800 (number)

Template:Redirect Template:Infobox number 800 (eight hundred) is the natural number following 799 and preceding 801.

It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal 40.<ref name="area of a square with diagonal 2n">Template:Cite OEIS</ref>

Integers from 801 to 899

800s

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• 801 = 3² × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins<ref>(sequence A229093 in the OEIS)</ref>
• 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<ref>(sequence A005893 in the OEIS)</ref> (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<ref>Template:Cite OEIS</ref>
• 804 = 2² × 3 × 67, nontotient, Harshad number, refactorable number<ref>Template:Cite OEIS</ref>
  • "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).<ref>Template:Cite newspaper</ref><ref>Template:Cite newspaper</ref>
• 805 = 5 × 7 × 23, sphenic number, number of partitions of 38 into nonprime parts<ref>Template:Cite OEIS</ref>
• 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51)<ref>Template:Cite OEIS</ref>
• 807 = 3 × 269, antisigma(42)<ref>Template:Cite OEIS</ref>
• 808 = 2³ × 101, refactorable number, strobogrammatic number<ref name=":0">Template:Cite OEIS</ref>
• 809 = prime number, Sophie Germain prime,<ref>Template:Cite OEIS</ref> 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,<ref>Template:Cite OEIS</ref> number of non-equivalent ways of expressing 100,000 as the sum of two prime numbers<ref>Template:Cite OEIS</ref>
• 811 = prime number, twin prime, 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,<ref name=":1">Template:Cite OEIS</ref> balanced number,<ref>Template:Cite OEIS</ref> the Mertens function of 812 returns 0
• 813 = 3 × 271, Blum integer (sequence A016105 in the OEIS)
• 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<ref>Template:Cite OEIS</ref>
• 816 = 2⁴ × 3 × 17, tetrahedral number,<ref>Template:Cite OEIS</ref> Padovan number,<ref>Template:Cite OEIS</ref> Zuckerman number
• 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277), centered hexagonal number<ref>Template:Cite OEIS</ref>
• 818 = 2 × 409, nontotient, strobogrammatic number<ref name=":0" />
• 819 = 3² × 7 × 13, square pyramidal number<ref>Template:Cite OEIS</ref>

820s

• 820 = 2² × 5 × 41, 40th triangular number, smallest triangular number that starts with the digit 8,<ref name=":2">Template:Cite OEIS</ref> Harshad number, happy number, repdigit (1111) in base 9
• 821 = prime number, twin prime, Chen prime, Eisenstein prime with no imaginary part, lazy caterer number (sequence A000124 in the OEIS), 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<ref>Template:Cite OEIS</ref>
• 823 = prime number, twin prime, lucky prime, the Mertens function of 823 returns 0, prime quadruplet with 821, 827, 829
• 824 = 2³ × 103, refactorable number, 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,<ref name=":3">Template:Cite OEIS</ref> 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<ref>Template:Cite OEIS</ref>
• 827 = prime number, twin prime, part of prime quadruplet with {821, 823, 829}, sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number<ref name=":4">Template:Cite OEIS</ref>
• 828 = 2² × 3² × 23, Harshad number, triangular matchstick number<ref>(sequence A045943 in the OEIS)</ref>
• 829 = prime number, twin prime, part of prime quadruplet with {827, 823, 821}, 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<ref>Template:Cite OEIS</ref>
• 832 = 2⁶ × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2)<ref>(sequence A085449 in the OEIS)</ref>
• 833 = 7² × 17, octagonal number (sequence A000567 in the OEIS), a centered octahedral number<ref>Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>

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• 836 = 2² × 11 × 19, weird number
• 837 = 3³ × 31, the 36th generalized heptagonal number<ref>Template:Cite OEIS</ref>
• 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i<j<k <= 23<ref>Template:Cite OEIS</ref>
• 839 = prime number, safe prime,<ref name=":5">Template:Cite OEIS</ref> sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number<ref>Template:Cite OEIS</ref>

