# 800 (number)

| ||||
---|---|---|---|---|

Cardinal | eight hundred | |||

Ordinal | 800th (eight hundredth) | |||

Factorization | 2^{5}× 5^{2} | |||

Greek numeral | Ω´ | |||

Roman numeral | DCCC | |||

Binary | 1100100000_{2} | |||

Ternary | 1002122_{3} | |||

Quaternary | 30200_{4} | |||

Quinary | 11200_{5} | |||

Senary | 3412_{6} | |||

Octal | 1440_{8} | |||

Duodecimal | 568_{12} | |||

Hexadecimal | 320_{16} | |||

Vigesimal | 200_{20} | |||

Base 36 | M8_{36} |

**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.

## Contents

## Integers from 801 to 899[edit]

### 800s[edit]

- 801 = 3
^{2}× 89, Harshad number - 802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number
- 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
- 804 = 2
^{2}× 3 × 67, nontotient, Harshad 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 = 5 × 7 × 23
- 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number
- 807 = 3 × 269
- 808 = 2
^{3}× 101, strobogrammatic number^{[1]} - 809 = prime number, Sophie Germain prime,
^{[2]}Chen prime, Eisenstein prime with no imaginary part

### 810s[edit]

- 810 = 2 × 3
^{4}× 5, Harshad number - 811 = prime number, sum of five consecutive primes (151 + 157 + 163 + 167 + 173), Chen prime, happy number, the Mertens function of 811 returns 0
- 812 = 2
^{2}× 7 × 29, pronic number,^{[3]}the Mertens function of 812 returns 0 - 813 = 3 × 271
- 814 = 2 × 11 × 37, sphenic number, the Mertens function of 814 returns 0, nontotient
- 815 = 5 × 163
- 816 = 2
^{4}× 3 × 17, tetrahedral number,^{[4]}Padovan number,^{[5]}Zuckerman number - 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277), centered hexagonal number
^{[6]} - 818 = 2 × 409, nontotient, strobogrammatic number
^{[1]} - 819 = 3
^{2}× 7 × 13, square pyramidal number^{[7]}

### 820s[edit]

- 820 = 2
^{2}× 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 = 2
^{3}× 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 × 5
^{2}× 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 = 2
^{2}× 3^{2}× 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[edit]

- 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 = 2
^{6}× 13, Harshad number - 833 = 7
^{2}× 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]}

- 836 = 2
^{2}× 11 × 19, weird number - 837 = 3
^{3}× 31 - 838 = 2 × 419
- 839 = prime number, safe prime,
^{[13]}sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number^{[14]}

### 840s[edit]

- 840 = 2
^{3}× 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 = 29
^{2}= 20^{2}+ 21^{2}, 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 = 2
^{2}× 211, nontotient - 845 = 5 × 13
^{2} - 846 = 2 × 3
^{2}× 47, sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127), nontotient, Harshad number - 847 = 7 × 11
^{2}, happy number - 848 = 2
^{4}× 53 - 849 = 3 × 283, the Mertens function of 849 returns 0

### 850s[edit]

- 850 = 2 × 5
^{2}× 17, the Mertens function of 850 returns 0, nontotient, the maximum possible Fair Isaac credit score, country calling code for North Korea - 851 = 23 × 37
- 852 = 2
^{2}× 3 × 71, pentagonal number,^{[21]}Smith number^{[10]}- country calling code for Hong Kong

- 853 = prime number, Perrin number,
^{[22]}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, nontotient
- 855 = 3
^{2}× 5 × 19, decagonal number,^{[23]}centered cube number^{[24]}- country calling code for Cambodia

- 856 = 2
^{3}× 107, nonagonal number,^{[25]}centered pentagonal number,^{[26]}happy 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
^{[27]} - 859 = prime number

### 860s[edit]

- 860 = 2
^{2}× 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 = 2
^{5}× 3^{3}, 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 × 17
^{2} - 868 = 2
^{2}× 7 × 31, nontotient - 869 = 11 × 79, the Mertens function of 869 returns 0

### 870s[edit]

- 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- This number is the magic constant of
*n*×*n*normal magic square and*n*-queens problem for*n*= 12.

- This number is the magic constant of
- 871 = 13 × 67
- 872 = 2
^{3}× 109, nontotient - 873 = 3
^{2}× 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 = 5
^{3}× 7 - 876 = 2
^{2}× 3 × 73 - 877 = prime number, Bell number,
^{[29]}Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number.^{[11]} - 878 = 2 × 439, nontotient
- 879 = 3 × 293

### 880s[edit]

- 880 = 2
^{4}× 5 × 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 (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part, happy number
- 882 = 2 × 3
^{2}× 7^{2}, 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 = 2
^{2}× 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

- 888 = 2
^{3}× 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number, strobogrammatic number^{[1]} - 889 = 7 × 127, the Mertens function of 889 returns 0

### 890s[edit]

- 890 = 2 × 5 × 89, sphenic number, sum of four consecutive primes (211 + 223 + 227 + 229), nontotient
- 891 = 3
^{4}× 11, sum of five consecutive primes (167 + 173 + 179 + 181 + 191), octahedral number - 892 = 2
^{2}× 223, nontotient - 893 = 19 × 47, the Mertens function of 893 returns 0
- 894 = 2 × 3 × 149, sphenic number, nontotient
- 895 = 5 × 179, Smith number,
^{[10]}Woodall number,^{[30]}the Mertens function of 895 returns 0 - 896 = 2
^{7}× 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[edit]

- ^
^{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. **^**Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{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. **^**Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**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.**^**Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{a}^{b}Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. **^**Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{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. - ^
^{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. **^**Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{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. **^**Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{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. **^**Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**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.**^**Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**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.**^**Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**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.**^**Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A007850 (Giuga numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.