800 (number) explained

Number:	800
Lang1:	Armenian
Lang1 Symbol:	Պ
Lang2:	Hebrew
Lang2 Symbol:	ת"ת / ף
Lang3:	Babylonian cuneiform
Lang3 Symbol:	⟪
Lang4:	Egyptirshd ian hieroglyph
Lang4 Symbol:

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.^[1]

Integers from 801 to 899

800s

See main article: 801 (number).

• 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^[2]
• 804 = 2² × 3 × 67, nontotient, Harshad number, refactorable number^[3]
  • "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, sphenic number, number of partitions of 38 into nonprime parts^[4]
• 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51)^[5]
• 807 = 3 × 269, antisigma(42)^[6]
• 808 = 2³ × 101, refactorable number, strobogrammatic number^[7]
• 809 = prime number, Sophie Germain prime,^[8] 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,^[9] number of non-equivalent ways of expressing 100,000 as the sum of two prime numbers^[10]
• 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,^[11] 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^[12]
• 816 = 2⁴ × 3 × 17, tetrahedral number,^[13] Padovan number,^[14] Zuckerman number
• 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277), centered hexagonal number^[15]
• 818 = 2 × 409, nontotient, strobogrammatic number
• 819 = 3² × 7 × 13, square pyramidal number^[16]

820s

• 820 = 2² × 5 × 41, 40th triangular number, smallest triangular number that starts with the digit 8,^[17] 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, 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^[18]
• 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,^[19] 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^[20]
• 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^[21]
• 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^[22]
• 832 = 2⁶ × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2)
• 833 = 7² × 17, octagonal number, a centered octahedral number^[23]
• 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^[24]

See main article: 836 (number).

• 836 = 2² × 11 × 19, weird number
• 837 = 3³ × 31, the 36th generalized heptagonal number^[25]
• 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i[26]
• 839 = prime number, safe prime,^[27] sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number^[28]

840s

See main article: 840 (number).

• 840 = 2³ × 3 × 5 × 7, highly composite number,^[29] smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,^[30] Harshad number in base 2 through base 10, idoneal number, balanced number, 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,^[31] centered heptagonal number,^[32] centered octagonal number^[33]
• 842 = 2 × 421, nontotient, 842!! - 1 is prime,^[34] number of series-reduced trees with 18 nodes
• 843 = 3 × 281, Lucas number^[35]
• 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 ^[36]
• 845 = 5 × 13², concentric pentagonal number,^[37] number of emergent parts in all partitions of 22 ^[38]
• 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^[39]
• 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^[40]
• 852 = 2² × 3 × 71, pentagonal number,^[41] Smith number
  • country calling code for Hong Kong
• 853 = prime number, Perrin number,^[42] 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^[43]
• 855 = 3² × 5 × 19, decagonal number,^[44] centered cube number^[45]
  • country calling code for Cambodia
• 856 = 2³ × 107, nonagonal number,^[46] centered pentagonal number,^[47] happy number, 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^[48]
• 859 = prime number, number of planar partitions of 11,^[49] prime index prime

860s

• 860 = 2² × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number^[50]
• 861 = 3 × 7 × 41, sphenic number, 41st triangular number, hexagonal number,^[51] 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,^[52] 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^[53]
• 868 = 2² × 7 × 31 = J₃(10),^[54] 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 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:^[55] 10³ – 5³
• 876 = 2² × 3 × 73, generalized pentagonal number^[56]
• 877 = prime number, Bell number,^[57] 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.^[58]
• 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices,^[59] candidate Lychrel seed number

880s

See main article: 880 (number).

• 880 = 2⁴ × 5 × 11 = 11!!!,^[60] Harshad number; 148-gonal number; the number of n×n magic squares for n = 4.
  • country calling code for Bangladesh

See main article: 881 (number).

• 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{ 9 }{ 5 } _{2} a trinomial coefficient,^[61] 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 (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^[62]
• 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.^[63]
• 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

See main article: 888 (number).

