870 (number)
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800 (eight hundred) is the natural number following
799 __NOTOC__ Year 799 ( DCCXCIX) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. The denomination 799 for this year has been used since the early medieval period, when the Anno Domini calendar e ...
and preceding 801. It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a
Harshad number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers ...
, an Achilles number and the area of a square with diagonal 40.


Integers from 801 to 899


800s

* 801 = 32 × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins * 802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number, sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231) * 803 = 11 × 73, sum of three consecutive primes (263 + 269 + 271), sum of nine consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), Harshad number, number of partitions of 34 into Fibonacci parts * 804 = 22 × 3 × 67, nontotient, Harshad number, ** "The 804" is a local nickname for the Greater Richmond Region of the U.S. state of Virginia, derived from its telephone area code (although the area code covers a larger area). * 805 = 5 × 7 × 23, number of partitions of 38 into nonprime parts * 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51) * 807 = 3 × 269, antisigma(42) * 808 = 23 × 101,
strobogrammatic number A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A strobogrammatic ...
* 809 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part


810s

* 810 = 2 × 34 × 5, Harshad number, number of distinct reduced words of length 5 in the Coxeter group of "Apollonian reflections" in three dimensions, number of different ways in which 100,000 can be expressed as the sum of two prime numbers * 811 = prime number, sum of five consecutive primes (151 + 157 + 163 + 167 + 173), Chen prime, happy number, largest minimal prime in base 9, the Mertens function of 811 returns 0 * 812 = 22 × 7 × 29, admirable number, pronic number, balanced number, the Mertens function of 812 returns 0 * 813 = 3 × 271, blum integer * 814 = 2 × 11 × 37, sphenic number, the Mertens function of 814 returns 0, nontotient, number of fixed hexahexes. * 815 = 5 × 163, number of graphs with 8 vertices and a distinguished bipartite block * 816 = 24 × 3 × 17, tetrahedral number, Padovan number, Zuckerman number * 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277),
centered hexagonal number In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following ...
* 818 = 2 × 409, nontotient,
strobogrammatic number A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A strobogrammatic ...
* 819 = 32 × 7 × 13,
square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broa ...


820s

* 820 = 22 × 5 × 41, triangular number, Harshad number, happy number, repdigit (1111) in base 9 * 821 = prime number, twin prime, Eisenstein prime with no imaginary part, lazy caterer number , prime quadruplet with 823, 827, 829 * 822 = 2 × 3 × 137, sum of twelve consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), sphenic number, member of the Mian–Chowla sequence * 823 = prime number, twin prime, lucky prime, the Mertens function of 823 returns 0, prime quadruplet with 821, 827, 829 * 824 = 23 × 103, sum of ten consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), the Mertens function of 824 returns 0, nontotient * 825 = 3 × 52 × 11, Smith number, the Mertens function of 825 returns 0, Harshad number * 826 = 2 × 7 × 59, sphenic number, number of partitions of 29 into parts each of which is used a different number of times * 827 = prime number, twin prime, part of prime quadruplet with , sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number * 828 = 22 × 32 × 23, Harshad number, triangular matchstick number * 829 = prime number, twin prime, part of prime quadruplet with , sum of three consecutive primes (271 + 277 + 281), Chen prime, centered triangular number


830s

* 830 = 2 × 5 × 83, sphenic number, sum of four consecutive primes (197 + 199 + 211 + 223), nontotient, totient sum for first 52 integers * 831 = 3 × 277, number of partitions of 32 into at most 5 parts * 832 = 26 × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2) * 833 = 72 × 17, octagonal number , a centered octahedral number * 834 = 2 × 3 × 139, cake number, sphenic number, sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151), nontotient * 835 = 5 × 167, Motzkin number * 836 = 22 × 11 × 19,
weird number In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those diviso ...
* 837 = 33 × 31, the 36th generalized heptagonal number * 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= isafe prime, sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part,
highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient fun ...


840s

* 840 = 23 × 3 × 5 × 7,
highly composite number __FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
, smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number, Harshad number in base 2 through base 10, idoneal number, balanced number. With 32 distinct divisors, it is the number below
1000 1000 or thousand may refer to: * 1000 (number), a natural number * AD 1000, a leap year in the Julian calendar * 1000 BC, a year of the Before Christ era * 1000 metres, a middle-distance running event * 1000°, a German electronic dance music magazi ...
with the largest amount of divisors. * 841 = 292 = 202 + 212, sum of three consecutive primes (277 + 281 + 283), sum of nine consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109), centered square number, centered heptagonal number, centered octagonal number * 842 = 2 × 421, nontotient, 842!! - 1 is prime, number of series-reduced trees with 18 nodes * 843 = 3 × 281, Lucas number * 844 = 22 × 211, nontotient, smallest 5 consecutive integers which are not squarefree are: 844 = 22 × 211, 845 = 5 × 132, 846 = 2 × 32 × 47, 847 = 7 × 112 and 848 = 24 × 53 * 845 = 5 × 132, concentric pentagonal number, number of emergent parts in all partitions of 22 * 846 = 2 × 32 × 47, sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127), nontotient, Harshad number * 847 = 7 × 112, happy number, number of partitions of 29 that do not contain 1 as a part * 848 = 24 × 53,
untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...
* 849 = 3 × 283, the Mertens function of 849 returns 0, blum integer


