germain prime
1584 = triangular matchstick number[86]
1585 = Riordan number
1588 = sum of totient function for first 72 integers
1593 = sum of the first 30 primes
1595 = number of non-isomorphic set-systems of weight 10
1596 = triangular number
1597 = Fibonacci prime,[122] Markov prime,[109] 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,[91] the novel 1601 (Mark Twain)
1617 = pentagonal number[63]
1618 = centered heptagonal number[59]
1619 = palindromic prime in binary, safe prime[18]
1621 = super-prime
1625 = centered square number[12]
1626 = centered pentagonal number[40]
1630 = number k such that k^64 + 1 is prime
1633 = star number[76]
1634 = Narcissistic number in base 10
1638 = harmonic divisor number[123]
1639 = nonagonal number[99]
1640 = pronic number[45]
1649 = highly cototient number,[38] Leyland number[85]
1651 = heptagonal number[58]
1653 = triangular number, hexagonal number[24]
1657 = cuban prime,[124] 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,[38] semiprime (23 × 73, see also Arecibo message)
1680 = highly composite number[104]
1681 = 412, smallest number yielded by the formula n2 + n + 41 that is not a prime; centered octagonal number[101]
1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)
1683 = triangular matchstick number[86]
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 = ${\displaystyle \left\{{8 \atop 4}\right\}}$ , 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[125]
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[63]
1720 = sum of the first 31 primes
1722 = Giuga number,[126] pronic number[45]
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[12]
1747 = balanced prime[81]
1753 = balanced prime[81]
1756 = centered pentagonal number[40]
1760 = the number of yards in a mile
1764 = 422
1770 = triangular number, hexagonal number,[24] Town of Seventeen Seventy in Australia
1771 = tetrahedral number[85]
1772 = centered heptagonal number,[59] sum of totient function for first 76 integers
1782 = heptagonal number[58]
1785 = square pyramidal number,[14] triangular matchstick number[86]
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,[99] number of partitions of 33 that do not contain 1 as a part[29]

### 1800 to 1899

1800 = pentagonal pyramidal number,[116] 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)[124]
1804 = number k such that k^64 + 1 is prime
1806 = pronic number,[45] product of first four terms of Sylvester's sequence, primary pseudoperfect number,[127] only number for which n equals the denominator of the nth Bernoulli number,[128] Schröder number[129]
1807 = fifth term of Sylvester's sequence[130]
1811 = Sophie Germain prime
1820 = pentagonal number,[63] pentatope number,[110] number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing[19]
1821 = member of the Mian–Chowla sequence[15]
1823 = super-prime, safe prime[18]
1827 = vampire number[105]
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,[92] sum of the cubes of the first five primes
1836 = factor by which a proton is more massive than an electron
1837 = star number[76]
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[101]
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,[12] 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[84]
1876 = number k such that k^64 + 1 is prime
1885 = Zeisel number[114]
1889 = Sophie Germain prime, highly cototient number[38]
1890 = triangular matchstick number[86]
1891 = triangular number, hexagonal number,[24] centered pentagonal number[40]
1892 = pronic number[45]
1896 = member of the Mian-Chowla sequence[15]
1897 = member of Padovan sequence,[64] number of triangle-free graphs on 9 vertices[131]

### 1900 to 1999

1900 = number of primes <= 214.[20] Also 1900 (film) or Novecento, 1976 movie
1901 = Sophie Germain prime, centered decagonal number
1907 = safe prime,[18] balanced prime[81]
1909 = hyperperfect number[132]
1913 = super-prime
1918 = heptagonal number[58]
1920 = sum of the nontriangular numbers between successive triangular numbers
1926 = pentagonal number[63]
1929 = Mertens function zero
1931 = Sophie Germain prime
1933 = centered heptagonal number,[59] prime number
1934 = sum of totient function for first 79 integers
1936 = 442, 18-gonal number,[133] 324-gonal number.
1938 = Mertens function zero
1944 = 3-smooth number (23×35)
1951 = cuban prime[124]
1953 = triangular number
1956 = nonagonal number[99]
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[134]
1973 = Sophie Germain prime, Leonardo prime
1980 = pronic number[45]
1985 = centered square number[12]
1987 = 300th prime number
1988 = sum of the first 33 primes
1993 = a number with the property that 41993 - 31993 is prime[135]
1998 = triangular matchstick number[86]

### Prime numbers

There are 135 prime numbers between 1000 and 2000:[136][137]

1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

## References

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4. ^ "Sloane's A122189 : Heptanacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on October 7, 2016. Retrieved July 13, 2017.
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6. ^ a b
7. ^
8. ^ Sloane, N. J. A. (ed.). "Sequence A034262". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
9. ^ a b Sloane, N. J. A. (ed.). "Sequence A020473". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
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11. "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
12. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
13. ^ Sloane, N. J. A. (ed.). "Sequence A000325". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
14. ^ a b c d "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
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17. ^ Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
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19. ^ a b Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
20. ^ a b Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
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22. ^
23. "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on April 5, 2016. Retrieved June 12, 2016.
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25. ^ a b
26. ^
27. ^
28. ^
29. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
30. ^ a b
31. ^
32. ^ a b
33. ^
34. ^
35. ^
36. ^
37. ^
38. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
39. ^
40. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
41. ^
42. ^
43. ^
44. ^
45. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
46. ^
47. ^
48. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
49. ^
50. ^ a b c
51. ^ "A347565: Primes p such that A241014(A000720(p)) is +1 or -1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on March 25, 2022. Retrieved January 19, 2022.
52. ^
53. ^
54. ^
55. ^
56. ^ a b
57. ^ a b
58. "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
59. "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
60. ^
61. ^
62. ^
63. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
64. ^ a b c "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
65. ^
66. ^
67. ^
68. ^ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
69. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on March 4, 2016. Retrieved June 12, 2016.
70. ^
71. ^
72. ^
73. ^ "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on October 17, 2015. Retrieved June 14, 2016.
74. ^
75. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
76. "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
77. ^
78. ^
79. ^
80. ^
81. "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
82. ^ a b "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
83. ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
84. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
85. "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
86. Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
87. ^ Sloane, N. J. A. (ed.). "Sequence A080040". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
88. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
89. ^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-07-10.
90. ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
91. ^ a b c d "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
92. ^ a b c "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
93. ^ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
94. ^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
95. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
96. ^ a b "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
97. ^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
98. ^ Higgins, ibid.
99. "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
100. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
101. "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
102. ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
103. ^ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
104. ^ a b "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
105. "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
106. ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
107. ^
108. ^ "Constitutional Court allows 'FCK CPS' sticker". The Local. 28 April 2015. "...state court in Karlsruhe ruled that a banner ... that read 'ACAB' – an abbreviation of 'all cops are bastards' ... a punishable insult. ... A court in Frankfurt ... the numbers '1312' constituted an insult ... the numerals stand for the letters ACAB's position in the alphabet.
109. ^ a b "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
110. ^ a b "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
111. ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
112. ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
113. ^ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
114. ^ a b "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
115. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
116. ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
117. ^
118. ^
119. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
120. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
121. ^ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
122. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
123. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
124. ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
125. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
126. ^ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
127. ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
128. ^ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
129. ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
130. ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
131. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
132. ^ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
133. ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
134. ^ Jon Froemke & Jerrold W. Grossman (Feb 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?". The American Mathematical Monthly. Mathematical Association of America. 100 (2): 180–183. doi:10.2307/2323780. JSTOR 2323780.
135. ^
136. ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
137. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.