• 888 = 2³ × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number, strobogrammatic number, happy number, 888!! - 1 is prime^[64]
• 889 = 7 × 127, the Mertens function of 889 returns 0

890s

• 890 = 2 × 5 × 89 = 19² + 23² (sum of squares of two successive primes),^[65] 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 .
• 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,^[66] 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
• 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
• 899 = 29 × 31 (a twin prime product),^[67] happy number, smallest number with digit sum 26,^[68] number of partitions of 51 into prime parts

Notes and References

1. a(n) = 2*n^2.
2. 2022-05-25.
3. 2023-10-16.
4. 2022-05-25.
5. Sum of totient function: a(n) = Sum_ phi(k), cf. A000010. 2022-05-25.
6. 2022-05-25.
7. A000787. Strobogrammatic numbers. 2016-06-11.
8. A005384. Sophie Germain primes. 2016-06-11.
9. 2022-05-25.
10. A065577. Number of Goldbach partitions of 10^n. 2023-08-31.
11. A002378. Oblong (or promic, pronic, or heteromecic) numbers. 2016-06-11.
12. 2022-05-25.
13. A000292. Tetrahedral numbers. 2016-06-11.
14. A000931. Padovan sequence. 2016-06-11.
15. A003215. Hex (or centered hexagonal) numbers. 2016-06-11.
16. A000330. Square pyramidal numbers. 2016-06-11.
17. A000217. Triangular numbers. 2016-06-11.
18. A005282. Mian-Chowla sequence. 2016-06-11.
19. A006753. Smith numbers. 2016-06-11.
20. 2022-05-25.
21. A016038. Strictly non-palindromic numbers. 2016-06-11.
22. 2022-05-25.
23. 2022-06-02.
24. A001006. Motzkin numbers. 2016-06-11.
25. 0, +-1, +-2 +-3, .... 2022-05-30.
26. i
27. A005385. Safe primes. 2016-06-11.
28. A100827. Highly cototient numbers. 2016-06-11.
29. A002182. Highly composite numbers. 2016-06-11.
30. A036913. Sparsely totient numbers. 2016-06-11.
31. A001844. Centered square numbers. 2016-06-11.
32. A069099. Centered heptagonal numbers. 2016-06-11.
33. A016754. Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers. 2016-06-11.
34. 2022-05-24.
35. A000032. Lucas numbers. 2016-06-11.
36. 2022-05-24.
37. 2022-05-24.
38. 2022-05-24.
39. 2022-05-24.
40. 2022-05-24.
41. A000326. Pentagonal numbers. 2016-06-11.
42. A001608. Perrin sequence. 2016-06-11.
43. 2022-05-24.
44. A001107. 10-gonal (or decagonal) numbers. 2016-06-11.
45. A005898. Centered cube numbers. 2016-06-11.
46. A001106. 9-gonal (or enneagonal or nonagonal) numbers. 2016-06-11.
47. A005891. Centered pentagonal numbers. 2016-06-11.
48. A007850. Giuga numbers. 2016-06-11.
49. 2022-05-24.
50. 2022-05-24.
51. A000384. Hexagonal numbers. 2016-06-11.
52. 2022-05-10.
53. 2022-05-24.
54. 2022-05-24.
55. A014439. Differences between two positive cubes in exactly 1 way.. 2019-08-18.
56. A001318. Generalized pentagonal numbers.. 2019-08-26.
57. A000110. Bell or exponential numbers. 2016-06-11.
58. A101929. Number of Pythagorean triples with hypotenuse < 10^n.. 2022-05-11.
59. A319190. Number of regular hypergraphs. 2019-08-18.
60. A007661. Triple factorial numbers. 2022-05-11.
61. A111808. Left half of trinomial triangle (A027907), triangle read by rows. 2022-05-11.
62. A005893. Number of points on surface of tetrahedron. 2022-05-11.
63. A319312. Number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of n. 2022-05-11.
64. 2022-05-24.
65. A069484. a(n) = prime(n+1)^2 + prime(n)^2.. 2022-05-11.
66. A003261. Woodall numbers. 2016-06-11.
67. A037074. Numbers that are the product of a pair of twin primes. 2022-05-11.
68. A051885. Smallest number whose sum of digits is n. 2022-05-11.