800 (eight hundred) is the natural number following 799 and preceding 801.
In mathematics 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.
Integers from 801 to 899
800s
801 801 is 3*3*89 and a Harshad number. 801 is the sum of a square and positive cube in more than one way, and a sum of distinct positive cubes in more than one way:
In the gematria of 2nd century bishop Irenaeus, 801 stands for both the Greek word for a dove, and for Alpha and Omega, and therefore represents God in two ways..
There are 801 club patterns in a 50x50 grid of coins.
802 802 = 2 × 401. It is a nontotient, a happy number, the sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), and the sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231).
803 803 = 11 × 73. It is a Harshad number, the sum of three consecutive primes (263 + 269 + 271), and the sum of nine consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107).
There are 803 partitions of 34 into Fibonacci parts.
804 804 = 22 × 3 × 67. It is a nontotient, a Harshad number, and a 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 (although the area code covers a larger area).
805 805 = 5 × 7 × 23. It is a sphenic number. There are 805 partitions of 38 into nonprime parts
806 806 = 2 × 13 × 31. It is a sphenic number, a nontotient, a happy number, and the totient sum for first 51 integers.
806 = Phi(51)
807 807 = 3 × 269 = antisigma(42)
808 808 = 23 × 101. It is a refactorable number and a strobogrammatic number. 809 809 is a prime number, a Sophie Germain prime, a Chen prime, and an Eisenstein prime with no imaginary part. 810s
810 810 = 2 × 34 × 5. It is a harshad number. There are 810 non-equivalent ways of expressing 100,000 as the sum of two prime numbers. There are 810 distinct reduced words of length 5 in the Coxeter group of "Apollonian reflections" in three dimensions.
811 811 is a prime number, a twin prime, a Chen prime, the largest minimal prime in base 9, and the sum of five consecutive primes (151 + 157 + 163 + 167 + 173). It is a happy number and a zero of Mertens function.
812 812 = 22 × 7 × 29. It is an admirable number, a pronic number, a balanced number, and a zero of Mertens function.
813 813 = 3 × 271. It is a Blum integer.
814 814 = 2 × 11 × 37. It is a sphenic number, a nontotient, and a zero of Mertens function. There are 814 fixed hexahexes.
815 815 = 5 × 163. There are 815 graphs with 8 vertices and a distinguished bipartite block.
816 816 = 24 × 3 × 17. It is a tetrahedral number, a Padovan number, and a Zuckerman number.
817 817 = 19 × 43. It is a centered hexagonal number and the sum of three consecutive primes (269 + 271 + 277).
818 818 = 2 × 409. It is a nontotient and a strobogrammatic number
819 819 = 32 × 7 × 13. It is a square pyramidal number.
820s
820 820 = 22 × 5 × 41. It is a Harshad number, a happy number, a repdigit (1111) in base 9, and the 40th triangular number.
821 821 is a prime number, a twin prime, a Chen prime, and an Eisenstein prime with no imaginary part. It forms a prime quadruplet with 823, 827, and 829. It is a lazy caterer number.
822 822 = 2 × 3 × 137. It is a sphenic number, a member of the Mian–Chowla sequence, and the sum of twelve consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97).
823 823 is a prime number, a twin prime, and a lucky prime. It forms a prime quadruplet with 821, 827, and 829. It is a zero of Mertens function.
824 824 = 23 × 103, refactorable number, nontotient, a zero of Mertens function, and the sum of ten consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103).
825 825 = 3 × 52 × 11. It is a Smith number, a Harshad number, and a zero of Mertens function.
826 826 = 2 × 7 × 59. It is a sphenic number. There are 825 partitions of 29 into parts each of which is used a different number of times.
827 827 is a prime number, a twin prime, a Chen prime, a Eisenstein prime with no imaginary part, and the sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137). It forms a prime quadruplet with 821, 823, and 829. It is a strictly non-palindromic number.
828 828 = 22 × 32 × 23. It is a Harshad number and a triangular matchstick number.
829 829 is a prime number, a twin prime, a Chen prime, and the sum of three consecutive primes (271 + 277 + 281). It forms a prime quadruplet with 821, 823, and 827. It is a centered triangular number. 830s
830 830 = 2 × 5 × 83. It is a sphenic number, a nontotient, the totient sum of the first 52 integers, and the sum of four consecutive primes (197 + 199 + 211 + 223).
831 831 = 3 × 277. There are 831 partitions of 32 into at most 5 parts.
832 832 = 26 × 13. It is a Harshad number and a member of the Horadam sequence (0,1,4,2).
833 833 = 72 × 17. It is an octagonal number and a centered octahedral number.
834 834 = 2 × 3 × 139. It is a cake number, a sphenic number, a nontotient, and the sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151).
835 835 = 5 × 167. It is a Motzkin number.
836
837 837 = 33 × 31. It is the 36th generalized heptagonal number.
838 838 = 2 × 419. It is a palindromic number. There are 838 distinct products ijk with 1 <= i<j<k <= 23.
839 839 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (157 + 163 + 167 + 173 + 179). It is a highly cototient number.
840s
840
841 841 = 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
842 842 = 2 × 421. It is a nontotient. There are 842 series-reduced trees with 18 nodes.
842!! - 1 is prime.
843 843 = 3 × 281. It is a Lucas number.
844 844 = 22 × 211. It is a nontotient. It is the smallest 5 consecutive integers which are not squarefree:
844 = 22 × 211, 845 = 5 × 132, 846 = 2 × 32 × 47, 847 = 7 × 112, and 848 = 24 × 53.
