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800 (eight hundred) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
799 and preceding
801.
It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a
Harshad number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...
, an
Achilles number and the area of a
square
In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
with diagonal 40.
Integers from 801 to 899
800s
* 801 = 3
2 × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins
* 802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113),
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231)
* 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, number of partitions of 34 into Fibonacci parts
* 804 = 2
2 × 3 × 67, nontotient, Harshad number,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
** "The 804" is a local nickname for the
Greater Richmond Region
The Greater Richmond Region, also known as the Richmond metropolitan area or Central Virginia, is a region and metropolitan area in the U.S. state of Virginia, centered on Richmond. The U.S. Office of Management and Budget (OMB) defines the are ...
of the U.S. state of
Virginia
Virginia, officially the Commonwealth of Virginia, is a U.S. state, state in the Southeastern United States, Southeastern and Mid-Atlantic (United States), Mid-Atlantic regions of the United States between the East Coast of the United States ...
, derived from
its telephone area code (although the area code covers a larger area).
* 805 = 5 × 7 × 23,
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, number of partitions of 38 into nonprime parts
* 806 = 2 × 13 × 31,
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, nontotient, totient sum for first 51 integers,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, Phi(51)
* 807 = 3 × 269, antisigma(42)
* 808 = 2
3 × 101,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
,
strobogrammatic number
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it Centrosymmetry, appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A ...
* 809 = prime number,
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...
,
Chen prime
In mathematics, a prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem.
The Chen primes are named a ...
,
Eisenstein prime
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form
: z = a + b\omega ,
where and are integers and
: \omega = \frac ...
with no imaginary part
810s
* 810 = 2 × 3
4 × 5, Harshad number, number of distinct reduced words of length 5 in the Coxeter group of "Apollonian reflections" in three dimensions, number of non-equivalent ways of expressing 100,000 as the sum of two prime numbers
* 811 = prime number, twin prime, sum of five consecutive primes (151 + 157 + 163 + 167 + 173), Chen prime,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, largest
minimal prime in base 9, the
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...
of 811 returns 0
* 812 = 2
2 × 7 × 29,
admirable number,
pronic number
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...
,
balanced number, the Mertens function of 812 returns 0
* 813 = 3 × 271,
Blum integer
In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/ ...
* 814 = 2 × 11 × 37, sphenic number, the Mertens function of 814 returns 0, nontotient, number of fixed
hexahexes.
* 815 = 5 × 163, number of graphs with 8 vertices and a distinguished bipartite block
* 816 = 2
4 × 3 × 17,
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...
,
Padovan number, Zuckerman number
* 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277),
centered hexagonal number
In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered polygonal number, centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot ...
* 818 = 2 × 409, nontotient,
strobogrammatic number
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it Centrosymmetry, appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A ...
* 819 = 3
2 × 7 × 13,
square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part ...
820s
* 820 = 2
2 × 5 × 41, 40th
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
, smallest triangular number that starts with the digit 8,
Harshad number,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, repdigit (1111) in base 9
* 821 = prime number,
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
, Chen prime, Eisenstein prime with no imaginary part, lazy caterer number ,
prime quadruplet
In number theory, a prime quadruplet (sometimes called a prime quadruple) is a set of four prime numbers of the form This represents the closest possible grouping of four primes larger than 3, and is the only prime constellation of length 4.
P ...
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
In mathematics, the Mian–Chowla sequence is an integer sequence defined
recursively in the following way. The sequence starts with
:a_1 = 1.
Then for n>1, a_n is the smallest integer such that every pairwise sum
:a_i + a_j
is distinct, for ...
* 823 = prime number,
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
,
lucky prime, the Mertens function of 823 returns 0, prime quadruplet with 821, 827, 829
* 824 = 2
3 × 103,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
, 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
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the ...
,
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
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
, part of prime quadruplet with , 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 = 2
2 × 3
2 × 23, Harshad number, triangular matchstick number
* 829 = prime number,
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
, part of prime quadruplet with , sum of three consecutive primes (271 + 277 + 281), Chen prime,
centered triangular number
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.
This is also t ...
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 = 2
6 × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2)
* 833 = 7
2 × 17,
octagonal number
In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o'n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlai ...
, a
centered octahedral number
* 834 = 2 × 3 × 139,
cake number
In mathematics, the cake number, denoted by ''Cn'', is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly ''n'' planes. The cake number is so called because one may imagine each partition of the cu ...
, sphenic number, sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151), nontotient
* 835 = 5 × 167,
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have ...
* 836 = 2
2 × 11 × 19,
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 (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divi ...
* 837 = 3
3 × 31, the 36th generalized heptagonal number
* 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i
safe prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...
,
sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part,
highly cototient number
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation
:x - \phi(x) = k
than any other integer below k and above 1. Here, \phi is Euler's totient func ...
840s
* 840 = 2
3 × 3 × 5 × 7,
highly composite number
A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...
, 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 = 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
In elementary number theory, a centered square number is a Centered polygonal number, centered figurate number that gives the number of dots in a Square (geometry), square with a dot in the center and all other dots surrounding the center dot i ...
