800 (number)

{{Redirect|Eight hundred|the film|The Eight Hundred|the year|800|other uses|800 (disambiguation)}}

{{Infobox number

| number = 800

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

It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal 40.{{cite OEIS|A001105|2=a(n) = 2*n^2}}

Integers from 801 to 899

= 800s =

801 = 3² × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins{{OEIS|A229093}}
802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number, sum of 4 consecutive triangular numbers{{OEIS|A005893}} (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{{cite OEIS|A003107|Number of partitions of n into Fibonacci parts (with a single type of 1)|access-date=2022-05-25}}
804 = 2² × 3 × 67, nontotient, Harshad number, refactorable number{{cite OEIS|A174457|Infinitely refactorable numbers|access-date=2023-10-16}}
"The 804" is a local nickname for the Greater Richmond Region of the U.S. state of Virginia, derived from its telephone area code (although the area code covers a larger area).{{cite newspaper|title=Richmond is getting a new area code. Not everyone is thrilled: 'I’ll be 804 forever'|url=https://www.wtvr.com/news/local-news/new-richmond-area-code-jan-02-2024|newspaper=WTVR-TV|access-date=2025-03-16}}{{cite newspaper|title=The 804 is running out of numbers|url=https://www.axios.com/local/richmond/2022/07/18/richmond-804-area-code-running-out-of-numbers|newspaper=AXIOS Richmond|access-date=2025-03-16|author=Karri Peifer}}
805 = 5 × 7 × 23, sphenic number, number of partitions of 38 into nonprime parts{{cite OEIS|A002095|Number of partitions of n into nonprime parts|access-date=2022-05-25}}
806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51){{cite OEIS|A002088|name=Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010|access-date=2022-05-25}}
807 = 3 × 269, antisigma(42){{cite OEIS|A024816|Antisigma(n): Sum of the numbers less than n that do not divide n|access-date=2022-05-25}}
808 = 2³ × 101, refactorable number, strobogrammatic number{{Cite OEIS|1=A000787|2=Strobogrammatic numbers|access-date=2016-06-11}}
809 = prime number, Sophie Germain prime,{{cite OEIS|1=A005384|2=Sophie Germain primes|access-date=2016-06-11}} Chen prime, Eisenstein prime with no imaginary part

= 810s =

{{redirect-multi|1|811 (number)|the phone number|8-1-1|other topics|811 (disambiguation)}}

810 = 2 × 3⁴ × 5, Harshad number, number of distinct reduced words of length 5 in the Coxeter group of "Apollonian reflections" in three dimensions,{{cite OEIS|A154638|a(n) is the number of distinct reduced words of length n in the Coxeter group of "Apollonian reflections" in three dimensions|access-date=2022-05-25}} number of non-equivalent ways of expressing 100,000 as the sum of two prime numbers{{Cite OEIS|1=A065577|2=Number of Goldbach partitions of 10^n|access-date=2023-08-31}}
811 = prime number, twin prime, sum of five consecutive primes (151 + 157 + 163 + 167 + 173), Chen prime, happy number, largest minimal prime in base 9, the Mertens function of 811 returns 0
812 = 2² × 7 × 29, admirable number, pronic number,{{Cite OEIS|1=A002378|2=Oblong (or promic, pronic, or heteromecic) numbers|access-date=2016-06-11}} balanced number,{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}} the Mertens function of 812 returns 0
813 = 3 × 271, Blum integer {{OEIS|id=A016105}}
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{{cite OEIS|A049312|Number of graphs with a distinguished bipartite block, by number of vertices|access-date=2022-05-25}}
816 = 2⁴ × 3 × 17, tetrahedral number,{{Cite OEIS|1=A000292|2=Tetrahedral numbers|access-date=2016-06-11}} Padovan number,{{Cite OEIS|1=A000931|2=Padovan sequence|access-date=2016-06-11}} Zuckerman number
817 = 19 × 43, sum of three consecutive primes (269 + 271 + 277), centered hexagonal number{{Cite OEIS|1=A003215|2=Hex (or centered hexagonal) numbers|access-date=2016-06-11}}
818 = 2 × 409, nontotient, strobogrammatic number
819 = 3² × 7 × 13, square pyramidal number{{Cite OEIS|1=A000330|2=Square pyramidal numbers|access-date=2016-06-11}}

