800 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 799 and preceding 801.

Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...	800 eight hundred
Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...	800th eight hundredth
Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
Roman numeral	DCCC
Roman numeral (Unicode)	DCCC, dccc
Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...	1100100000
Octal Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...	1440
Duodecimal Duodecimal The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...	568
Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...	320

It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number

Harshad number

A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

.

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801 = 3² × 89, Harshad number
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802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient

Nontotient

In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...

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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
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804 = 2² × 3 × 67, nontotient, Harshad number
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805 = 5 × 7 × 23
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806 = 2 × 13 × 31, sphenic number

Sphenic number

In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

, nontotient, totient sum for first 51 integers
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807 = 3 × 269
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808 = 2³ × 101, strobogrammatic number

Strobogrammatic number

A strobogrammatic number is a number that, given a base and given a set of glyphs, appears the same whether viewed normally or upside down. In base 10, given a set of glyphs where 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down , the first...

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809 prime number, Sophie Germain prime

Sophie Germain prime

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number...

, Chen prime

Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....

, Eisenstein prime

Eisenstein prime

In mathematics, an Eisenstein prime is an Eisenstein integerz = a + b\,\omega\qquadthat is irreducible in the ring-theoretic sense: its only Eisenstein divisors are the units , a + bω itself and its associates.The associates and the complex conjugate...

 with no imaginary part
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810 = 2 × 3⁴ × 5, Harshad number
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811 prime number, sum of five consecutive primes (151 + 157 + 163 + 167 + 173), Chen prime, Mertens function(811) returns 0
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812 = 2² × 7 × 29, pronic number

Pronic number

A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...

, Mertens function(812) returns 0
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813 = 3 × 271
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814 = 2 × 11 × 37, sphenic number, Mertens function(814) returns 0, nontotient
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815 = 5 × 163
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816 = 2⁴ × 3 × 17, tetrahedral number

Tetrahedral number

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

, member of the Padovan sequence

Padovan sequence

The Padovan sequence is the sequence of integers P defined by the initial valuesP=P=P=1,and the recurrence relationP=P+P.The first few values of P are...

, Zuckerman number
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817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277), centered hexagonal number

Centered hexagonal number

A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice....

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818 = 2 × 409, nontotient
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819 = 3² × 7 × 13, square pyramidal number

Square pyramidal number

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...

----
820 = 2² × 5 × 41, triangular number

Triangular number

A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

, Harshad number
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821 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, Eisenstein prime with no imaginary part, prime quadruplet with 823, 827, 829
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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
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823 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, Mertens function(823) returns 0, prime quadruplet with 821, 827, 829
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824 = 2³ × 103, sum of ten consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), Mertens function(824) returns 0, nontotient
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825 = 3 × 5² × 11, Smith number

Smith number

A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...

, Mertens function(825) returns 0, Harshad number
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826 = 2 × 7 × 59, sphenic number
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827 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, 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

Strictly non-palindromic number

A strictly non-palindromic number is an integer n that is not palindromic in any numeral system with a base b in the range 2 ≤ b ≤ n − 2...

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828 = 2² × 3² × 23, Harshad number
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829 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, part of prime quadruplet with {827, 823, 821}, sum of three consecutive primes (271 + 277 + 281), Chen prime
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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
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831 = 3 × 277
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832 = 2⁶ × 13, Harshad number
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833 = 7² × 17
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834 = 2 × 3 × 139, sphenic number, sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151), nontotient
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835 = 5 × 167, Motzkin number

Motzkin number

In mathematics, a Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points. The Motzkin numbers have very diverse applications in geometry, combinatorics and number theory...

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836 = 2² × 11 × 19, weird number

Weird number

In number theory, a weird number is a natural number that is abundant but not semiperfect.In other words, the sum of the proper divisors of the number is greater than the number, but no subset of those divisors sums to the number itself.- Examples :The smallest weird number is 70...

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837 = 3³ × 31
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838 = 2 × 419
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839 prime number, safe prime

Safe prime

A safe prime is a prime number of the form 2p + 1, where p is also a prime. The first few safe primes are...

, sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number

Highly cototient number

In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...

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840 = 2³ × 3 × 5 × 7, highly composite number

Highly composite number

A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....

, smallest numbers divisible by the numbers 1 to 8, sparsely totient number, Harshad number in base 2 through base 10
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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 square number

In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...

, centered heptagonal number

Centered heptagonal number

A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers...

, centered octagonal number

Centered octagonal number

A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers...

