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800 (eight hundred) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
799
__NOTOC__
Year 799 ( DCCXCIX) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. The denomination 799 for this year has been used since the early medieval period, when the Anno Domini calendar ...
and preceding
801
__NOTOC__
Year 801 ( DCCCI) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* Emperor Charlemagne formally cedes Nordalbian territory (modern-day Schleswig-H ...
.
It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a
Harshad number, an
Achilles number
An Achilles number is a number that is powerful but not a perfect power.
A positive integer is a powerful number if, for every prime factor of , is also a divisor. In other words, every prime factor appears at least squared in the factoriza ...
and the area of a square 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 nontotien ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
, 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,
** "The 804" is a local nickname for the
Greater Richmond Region
The Greater Richmond Region, 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 area as the Richm ...
of the U.S. state of
Virginia
Virginia, officially the Commonwealth of Virginia, is a state in the Mid-Atlantic and Southeastern regions of the United States, between the Atlantic Coast and the Appalachian Mountains. The geography and climate of the Commonwealth ar ...
, derived from
its telephone area code (although the area code covers a larger area).
* 805 = 5 × 7 × 23, number of partitions of 38 into nonprime parts
* 806 = 2 × 13 × 31,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, '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.
Definit ...
, nontotient, totient sum for first 51 integers,
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
, Phi(51)
* 807 = 3 × 269, antisigma(42)
* 808 = 2
3 × 101,
strobogrammatic number
* 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 + ...
,
Chen prime
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 after Chen Jingru ...
,
Eisenstein prime
In mathematics, an Eisenstein prime is an Eisenstein integer
: z = a + b\,\omega, \quad \text \quad \omega = e^,
that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...
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 different ways in which 100,000 can be expressed as the sum of two prime numbers
* 811 = prime number, 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 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 because ...
, 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 re ...
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/tal ...
* 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 with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
,
Padovan number
In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values
:P(0)=P(1)=P(2)=1,
and the recurrence relation
:P(n)=P(n-2)+P(n-3).
The first few values of ''P''(''n'') are
:1, 1, 1, 2, 2, 3, 4, 5 ...
, Zuckerman number
* 817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277),
centered hexagonal number
* 818 = 2 × 409, nontotient,
strobogrammatic number
* 819 = 3
2 × 7 × 13,
square pyramidal number
820s
* 820 = 2
2 × 5 × 41,
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 i ...
,
Harshad number,
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
, 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
, Eisenstein prime with no imaginary part, lazy caterer number ,
prime quadruplet
In number theory, a prime quadruplet (sometimes called 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.
Prim ...
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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
,
lucky prime
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...
, the Mertens function of 823 returns 0, prime quadruplet with 821, 827, 829
* 824 = 2
3 × 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 × 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 given number base. In the case of numbers that are not square-f ...
,
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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
, 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
, 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.
The followin ...
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
An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are
: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 34 ...
, a
centered octahedral number
A centered octahedral number or Haüy octahedral number is a figurate number that counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of t ...
* 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 d ...
* 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 divis ...
* 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 + ...
,
sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part,
highly cototient number
840s
* 840 = 2
3 × 3 × 5 × 7,
highly composite number
__FORCETOC__
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
, 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 In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers ''D'' such that any integer expressible in only one way as ''x''2 ± ''Dy''2 (where ''x''2 is relatively prime to ''Dy ...
, balanced number. With 32 distinct divisors, it is the number below
1000 1000 or thousand may refer to:
* 1000 (number), a natural number
* AD 1000, a leap year in the Julian calendar
* 1000 BC, a year of the Before Christ era
* 1000 metres, a middle-distance running event
* 1000°, a German electronic dance music magazi ...
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 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 cen ...
,
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 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 the same as the od ...
* 842 = 2 × 421, nontotient, 842!! - 1 is prime, number of series-reduced trees with 18 nodes
* 843 = 3 × 281,
Lucas number
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci n ...
* 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 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 because ...
, number of partitions of 29 that do not contain 1 as a part
* 848 = 2
4 × 53,
untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...
* 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/tal ...
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 and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...
, Smith number
** country calling code for Hong Kong
* 853 = prime number,
Perrin number, 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 re ...
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, nontotient, number of unlabeled planar trees with 11 nodes
* 855 = 3
2 × 5 × 19,
decagonal number
A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...
,
centered cube number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equival ...
** 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 and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the constr ...
,
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. The centered pentagonal number for ''n'' is given by th ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
** 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, triangular number,
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
An Achilles number is a number that is powerful but not a perfect power.
A positive integer is a powerful number if, for every prime factor of , is also a divisor. In other words, every prime factor appears at least squared in the factoriza ...
, 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 of ''n''×''n'' normal
magic square and
''n''-queens problem for ''n'' = 12.
* 871 = 13 × 67, thirteenth
tridecagonal number
* 872 = 2
3 × 109, 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, 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 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 because ...
* 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 eponymy ...
, 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 squares 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
, 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 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 because ...
* 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
, sum of three consecutive primes (283 + 293 + 307), 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 grc, σφήνα, '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.
Definit ...
, 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,
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
, 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 ''n''th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahed ...
* 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, 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 ter ...
''.
* 894 = 2 × 3 × 149, sphenic number, nontotient
* 895 = 5 × 179, Smith number,
Woodall number
In number theory, a Woodall number (''W'n'') is any natural number of the form
:W_n = n \cdot 2^n - 1
for some natural number ''n''. The first few Woodall numbers are:
:1, 7, 23, 63, 159, 383, 895, … .
History
Woodall numbers were first st ...
, the Mertens function of 895 returns 0
* 896 = 2
7 × 7, 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
product),
happy number
In number theory, a happy number is a number which eventually reaches 1 when 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 because ...
, smallest number with digitsum 26,
References
{{Integers, 8
Integers