800 (number)

This article is about the number. For the year, see 800. For other uses, see 800 (disambiguation).
 ← 799 800 801 →
Cardinal eight hundred
Ordinal 800th
(eight hundredth)
Factorization 25× 52
Roman numeral DCCC
Binary 11001000002
Ternary 10021223
Quaternary 302004
Quinary 112005
Senary 34126
Octal 14408
Duodecimal 56812
Hexadecimal 32016
Vigesimal 20020
Base 36 M836

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.

801 = 32 × 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 = 22 × 3 × 67, nontotient, Harshad number

805 = 5 × 7 × 23

806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number

807 = 3 × 269

808 = 23 × 101, strobogrammatic number[1]

809 prime number, Sophie Germain prime,[2] Chen prime, Eisenstein prime with no imaginary part

810 = 2 × 34 × 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 = 22 × 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 = 24 × 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 = 32 × 7 × 13, square pyramidal number[7]

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 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

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]

836 = 22 × 11 × 19, weird number

837 = 33 × 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]

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

850 = 2 × 52 × 17, the Mertens function 850 returns 0, nontotient, the maximum possible Fair Isaac credit score, country calling code for North Korea

851 = 23 × 37

852 = 22 × 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 = 32 × 5 × 19, decagonal number,[23] centered cube number[24]

• country calling code for Cambodia

• 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

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 869 returns 0

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.

871 = 13 × 67

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

876 = 22 × 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

880 = 24 × 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

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, happy number

884 = 22 × 13 × 17, the Mertens function 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 = 23 × 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

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 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,[30] the Mertens function 895 returns 0

896 = 27 × 7, sum of six consecutive primes (137 + 139 + 149 + 151 + 157 + 163), the Mertens function 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. "Sloane's A000787 : Strobogrammatic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
2. "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
3. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
5. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
6. "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
7. "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
8. "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
9. "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
10. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
11. "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
12. "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
13. "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
14. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
15. "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
16. "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
17. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
18. "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
19. "Sloane's 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's A000032 : Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
21. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
22. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
23. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
24. "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
25. "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
26. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
27. "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
28. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
29. "Sloane's A000110 : Bell or exponential numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
30. "Sloane's A003261 : Woodall numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
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