,
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. The centered heptagonal number for ''n'' is given by ...
,
centered octagonal number
A centered octagonal number is a centered number, 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.. The centered octagonal numbers are th ...
* 842 = 2 × 421, nontotient, 842!! - 1 is prime, number of series-reduced trees with 18 nodes
* 843 = 3 × 281,
Lucas number
The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence ar ...
* 844 = 2
2 × 211, nontotient, smallest 5 consecutive integers which are not squarefree are: 844 = 2
2 × 211, 845 = 5 × 13
2, 846 = 2 × 3
2 × 47, 847 = 7 × 11
2 and 848 = 2
4 × 53
* 845 = 5 × 13
2, concentric pentagonal number, number of emergent parts in all partitions of 22
* 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
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, number of partitions of 29 that do not contain 1 as a part
* 848 = 2
4 × 53,
untouchable number
In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at l ...
* 849 = 3 × 283, the Mertens function of 849 returns 0,
Blum integer
In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/ ...
850s
* 850 = 2 × 5
2 × 17, the Mertens function of 850 returns 0, nontotient, the sum of the squares of the divisors of 26 is 850 . The maximum possible
Fair Isaac credit score, country calling code for North Korea
* 851 = 23 × 37, number of compositions of 18 into distinct parts
* 852 = 2
2 × 3 × 71,
pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational ...
, Smith number
** country calling code for Hong Kong
* 853 = prime number,
Perrin number
In mathematics, the Perrin numbers are a doubly infinite constant-recursive sequence, constant-recursive integer sequence with Characteristic equation (calculus), characteristic equation . The Perrin numbers, named after the French engineer , bear ...
, the
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...
of 853 returns 0, average of first 853 prime numbers is an integer , strictly non-palindromic number, number of connected graphs with 7 nodes
** country calling code for Macau
* 854 = 2 × 7 × 61,
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, nontotient, number of unlabeled planar trees with 11 nodes
* 855 = 3
2 × 5 × 19,
decagonal number,
centered cube number
** country calling code for Cambodia
* 856 = 2
3 × 107,
nonagonal number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns in ...
,
centered pentagonal number
In mathematics, a centered pentagonal number is a centered polygonal number, centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered p ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
** 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
* 859 = prime number, number of planar partitions of 11,
prime index prime
860s
* 860 = 2
2 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number
* 861 = 3 × 7 × 41, sphenic number, 41st
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
,
hexagonal number
A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...
, Smith number
* 862 = 2 × 431, lazy caterer number
* 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 = 2
5 × 3
3,
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 × 17
2, number of 5-chromatic simple graphs on 8 nodes
* 868 = 2
2 × 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
** This number is the
magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
of ''n''×''n'' normal
magic square
In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ...
and
''n''-queens problem for ''n'' = 12.
* 871 = 13 × 67, thirteenth
tridecagonal number
* 872 = 2
3 × 109,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
, nontotient, 872! + 1 is
prime
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
* 873 = 3
2 × 97, sum of the first six factorials from 1
* 874 = 2 × 19 × 23,
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, sum of the first twenty-three primes, sum of the first seven factorials from 0, nontotient, Harshad number,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
* 875 = 5
3 × 7, unique expression as difference of positive cubes: 10
3 – 5
3
* 876 = 2
2 × 3 × 73, generalized pentagonal number
* 877 = prime number,
Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of epony ...
, Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number,
* 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 = 2
4 × 5 × 11 = 11!!!, Harshad number; 148-
gonal number; the number of ''n''×''n''
magic square
In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ...
s for n = 4.
** country calling code for Bangladesh
* 881 = prime number,
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''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
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
* 882 = 2 × 3
2 × 7
2 =
a
trinomial coefficient, Harshad number, totient sum for first 53 integers, area of a square with diagonal 42
* 883 = prime number,
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''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 = 2
2 × 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
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, 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 = 2
3 × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number,
strobogrammatic number
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it Centrosymmetry, appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, 888!! - 1 is prime
* 889 = 7 × 127, the Mertens function of 889 returns 0
890s
* 890 = 2 × 5 × 89 = 19
2 + 23
2 (sum of squares of two successive primes), 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
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahedral ...
* 892 = 2
2 × 223, nontotient, number of regions formed by drawing the line segments connecting any two perimeter points of a 6 times 2 grid of squares lik
this.
* 893 = 19 × 47, the Mertens function of 893 returns 0
** Considered an unlucky number in
Japan
Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...
, because its digits read sequentially are the literal translation of ''
yakuza
, also known as , are members of transnational organized crime syndicates originating in Japan. The Japanese police and media (by request of the police) call them , while the yakuza call themselves . The English equivalent for the term ''yak ...
''.
* 894 = 2 × 3 × 149, sphenic number, nontotient
* 895 = 5 × 179, Smith number,
, the Mertens function of 895 returns 0
* 896 = 2
7 × 7,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...
, 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
* 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
* 899 = 29 × 31 (a
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
product),
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
, smallest number with digit sum 26,
References
{{Integers, 8
Integers