# 800 (number)

(Redirected from 849 (number))

800 (eight hundred) is the natural number following 799 and preceding 801.

 ← 799 800 801 →
Cardinaleight hundred
Ordinal800th
(eight hundredth)
Factorization25 × 52
Greek numeralΩ´
Roman numeralDCCC
Binary11001000002
Ternary10021223
Senary34126
Octal14408
Duodecimal56812

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.

## Integers from 801 to 899

### 820s

• 820 = 22 × 5 × 41, triangular number, smallest triangular number that starts with the digit 8 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
• 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, 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
• 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
• 828 = 22 × 32 × 23, Harshad number, triangular matchstick number
• 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

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

### 840s

• 840 = 23 × 3 × 5 × 7, highly composite number, smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number, 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, centered heptagonal number, centered octagonal number
• 842 = 2 × 421, nontotient, 842!! - 1 is prime, number of series-reduced trees with 18 nodes
• 843 = 3 × 281, Lucas number
• 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 
• 845 = 5 × 132, concentric pentagonal number, number of emergent parts in all partitions of 22 
• 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
• 848 = 24 × 53, untouchable number
• 849 = 3 × 283, the Mertens function of 849 returns 0, blum integer

### 860s

• 860 = 22 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number
• 861 = 3 × 7 × 41, sphenic number, triangular number, hexagonal number, Smith number
• 862 = 2 × 431, lazy caterer number (sequence A000124 in the OEIS)
• 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, 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
• 868 = 22 × 7 × 31 = J3(10), 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
• 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: 103 - 53
• 876 = 22 × 3 × 73, generalized pentagonal number
• 877 = prime number, Bell number, 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.
• 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices, candidate Lychrel seed number

### 880s

• 880 = 24 × 5 × 11 = 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 × 32 × 72 = ${\binom {9}{5}}_{2}$  a trinomial coefficient, Harshad number, totient sum for first 53 integers, area of a square with diagonal 42
• 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, number of points on surface of tetrahedron with sidelength 21
• 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.
• 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   • 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
• 889 = 7 × 127, the Mertens function of 889 returns 0

### 890s

• 890 = 2 × 5 × 89 = 192 + 232 (sum of squares of two successive primes), 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, Woodall number, 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), happy number, smallest number with digitsum 26, number of partitions of 51 into prime parts