845 845 = 5 × 132. It is a concentric pentagonal number.There are 845 emergent parts in all partitions of 22.
846 846 = 2 × 32 × 47. It is a nontotient, a Harshad number, and the sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127).
847 847 = 7 × 112. It is a happy number. There are 847 partitions of 29 that do not contain 1 as a part.
848 848 = 24 × 53. It is an untouchable number.
849 849 = 3 × 283, It is a zero of Mertens function and a Blum integer. 850s
850 850 = 2 × 52 × 17. It is a zero of Mertens function and a nontotient. The sum of the squares of the divisors of 26 is 850 .
The maximum possible Fair Isaac credit score is 850.
851 851 = 23 × 37 There are 851 compositions of 18 into distinct parts
852 852 = 22 × 3 × 71. It is a pentagonal number and a Smith number.
853 853 is a prime number, a Perrin number, a zero of Mertens function, and a strictly non-palindromic number. The average of first 853 prime numbers is an integer . There are 853 connected graphs with 7 nodes.
854 854 = 2 × 7 × 61. It is a sphenic number and a nontotient. There are 854 unlabeled planar trees with 11 nodes.
855 855 = 32 × 5 × 19. It is a decagonal number and a centered cube number.
856 856 = 23 × 107. It is a nonagonal number, a centered pentagonal number, and a refactorable number.
857 857 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of three consecutive primes (281 + 283 + 293).
858 858 = 2 × 3 × 11 × 13. It is a Giuga number.
859 859 is a prime number and a prime index prime. There are 859 planar partitions of 11.
860s
860 860 = 22 × 5 × 43. It is aHoax number and the sum of four consecutive primes (199 + 211 + 223 + 227).
861 861 = 3 × 7 × 41. It is a sphenic number, a hexagonal number, a Smith number, and the 41st triangular number.
862 862 = 2 × 431. It is a lazy caterer number.
863 863 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, and an index of a prime Lucas number.It is the sum of five consecutive primes (163 + 167 + 173 + 179 + 181) and the sum of seven consecutive primes (107 + 109 + 113 + 127 + 131 + 137 + 139).
864 864 = 25 × 33. It is an Achilles number and a Harshad number. It the sum of a twin prime pair (431 + 433) and the sum of six consecutive primes (131 + 137 + 139 + 149 + 151 + 157).
865 865 = 5 × 173.
866 866 = 2 × 433. It is a nontotient and the number of cubes of edge length 1 required to make a hollow cube of edge length 13. There are 866 one-sided noniamonds.
867 867 = 3 × 172. There are 867 5-chromatic simple graphs on 8 nodes.
868 868 = 22 × 7 × 31 = J3(10). It is a nontotient.
869 869 = 11 × 79. It is a zero of Mertens function.
870s
870 870 = 2 × 3 × 5 × 29. It is a pronic number, a nontotient, a sparsely totient number, a Harshad number, and the sum of ten consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107). It is the magic constant of n×n normal magic square and n-queens problem for n = 12.
871 871 = 13 × 67. It is the thirteenth tridecagonal number.
872 872 = 23 × 109. It is a refactorable number and anontotient.
872! + 1 is prime.
873 873 = 32 × 97 = 1! + 2! + 3! + 4! + 5! + 6!.
874 874 = 2 × 19 × 23 = 0! + 1! + 2! + 3! + 4! + 5! + 6!. It is a sphenic number, a nontotient, a Harshad number, a happy number, and the sum of the first twenty-three primes.
875 875 = 53 × 7. It can be uniquely expressed as a difference of two positive cubes: 875 = 103 – 53.
876 876 = 22 × 3 × 73. It is a generalized pentagonal number.
877 877 is a prime number, a prime index prime, a Chen prime, a zero of Mertens function, a Bell number, and a strictly non-palindromic number.
878 878 = 2 × 439. It is a nontotient. There are 878 Pythagorean triples with a hypotenuse less than 1000.
879 879 = 3 × 293. It is a candidate Lychrel seed number. There are 879 regular hypergraphs spanning 4 vertices.
880s
880 880 = 24 × 5 × 11 = 11!!!. It is a Harshad number and a 148-gonal number. There are 880 n×n magic squares for n = 4.
881 881 is a prime number, a twin prime, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of nine consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113). It is a happy number.
881 is a bilingual play on words when text chatting in Mandarin Chinese or bilingually Mandarin Chinese and English. "881" is pronounced ba ba yi in Mandarin, and thus puns on "bye-bye." Probably an elaboration of the similar pun on "88" (ba-ba). See 88 (number).
882 882 = 2 × 32 × 72 = It is a trinomial coefficient, a Harshad number, and the totient sum of the first 53 integers.
883 883 is a prime number, a twin prime, a lucky prime, the sum of three consecutive primes (283 + 293 + 307), and the sum of eleven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103). It is a zero of Mertens function.
884 884 = 22 × 13 × 17. It is a zero of Mertens function. There are 884 points on surface of tetrahedron with sidelength 21.
885 885 = 3 × 5 × 59. It is a sphenic number. There are 885 series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of 7.
886 886 = 2 × 443. It is a zero of Mertens function.
887 887 is a prime number followed by primal gap of 20, a safe prime, a Chen prime, and an Eisenstein prime with no imaginary part. It is the first iteration of the 196 trajectory (196 + 691 = 887).
888
889 889 = 7 × 127. It is a zero of Mertens function.
890s
890