850s

* 850 = 2 × 52 × 17, the Mertens function of 850 returns 0, nontotient, the sum of the squares of the divisors of 26 is 850 . The maximum possible Fair Isaac credit score, country calling code for North Korea * 851 = 23 × 37, number of compositions of 18 into distinct parts * 852 = 22 × 3 × 71, pentagonal number, Smith number ** country calling code for Hong Kong * 853 = prime number,
Perrin number In mathematics, the Perrin numbers are defined by the recurrence relation : for , with initial values :. The sequence of Perrin numbers starts with : 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, ... The number of different maxima ...
, the Mertens function of 853 returns 0, average of first 853 prime numbers is an integer , strictly non-palindromic number, number of connected graphs with 7 nodes ** country calling code for Macau * 854 = 2 × 7 × 61, nontotient, number of unlabeled planar trees with 11 nodes * 855 = 32 × 5 × 19, decagonal number, centered cube number ** country calling code for Cambodia * 856 = 23 × 107, nonagonal number, centered pentagonal number, happy number ** country calling code for Laos * 857 = prime number, sum of three consecutive primes (281 + 283 + 293), Chen prime, Eisenstein prime with no imaginary part * 858 = 2 × 3 × 11 × 13,
Giuga number A Giuga number is a composite number ''n'' such that for each of its distinct prime factors ''p'i'' we have p_i , \left( - 1\right), or equivalently such that for each of its distinct prime factors ''p'i'' we have p_i^2 , (n - p_i). The Gi ...
* 859 = prime number, number of planar partitions of 11, prime index prime


860s

* 860 = 22 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number * 861 = 3 × 7 × 41, sphenic number, triangular number, hexagonal number, Smith number * 862 = 2 × 431, lazy caterer number * 863 = prime number, safe prime, sum of five consecutive primes (163 + 167 + 173 + 179 + 181), sum of seven consecutive primes (107 + 109 + 113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, index of prime Lucas number * 864 = 25 × 33, Achilles number, sum of a twin prime (431 + 433), sum of six consecutive primes (131 + 137 + 139 + 149 + 151 + 157), Harshad number * 865 = 5 × 173, * 866 = 2 × 433, nontotient, number of one-sided noniamonds, number of cubes of edge length 1 required to make a hollow cube of edge length 13 * 867 = 3 × 172, number of 5-chromatic simple graphs on 8 nodes * 868 = 22 × 7 × 31 = J3(10), nontotient * 869 = 11 × 79, the Mertens function of 869 returns 0


870s

* 870 = 2 × 3 × 5 × 29, sum of ten consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), pronic number, nontotient, sparsely totient number, Harshad number ** This number is the
magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
of ''n''×''n'' normal
magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
and ''n''-queens problem for ''n'' = 12. * 871 = 13 × 67, thirteenth tridecagonal number * 872 = 23 × 109, nontotient, 872! + 1 is prime * 873 = 32 × 97, sum of the first six factorials from 1 * 874 = 2 × 19 × 23, sum of the first twenty-three primes, sum of the first seven factorials from 0, nontotient, Harshad number, happy number * 875 = 53 × 7, unique expression as difference of positive cubes: 103 - 53 * 876 = 22 × 3 × 73, generalized pentagonal number * 877 = prime number, Bell number, Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number, prime index prime * 878 = 2 × 439, nontotient, number of Pythagorean triples with hypotenuse < 1000. * 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices, candidate Lychrel seed number


880s

* 880 = 24 × 5 × 11 = 11!!!, Harshad number; 148- gonal number; the number of ''n''×''n''
magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
s for n = 4. ** country calling code for Bangladesh * 881 = prime number, twin prime, sum of nine consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part, happy number * 882 = 2 × 32 × 72 = \binom_2 a trinomial coefficient, Harshad number, totient sum for first 53 integers, area of a square with diagonal 42 * 883 = prime number, twin prime, sum of three consecutive primes (283 + 293 + 307), the Mertens function of 883 returns 0 * 884 = 22 × 13 × 17, the Mertens function of 884 returns 0, number of points on surface of tetrahedron with sidelength 21 * 885 = 3 × 5 × 59, sphenic number, number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of 7. * 886 = 2 × 443, the Mertens function of 886 returns 0 ** country calling code for Taiwan * 887 = prime number followed by primal gap of 20, safe prime, Chen prime, Eisenstein prime with no imaginary part * 888 = 23 × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number,
strobogrammatic number A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A strobogrammatic ...
, happy number, 888!! - 1 is prime * 889 = 7 × 127, the Mertens function of 889 returns 0


890s

* 890 = 2 × 5 × 89 = 192 + 232 (sum of squares of two successive primes), sphenic number, sum of four consecutive primes (211 + 223 + 227 + 229), nontotient * 891 = 34 × 11, sum of five consecutive primes (167 + 173 + 179 + 181 + 191), octahedral number * 892 = 22 × 223, nontotient, number of regions formed by drawing the line segments connecting any two perimeter points of a 6 times 2 grid of squares lik
this
. * 893 = 19 × 47, the Mertens function of 893 returns 0 ** Considered an unlucky number in
Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
, because its digits read sequentially are the literal translation of '' yakuza''. * 894 = 2 × 3 × 149, sphenic number, nontotient * 895 = 5 × 179, Smith number, Woodall number, the Mertens function of 895 returns 0 * 896 = 27 × 7, sum of six consecutive primes (137 + 139 + 149 + 151 + 157 + 163), the Mertens function of 896 returns 0 * 897 = 3 × 13 × 23, sphenic number, cullen number * 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient * 899 = 29 × 31 (a twin prime product), happy number, smallest number with digitsum 26, number of partitions of 51 into prime parts


References

{{Integers, 8 Integers