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800 (number)
800 (number)
800 (number)
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← 799 800 801 →
Cardinaleight hundred
Ordinal800th
(eight hundredth)
Factorization25 × 52
Divisors1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800
Greek numeralΩ´
Roman numeralDCCC, dccc
Binary11001000002
Ternary10021223
Senary34126
Octal14408
Duodecimal56812
Hexadecimal32016
ArmenianՊ
Hebrewת"ת / ף
Babylonian cuneiform𒌋𒐗⟪
Egyptian hieroglyph𓍩

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

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800s

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Main article: 801 (number)

810s

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"811 (number)" redirects here. For the phone number, see 8-1-1. For other topics, see 811 (disambiguation).

820s

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  • 820 = 22 × 5 × 41, 40th triangular number, smallest triangular number that starts with the digit 8,[22] 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 (sequence A000124 in the OEIS), 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[23]
  • 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,[24] 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[25]
  • 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[26]
  • 828 = 22 × 32 × 23, Harshad number, triangular matchstick number[27]
  • 829 = prime number, twin prime, part of prime quadruplet with {827, 823, 821}, sum of three consecutive primes (271 + 277 + 281), Chen prime, centered triangular number

830s

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  • 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[28]
  • 832 = 26 × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2)[29]
  • 833 = 72 × 17, octagonal number (sequence A000567 in the OEIS), a centered octahedral number[30]
  • 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[31]
Main article: 836 (number)
  • 836 = 22 × 11 × 19, weird number
  • 837 = 33 × 31, the 36th generalized heptagonal number[32]
  • 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i<j<k <= 23[33]
  • 839 = prime number, safe prime,[34] sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number[35]

840s

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Main article: 840 (number)
  • 840 = 23 × 3 × 5 × 7, highly composite number,[36] smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,[37] Harshad number in base 2 through base 10, idoneal number, balanced number,[38] 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,[39] centered heptagonal number,[40] centered octagonal number[41]
  • 842 = 2 × 421, nontotient, 842!! - 1 is prime,[42] number of series-reduced trees with 18 nodes[43]
  • 843 = 3 × 281, Lucas number[44]
  • 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 [45]
  • 845 = 5 × 132, concentric pentagonal number,[46] number of emergent parts in all partitions of 22 [47]
  • 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[48]
  • 848 = 24 × 53, untouchable number
  • 849 = 3 × 283, the Mertens function of 849 returns 0, Blum integer

850s

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860s

[edit]
  • 860 = 22 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number[59]
  • 861 = 3 × 7 × 41, sphenic number, 41st triangular number,[22] hexagonal number,[60] Smith number[24]
  • 862 = 2 × 431, lazy caterer number (sequence A000124 in the OEIS)
  • 863 = prime number, safe prime,[34] 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[61]
  • 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,[62] 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[63]
  • 868 = 22 × 7 × 31 = J3(10),[64] nontotient
  • 869 = 11 × 79, the Mertens function of 869 returns 0

870s

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  • 870 = 2 × 3 × 5 × 29, sum of ten consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), pronic number,[15] nontotient, sparsely totient number,[37] Harshad number
  • 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:[65] 103 – 53
  • 876 = 22 × 3 × 73, generalized pentagonal number[66]
  • 877 = prime number, Bell number,[67] Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number,[26] prime index prime
  • 878 = 2 × 439, nontotient, number of Pythagorean triples with hypotenuse < 1000.[68]
  • 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices,[69] candidate Lychrel seed number

880s

[edit]
Main article: 880 (number)
  • 880 = 24 × 5 × 11 = 11!!!,[70] 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 = a trinomial coefficient,[71] Harshad number, totient sum for first 53 integers, area of a square with diagonal 42[1]
  • 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[72]
  • 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.[73]
  • 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,[34] Chen prime, Eisenstein prime with no imaginary part
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,[11] happy number, 888!! - 1 is prime[74]
  • 889 = 7 × 127, the Mertens function of 889 returns 0

890s

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  • 890 = 2 × 5 × 89 = 192 + 232 (sum of squares of two successive primes),[75] 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 (sequence A331452 in the OEIS).
  • 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,[24] Woodall number,[76] 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 (sequence A002064 in the OEIS)
  • 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
  • 899 = 29 × 31 (a twin prime product),[77] happy number, smallest number with digit sum 26,[78] number of partitions of 51 into prime parts

References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

800 (number)

View on Grokipedia
from Grokipedia
800 is a , the immediately following and preceding 801, often expressed in words as "eight hundred" and in as DCCC. As a , it has the prime 25×522^5 \times 5^2, making it divisible by 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and itself, for a total of eighteen positive divisors. Mathematically, 800 qualifies as an , where the sum of its proper divisors exceeds the number itself (specifically, 1,153 > 800), and a since it is evenly divisible by the sum of its digits (8 + 0 + 0 = 8). Its value is 320, indicating the count of integers up to 800 that are coprime to it, while its is 8. In binary representation, 800 is 1100100000. These properties highlight 800's role in , though it lacks special status like primality or . Beyond , 800 holds practical significance in as the original prefix for toll-free numbers in , introduced by in 1967 to allow businesses to receive calls without charging the caller. This system revolutionized customer service, enabling nationwide "1-800" dialing, with portability across carriers mandated by the FCC in 1993. Historically, the year 800 AD marks pivotal events, including the crowning of as by on December 25 in , symbolizing the revival of the and a key moment in medieval European history.

Mathematical Properties

Definition and Basic Characteristics

800 (eight hundred) is the natural number following 799 and preceding 801 in the sequence of positive . As an even , it is divisible by 2, and in the decimal numeral system, it is classified as a three-digit number, ranging from 100 to 999. The standard English cardinal name for 800 is "eight hundred," while its ordinal form is "eight hundredth" or abbreviated as "800th." One notable mathematical representation of 800 involves sums of s. Specifically, 800 equals the sum of the four consecutive primes , 197, , and 211:
193+197+199+211=800.193 + 197 + 199 + 211 = 800.
This property highlights 800's connection to sequences. In , 800 serves as the area of whose diagonal measures 40 units. The for the area AA of a square with diagonal length dd is
A=d22,A = \frac{d^2}{2},
yielding
A=4022=16002=800.A = \frac{40^2}{2} = \frac{1600}{2} = 800.
This follows from the relationship where the diagonal d=s2d = s\sqrt{2}
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