= 820s =

820 = 2² × 5 × 41, 40th triangular number, smallest triangular number that starts with the digit 8,{{Cite OEIS|1=A000217|2=Triangular numbers|access-date=2016-06-11}} 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 {{OEIS|id=A000124}}, 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{{Cite OEIS|1=A005282|2=Mian-Chowla sequence|access-date=2016-06-11}}
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,{{Cite OEIS|1=A006753|2=Smith numbers|access-date=2016-06-11}} 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{{cite OEIS|A098859|Number of partitions of n into parts each of which is used a different number of times|access-date=2022-05-25}}
827 = prime number, twin prime, part of prime quadruplet with {821, 823, 829}, sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number{{Cite OEIS|1=A016038|2=Strictly non-palindromic numbers|access-date=2016-06-11}}
828 = 2² × 3² × 23, Harshad number, triangular matchstick number{{OEIS|A045943|access-date=2022-05-30}}
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{{cite OEIS|A001401|Number of partitions of n into at most 5 parts|access-date=2022-05-25}}
832 = 2⁶ × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2){{OEIS|A085449}}
833 = 7² × 17, octagonal number {{OEIS|id=A000567}}, a centered octahedral number{{cite OEIS|A001845|Centered octahedral numbers (crystal ball sequence for cubic lattice)|access-date=2022-06-02}}
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{{Cite OEIS|1=A001006|2=Motzkin numbers|access-date=2016-06-11}}

836 = 2² × 11 × 19, weird number
837 = 3³ × 31, the 36th generalized heptagonal number{{cite OEIS|A085787|2=Generalized heptagonal numbers: m*(5*m – 3)/2, m = 0, +-1, +-2 +-3, ...|access-date=2022-05-30}}
838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i{{cite OEIS|A027430|2=Number of distinct products ijk with 1 <= i
839 = prime number, safe prime,{{Cite OEIS|1=A005385|2=Safe primes|access-date=2016-06-11}} sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number{{Cite OEIS|1=A100827|2=Highly cototient numbers|access-date=2016-06-11}}

= 840s =

840 = 2³ × 3 × 5 × 7, highly composite number,{{Cite OEIS|1=A002182|2=Highly composite numbers|access-date=2016-06-11}} smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,{{Cite OEIS|1=A036913|2=Sparsely totient numbers|access-date=2016-06-11}} Harshad number in base 2 through base 10, idoneal number, balanced number,{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}} 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,{{Cite OEIS|1=A001844|2=Centered square numbers|access-date=2016-06-11}} centered heptagonal number,{{Cite OEIS|1=A069099|2=Centered heptagonal numbers|access-date=2016-06-11}} centered octagonal number{{Cite OEIS|1=A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers|access-date=2016-06-11}}
842 = 2 × 421, nontotient, 842!! - 1 is prime,{{cite OEIS|A007749|Numbers k such that k!! - 1 is prime|access-date=2022-05-24}} number of series-reduced trees with 18 nodes{{cite OEIS|A000014|Number of series-reduced trees with n nodes}}
843 = 3 × 281, Lucas number{{Cite OEIS|1=A000032|2=Lucas numbers|access-date=2016-06-11}}
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 {{cite OEIS|A045882|Smallest term of first run of (at least) n consecutive integers which are not squarefree|access-date=2022-05-24}}
845 = 5 × 13², concentric pentagonal number,{{cite OEIS|A032527|Concentric pentagonal numbers: floor( 5*n^2 / 4 )|access-date=2022-05-24}} number of emergent parts in all partitions of 22 {{cite OEIS|A182699|Number of emergent parts in all partitions of n|access-date=2022-05-24}}
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{{cite OEIS|A002865|Number of partitions of n that do not contain 1 as a part|access-date=2022-05-24}}
848 = 2⁴ × 53, untouchable number
849 = 3 × 283, the Mertens function of 849 returns 0, Blum integer

= 850s =

850 = 2 × 5² × 17, the Mertens function of 850 returns 0, nontotient, the sum of the squares of the divisors of 26 is 850 {{OEIS|id=A001157}}. The maximum possible Fair Isaac credit score, country calling code for North Korea
851 = 23 × 37, number of compositions of 18 into distinct parts{{cite OEIS|A032020|Number of compositions (ordered partitions) of n into distinct parts|access-date=2022-05-24}}
852 = 2² × 3 × 71, pentagonal number,{{Cite OEIS|1=A000326|2=Pentagonal numbers|access-date=2016-06-11}} Smith number
country calling code for Hong Kong
853 = prime number, Perrin number,{{Cite OEIS|1=A001608|2=Perrin sequence|access-date=2016-06-11}} the Mertens function of 853 returns 0, average of first 853 prime numbers is an integer {{OEIS|id=A045345}}, strictly non-palindromic number, number of connected graphs with 7 nodes
country calling code for Macau
854 = 2 × 7 × 61, sphenic number, nontotient, number of unlabeled planar trees with 11 nodes{{cite OEIS|A002995|Number of unlabeled planar trees (also called plane trees) with n nodes|access-date=2022-05-24}}
855 = 3² × 5 × 19, decagonal number,{{Cite OEIS|1=A001107|2=10-gonal (or decagonal) numbers|access-date=2016-06-11}} centered cube number{{Cite OEIS|1=A005898|2=Centered cube numbers|access-date=2016-06-11}}
country calling code for Cambodia
856 = 2³ × 107, nonagonal number,{{Cite OEIS|1=A001106|2=9-gonal (or enneagonal or nonagonal) numbers|access-date=2016-06-11}} centered pentagonal number,{{Cite OEIS|1=A005891|2=Centered pentagonal numbers|access-date=2016-06-11}} happy number, refactorable number
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{{Cite OEIS|1=A007850|2=Giuga numbers|access-date=2016-06-11}}
859 = prime number, number of planar partitions of 11,{{cite OEIS|A000219|Number of planar partitions (or plane partitions) of n|access-date=2022-05-24}} prime index prime