840s

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• 840 = 2³ × 3 × 5 × 7, highly composite number,<ref>Template:Cite OEIS</ref> smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,<ref name=":6">Template:Cite OEIS</ref> Harshad number in base 2 through base 10, idoneal number, balanced number,<ref>Template:Cite OEIS</ref> sum of a twin prime (419 + 421). With 32 distinct divisors, it is the number below 1000 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,<ref>Template:Cite OEIS</ref> centered heptagonal number,<ref>Template:Cite OEIS</ref> centered octagonal number<ref>Template:Cite OEIS</ref>
• 842 = 2 × 421, nontotient, 842!! - 1 is prime,<ref>Template:Cite OEIS</ref> number of series-reduced trees with 18 nodes<ref>Template:Cite OEIS</ref>
• 843 = 3 × 281, Lucas number<ref>Template:Cite OEIS</ref>
• 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 <ref>Template:Cite OEIS</ref>
• 845 = 5 × 13², concentric pentagonal number,<ref>Template:Cite OEIS</ref> number of emergent parts in all partitions of 22 <ref>Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>
• 848 = 2⁴ × 53, untouchable number
• 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 (sequence A001157 in the OEIS). The maximum possible Fair Isaac credit score, country calling code for North Korea
• 851 = 23 × 37, number of compositions of 18 into distinct parts<ref>Template:Cite OEIS</ref>
• 852 = 2² × 3 × 71, pentagonal number,<ref>Template:Cite OEIS</ref> Smith number<ref name=":3" />
  • country calling code for Hong Kong
• 853 = prime number, Perrin number,<ref>Template:Cite OEIS</ref> the Mertens function of 853 returns 0, average of first 853 prime numbers is an integer (sequence A045345 in the OEIS), strictly non-palindromic number, number of connected graphs with 7 nodes
  • country calling code for Macau
• 854 = 2 × 7 × 61, sphenic number, nontotient, number of unlabeled planar trees with 11 nodes<ref>Template:Cite OEIS</ref>
• 855 = 3² × 5 × 19, decagonal number,<ref>Template:Cite OEIS</ref> centered cube number<ref>Template:Cite OEIS</ref>
  • country calling code for Cambodia
• 856 = 2³ × 107, nonagonal number,<ref>Template:Cite OEIS</ref> centered pentagonal number,<ref>Template:Cite OEIS</ref> refactorable 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<ref>Template:Cite OEIS</ref>
• 859 = prime number, number of planar partitions of 11,<ref>Template:Cite OEIS</ref> prime index prime

860s

• 860 = 2² × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number<ref>Template:Cite OEIS</ref>
• 861 = 3 × 7 × 41, sphenic number, 41st triangular number,<ref name=":2" /> hexagonal number,<ref>Template:Cite OEIS</ref> Smith number<ref name=":3" />
• 862 = 2 × 431, lazy caterer number (sequence A000124 in the OEIS)
• 863 = prime number, safe prime,<ref name=":5" /> 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<ref>Template:Cite OEIS</ref>
• 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,<ref>Template:Cite OEIS</ref> 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<ref>Template:Cite OEIS</ref>
• 868 = 2² × 7 × 31 = J₃(10),<ref>Template:Cite OEIS</ref> 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,<ref name=":1" /> nontotient, sparsely totient number,<ref name=":6" /> Harshad number
  • This number is the magic constant of n×n normal magic square and n-queens problem for n = 12.
• 871 = 13 × 67, thirteenth tridecagonal number
• 872 = 2³ × 109, refactorable number, nontotient, 872! + 1 is prime
• 873 = 3² × 97, sum of the first six factorials from 1
• 874 = 2 × 19 × 23, sphenic number, 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:<ref>Template:Cite OEIS</ref> 10³ – 5³
• 876 = 2² × 3 × 73, generalized pentagonal number<ref>Template:Cite OEIS</ref>
• 877 = prime number, Bell number,<ref>Template:Cite OEIS</ref> Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number,<ref name=":4" /> prime index prime
• 878 = 2 × 439, nontotient, number of Pythagorean triples with hypotenuse < 1000.<ref>Template:Cite OEIS</ref>
• 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices,<ref>Template:Cite OEIS</ref> candidate Lychrel seed number

880s

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• 880 = 2⁴ × 5 × 11 = 11!!!,<ref>Template:Cite OEIS</ref> Harshad number; 148-gonal number; the number of n×n magic squares for n = 4.
  • country calling code for Bangladesh

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• 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 = <math>\binom{9}{5}_2</math> a trinomial coefficient,<ref>Template:Cite OEIS</ref> Harshad number, totient sum for first 53 integers, area of a square with diagonal 42<ref name="area of a square with diagonal 2n" />
• 883 = prime number, twin prime, lucky prime, sum of three consecutive primes (283 + 293 + 307), sum of eleven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), 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<ref>Template:Cite OEIS</ref>
• 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.<ref>Template:Cite OEIS</ref>
• 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,<ref name=":5" /> Chen prime, Eisenstein prime with no imaginary part

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• 888 = 2³ × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number, strobogrammatic number,<ref name=":0" /> happy number, 888!! - 1 is prime<ref>Template:Cite OEIS</ref>
• 889 = 7 × 127, the Mertens function of 889 returns 0

890s

• 890 = 2 × 5 × 89 = 19² + 23² (sum of squares of two successive primes),<ref>Template:Cite OEIS</ref> 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 like this (sequence A331452 in the OEIS).
• 893 = 19 × 47, the Mertens function of 893 returns 0
  • Considered an unlucky number in Japan, because its digits read sequentially are the literal translation of yakuza.
• 894 = 2 × 3 × 149, sphenic number, nontotient
• 895 = 5 × 179, Smith number,<ref name=":3" /> Woodall number,<ref>Template:Cite OEIS</ref> the Mertens function of 895 returns 0
• 896 = 2⁷ × 7, refactorable number, 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 (sequence A002064 in the OEIS)
• 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
• 899 = 29 × 31 (a twin prime product),<ref>Template:Cite OEIS</ref> happy number, smallest number with digit sum 26,<ref>Template:Cite OEIS</ref> number of partitions of 51 into prime parts