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842 = 2 × 421, nontotient
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843 = 3 × 281
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844 = 2² × 211, nontotient
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845 = 5 × 13²
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846 = 2 × 3² × 47, sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127), nontotient, Harshad number
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847 = 7 × 11²
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848 = 2⁴ × 53
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849 = 3 × 283, Mertens function(849) returns 0
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850 = 2 × 5² × 17, Mertens function(850) returns 0, nontotient, the maximum possible Fair Isaac credit score.
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851 = 23 × 37
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852 = 2² × 3 × 71, Smith number
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853 prime number, Mertens function(853) returns 0, average of first 853 prime numbers is an integer , strictly non-palindromic number
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854 = 2 × 7 × 61, nontotient
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855 = 3² × 5 × 19, decagonal number

Decagonal number

A decagonal number is a figurate number that represents a decagon. The n-th decagonal number is given by the formulaThe first few decagonal numbers are:...

, centered cube number

Centered cube number

A centered cube number is a centered figurate number that represents a cube. The centered cube number for n is given byn^3 + ^3.The first few centered cube numbers are...

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856 = 2³ × 107, nonagonal number, centered pentagonal number

Centered pentagonal number

A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers...

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857 prime number, sum of three consecutive primes (281 + 283 + 293), Chen prime, Eisenstein prime with no imaginary part
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858 = 2 × 3 × 11 × 13, Giuga number

Giuga number

A Giuga number is a composite number n such that for each of its distinct prime factors pi we have p_i | , or equivalently such that for each of its distinct prime factors pi we have p_i^2 | ....

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859 prime number
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860 = 2² × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227)
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861 = 3 × 7 × 41, sphenic number, triangular number, hexagonal number

Hexagonal number

A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...

, Smith number
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862 = 2 × 431
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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
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864 = 2⁵ × 3³, sum of a twin prime (431 + 433), sum of six consecutive primes (131 + 137 + 139 + 149 + 151 + 157), Harshad number
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865 = 5 × 173
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866 = 2 × 433, nontotient
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867 = 3 × 17²
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868 = 2² × 7 × 31, nontotient
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869 = 11 × 79, Mertens function(869) returns 0
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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, nontotient, sparsely totient number, Harshad number

This number is the magic constant

Magic constant

The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....

 of n×n normal magic square

Magic square

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...

 and n-queens problem

Eight queens puzzle

The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...

 for n = 12.
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871 = 13 × 67
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872 = 2³ × 109, nontotient
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873 = 3² × 97, sum of the first six factorials from 1
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874 = 2 × 19 × 23, sum of the first twenty-three primes, sum of the first seven factorials from 0, nontotient, Harshad number
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875 = 5³ × 7
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876 = 2² × 3 × 73
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877 prime number, Bell number

Bell number

In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it...

, Chen prime, Mertens function(877) returns 0, strictly non-palindromic number.
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878 = 2 × 439, nontotient
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879 = 3 × 293
----
880 = 2⁴ × 5 × 11, Harshad number; 148-gonal number

Polygonal number

In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...

; the number of n×n magic square

Magic square

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...

s for n = 4.
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881 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, sum of nine consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part
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882 = 2 × 3² × 7², Harshad number, totient sum for first 53 integers
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883 prime number, twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

, sum of three consecutive primes (283 + 293 + 307), Mertens function(883) returns 0
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884 = 2² × 13 × 17, Mertens function(884) returns 0
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885 = 3 × 5 × 59, sphenic number
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886 = 2 × 443, Mertens function(886) returns 0
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887 prime number followed by primal gap of 20, safe prime, Chen prime, Eisenstein prime with no imaginary part
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888 = 2³ × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number.
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889 = 7 × 127, Mertens function(889) returns 0
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890 = 2 × 5 × 89, sphenic number, sum of four consecutive primes (211 + 223 + 227 + 229), nontotient
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891 = 3⁴ × 11, sum of five consecutive primes (167 + 173 + 179 + 181 + 191), octahedral number

Octahedral number

In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres...

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892 = 2² × 223, nontotient
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893 = 19 × 47, Mertens function(893) returns 0
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894 = 2 × 3 × 149, sphenic number, nontotient
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895 = 5 × 179, Smith number, Woodall number

Woodall number

In number theory, a Woodall number is any natural number of the formfor some natural number n. The first few Woodall numbers are:Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers...

, Mertens function(895) returns 0
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896 = 2⁷ × 7, sum of six consecutive primes (137 + 139 + 149 + 151 + 157 + 163), Mertens function(896) returns 0
----
897 = 3 × 13 × 23, sphenic number
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898 = 2 × 449, Mertens function(898) returns 0, nontotient
----
899 = 29 × 31