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800 (number)

This article is about the number. For the year, see 800. For other uses, see 800 (disambiguation).
← 799 800 801 →
Cardinaleight hundred
Ordinal800th
(eight hundredth)
Factorization25 × 52
Greek numeralΩ´
Roman numeralDCCC
Binary11001000002
Ternary10021223
Quaternary302004
Quinary112005
Senary34126
Octal14408
Duodecimal56812
Hexadecimal32016
Vigesimal20020
Base 36M836

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.

Integers from 801 to 899

800s

Main article: 801 (number)

810s

820s

  • 820 = 22 × 5 × 41, triangular number,[8] Harshad number, happy number, repdigit (1111) in base 9
  • 821 = prime number, twin prime, Eisenstein prime with no imaginary part, 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[9]
  • 823 = prime number, twin 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,[10] the Mertens function of 825 returns 0, Harshad number
  • 826 = 2 × 7 × 59, sphenic number
  • 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[11]
  • 828 = 22 × 32 × 23, Harshad number
  • 829 = prime number, twin prime, part of prime quadruplet with {827, 823, 821}, sum of three consecutive primes (271 + 277 + 281), Chen prime

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
  • 832 = 26 × 13, Harshad number
  • 833 = 72 × 17
  • 834 = 2 × 3 × 139, sphenic number, sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151), nontotient
  • 835 = 5 × 167, Motzkin number[12]
Main article: 836 (number)

840s

  • 840 = 23 × 3 × 5 × 7, highly composite number,[15] smallest numbers divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,[16] Harshad number in base 2 through base 10
  • 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,[17] centered heptagonal number,[18] centered octagonal number[19]
  • 842 = 2 × 421, nontotient
  • 843 = 3 × 281, Lucas number[20]
  • 844 = 22 × 211, nontotient
  • 845 = 5 × 132
  • 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
  • 848 = 24 × 53
  • 849 = 3 × 283, the Mertens function of 849 returns 0

850s

860s

  • 860 = 22 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227)
  • 861 = 3 × 7 × 41, sphenic number, triangular number,[8] hexagonal number,[28] Smith number[10]
  • 862 = 2 × 431
  • 863 = prime number, safe prime,[13] 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
  • 864 = 25 × 33, 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
  • 867 = 3 × 172
  • 868 = 22 × 7 × 31, 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,[3] nontotient, sparsely totient number,[16] Harshad number
  • 871 = 13 × 67, thirteenth tridecagonal number
  • 872 = 23 × 109, nontotient
  • 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[29]: 103 - 53
  • 876 = 22 × 3 × 73, generalized pentagonal number[30]
  • 877 = prime number, Bell number,[31] Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number.[11]
  • 878 = 2 × 439, nontotient
  • 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices[32]

880s

Main article: 880 (number)
  • 880 = 24 × 5 × 11, Harshad number; 148-gonal number; the number of n×n magic squares for n = 4.
    • country calling code for Bangladesh
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, Harshad number, totient sum for first 53 integers
  • 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
  • 885 = 3 × 5 × 59, sphenic number
  • 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,[13] Chen prime, Eisenstein prime with no imaginary part
Seven-segment 8.svgSeven-segment 8.svgSeven-segment 8.svg
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[1], happy number
  • 889 = 7 × 127, the Mertens function of 889 returns 0

890s

  • 890 = 2 × 5 × 89, 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
  • 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,[10] Woodall number,[33] 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
  • 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
  • 899 = 29 × 31, happy number

References

  1. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  3. ^ a b Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  8. ^ a b Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  10. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  11. ^ a b Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  13. ^ a b c Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  16. ^ a b Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  26. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A007850 (Giuga numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A014439 (Differences between two positive cubes in exactly 1 way.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2019-08-18.
  30. ^ Sloane, N. J. A. (ed.). "Sequence A001318 (Generalized pentagonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2019-08-26.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A319190 (Number of regular hypergraphs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2019-08-18.
  33. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.