= 860s =

860 = 2² × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number{{cite OEIS|A019506|Hoax numbers|access-date=2022-05-24}}
861 = 3 × 7 × 41, sphenic number, 41st triangular number, hexagonal number,{{Cite OEIS|1=A000384|2=Hexagonal numbers|access-date=2016-06-11}} Smith number
862 = 2 × 431, lazy caterer number {{OEIS|id=A000124}}
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{{cite OEIS|A001606|Indices of prime Lucas numbers}}
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,{{Cite OEIS|A006534|access-date=2022-05-10}} 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{{cite OEIS|A076281|Number of 5-chromatic (i.e., chromatic number equals 5) simple graphs on n nodes|access-date=2022-05-24}}
868 = 2² × 7 × 31 = J₃(10),{{cite OEIS|A059376|Jordan function J_3(n)|access-date=2022-05-24}} 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 = 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:{{cite OEIS|1=A014439|2=Differences between two positive cubes in exactly 1 way.|access-date=2019-08-18}} 10³ – 5³
876 = 2² × 3 × 73, generalized pentagonal number{{cite OEIS|1=A001318|2=Generalized pentagonal numbers.|access-date=2019-08-26}}
877 = prime number, Bell number,{{Cite OEIS|1=A000110|2=Bell or exponential numbers|access-date=2016-06-11}} 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.{{cite OEIS|1=A101929|2=Number of Pythagorean triples with hypotenuse < 10^n.|access-date=2022-05-11}}
879 = 3 × 293, number of regular hypergraphs spanning 4 vertices,{{cite OEIS|1=A319190|2=Number of regular hypergraphs|access-date=2019-08-18}} candidate Lychrel seed number

= 880s =

880 = 2⁴ × 5 × 11 = 11!!!,{{cite OEIS|1=A007661|2=Triple factorial numbers|access-date=2022-05-11}} 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,{{cite OEIS|1=A111808|2=Left half of trinomial triangle (A027907), triangle read by rows|access-date=2022-05-11}} Harshad number, totient sum for first 53 integers, area of a square with diagonal 42
883 = prime number, twin prime, lucky prime, sum of three consecutive primes (283 + 293 + 307), sum of eleven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), the Mertens function of 883 returns 0
884 = 2² × 13 × 17, the Mertens function of 884 returns 0, number of points on surface of tetrahedron with sidelength 21{{Cite OEIS|1=A005893|2=Number of points on surface of tetrahedron|access-date=2022-05-11}}
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.{{Cite OEIS|1=A319312|2=Number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of n|access-date=2022-05-11}}
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

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| File:Seven-segment 8.svg File:Seven-segment 8.svg File:Seven-segment 8.svg

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{{cite OEIS|A007749|Numbers k such that k!! - 1 is prime|access-date=2022-05-24}}
889 = 7 × 127, the Mertens function of 889 returns 0

= 890s =

890 = 2 × 5 × 89 = 19² + 23² (sum of squares of two successive primes),{{Cite OEIS|1=A069484|2=a(n) = prime(n+1)^2 + prime(n)^2.|access-date=2022-05-11}} 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 [https://oeis.org/A331452/a331452_16.png this] {{OEIS|id=A331452}}.
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,{{Cite OEIS|1=A003261|2=Woodall numbers|access-date=2016-06-11}} 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 {{OEIS|id=A002064}}
898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
899 = 29 × 31 (a twin prime product),{{Cite OEIS|1=A037074|2=Numbers that are the product of a pair of twin primes|access-date=2022-05-11}} happy number, smallest number with digit sum 26,{{Cite OEIS|1=

A051885|2=Smallest number whose sum of digits is n|access-date=2022-05-11}} number of partitions of 51 into prime parts

References

Category:Integers