800 (number)

800 is the natural number following 799 and preceding 801.
It is the sum of four consecutive primes. It is a Harshad number, 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, nontotient, happy number, sum of 4 consecutive triangular numbers
803 = 11 × 73, sum of three consecutive primes, sum of nine consecutive primes, Harshad number, number of partitions of 34 into Fibonacci parts
804 = 2² × 3 × 67, nontotient, Harshad number, refactorable 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.
805 = 5 × 7 × 23, sphenic number, number of partitions of 38 into nonprime parts
806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi
807 = 3 × 269, antisigma
808 = 2³ × 101, refactorable number, strobogrammatic number
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 non-equivalent ways of expressing 100,000 as the sum of two prime numbers
811 = prime number, twin prime, sum of five consecutive primes, 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, centered hexagonal number
818 = 2 × 409, nontotient, strobogrammatic number
819 = 3² × 7 × 13, square pyramidal number

820s

820 = 2² × 5 × 41, 40th triangular number, smallest triangular number that starts with the digit 8, Harshad number, happy number, repdigit in base 9
821 = prime number, twin prime, Chen 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, 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, refactorable number, sum of ten consecutive primes, 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, 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, Chen prime, centered triangular number

830s

830 = 2 × 5 × 83, sphenic number, sum of four consecutive primes, 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
833 = 7² × 17, octagonal number, a centered octahedral number
834 = 2 × 3 × 139, cake number, sphenic number, sum of six consecutive primes, nontotient
835 = 5 × 167, Motzkin number
836 = 2² × 11 × 19, weird number
837 = 3³ × 31, the 36th generalized heptagonal number
838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i
839 = prime number, safe prime, sum of five consecutive primes, Chen prime, Eisenstein prime with no imaginary part, highly cototient number

840s

840 = 2³ × 3 × 5 × 7, highly composite number, smallest number divisible by the numbers 1 to 8, sparsely totient number, Harshad number in base 2 through base 10, idoneal number, balanced number, sum of a twin prime. 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, sum of nine consecutive primes, 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, 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
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, 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, sphenic number, 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, refactorable number
* country calling code for Laos
857 = prime number, sum of three consecutive primes, Chen prime, Eisenstein prime with no imaginary part
858 = 2 × 3 × 11 × 13, Giuga number
859 = prime number, number of planar partitions of 11, prime index prime

860s

860 = 2² × 5 × 43, sum of four consecutive primes, Hoax number
861 = 3 × 7 × 41, sphenic number, 41st triangular number, hexagonal number, Smith number
862 = 2 × 431, lazy caterer number
863 = prime number, safe prime, sum of five consecutive primes, sum of seven consecutive primes, Chen prime, Eisenstein prime with no imaginary part, index of prime Lucas number
864 = 2⁵ × 3³, Achilles number, sum of a twin prime, sum of six consecutive primes, 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, pronic number, nontotient, sparsely totient number, 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: 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 squares for n = 4.
* country calling code for Bangladesh
881 = prime number, twin prime, sum of nine consecutive primes, Chen prime, Eisenstein prime with no imaginary part, happy number
882 = 2 × 3² × 7² = a trinomial coefficient, Harshad number, totient sum for first 53 integers, area of a square with diagonal 42
883 = prime number, twin prime, lucky prime, sum of three consecutive primes, sum of eleven consecutive primes, 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, Harshad number, strobogrammatic number, happy number, 888!! - 1 is prime
889 = 7 × 127, the Mertens function of 889 returns 0

890s

890 = 2 × 5 × 89 = 19² + 23², sphenic number, sum of four consecutive primes, nontotient
891 = 3⁴ × 11, sum of five consecutive primes, 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 .
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, Woodall number, the Mertens function of 895 returns 0
896 = 2⁷ × 7, refactorable number, sum of six consecutive primes, 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, happy number, smallest number with digit sum 26, number of partitions of 51 into prime parts