900 (number)

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900 (nine hundred) is the natural number following 899 and preceding 901.

In mathematics

It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number. It is also the first number to be the square of a sphenic number.

In other fields

900 is also:

Integers from 901 to 999

900s

901

901 = 17 × 53. It is a centered triangular number and a happy number.

902

902 = 2 × 11 × 41. It is a sphenic number, a nontotient, and a Harshad number.

903

903 = 3 × 7 × 43. It is a sphenic number, a little Schroeder number, a Schröder–Hipparchus number, a zero of Mertens function, and the 42nd triangular number.[3]

904

904 = 23 × 113. It is a refactorable number, a lazy caterer number, and a zero of Mertens function. There are 904 1's in all partitions of 26 into odd parts.[4]

905

905 = 5 × 181. It is the smallest composite de Polignac number[5] and the sum of seven consecutive primes (109 + 113 + 127 + 131 + 137 + 139 + 149).

"The 905" is a common nickname for the suburban portions of the Greater Toronto Area in Canada, a region whose telephones used area code 905 before overlay plans added two more area codes.

906

906 = 2 × 3 × 151. It is a strobogrammatic number, a sphenic number, and a zero of Mertens function.

907

907 is a prime number.

908

908 = 22 × 227. It is a nontotient. There are 908 primitive sorting networks on 6 elements.[6] There are 908 rhombic tilings of a 12-gon.[6]

909

909 = 32 × 101. There are 909 non-isomorphic aperiodic multiset partitions of weight 7.[7]

910s

910

910 = 2 × 5 × 7 × 13. It is a Harshad number, a happy number, a zreo of Mertens function, and a balanced number.[8] There are 910 polynomial symmetric functions of matrix of order 7 under separate row and column permutations.[9]

911

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It is a prime number, a Sophie Germain prime,[10] and the sum of three consecutive primes (293 + 307 + 311). It is an Eisenstein prime with no imaginary part[11] and real part of the form 3n−1. Since 913 is a semiprime, 911 is a Chen prime.[12]

It is also a centered decagonal number.[13][10]

There are 911 inverse semigroups of order 7.[14]

911 is obtained by concatenating its product of digits and sum of digits.

911 can be a short form of referring to the terrorist attack in the United States in 2001.

912

912 = 24 × 3 × 19. It is a Harshad number, the sum of four consecutive primes (223 + 227 + 229 + 233), and the sum of ten consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109).

913

913 = 11 × 83. It is a Smith number[15] and a zero of Mertens function.

914

914 = 2 × 457. It is a nontotient. There are 914 compositions of 11 that are neither weakly increasing nor weakly decreasing.[16]

915

915 = 3 × 5 × 61. It is a sphenic number, a Smith number,[15] a Harshad number, and a zero of Mertens function.

916

916 = 22 × 229. It is a strobogrammatic number, a zero of Mertens function, a nontotient, and a member of the Mian–Chowla sequence.[17]

917

917 = 7 × 131. It is the sum of five consecutive primes (173 + 179 + 181 + 191 + 193).

918

918 = 2 × 33 × 17. It is a Harshad number.

919

919 is a prime number, a cuban prime,[18] a prime index prime, a Chen prime, a palindromic prime, acentered hexagonal number,[19] and a zero of Mertens function.

920s

920

920 = 23 × 5 × 23. It is a zero of Mertens function. There are a total of 920 nodes in all rooted trees with 8 nodes.[20]

921

921 = 3 × 307. There are 921 enriched r-trees of size 7.[21]

922

922 = 2 × 461. It is a nontotient and a Smith number.[15]

923

923 = 13 × 71. There are 923 combinations of 6 things from 1 to 6 at a time.[22]

924

924 = 22 × 3 × 7 × 11. It is the sum of a twin prime (461 + 463), central binomial coefficient (126).[23]

925

925 = 52 × 37. It is a pentagonal number[24] and a centered square number.[25]

925 is the millesimal fineness number for Sterling silver.

926

926 = 2 × 463. It is a nontotient and the sum of six consecutive primes (139 + 149 + 151 + 157 + 163 + 167).

927

927 = 32 × 103. It is a tribonacci number.[26]

928

928 = 25 × 29. It is a happy number, the sum of four consecutive primes (227 + 229 + 233 + 239), and the sum of eight consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131 + 137).

929

929 is a prime number, a Proth prime,[27] a palindromic prime, an Eisenstein prime with no imaginary part, and the sum of nine consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127).

There are 929 chapters in Tanakh, giving the name to 929: Tanakh B'yachad.[28]

The PDF417 barcode format uses a GF(929) error-correction code.[29]

930s

930

930 = 2 × 3 × 5 × 31. It is a pronic number.[30]

931

931 = 72 × 19. It is the sum of three consecutive primes (307 + 311 + 313). It is a repdigit in two different bases 11130 and 77711. There are 931 regular simple graphs spanning 7 vertices.[31]

932

932 = 22 × 233. There are 932 regular simple graphs on 7 labeled nodes.[32]

933

933 = 3 × 311.

934

934 = 2 × 467. It is a nontotient.

935

935 = 5 × 11 × 17. It is a sphenic number, a Lucas–Carmichael number,[33] and a Harshad number.

936

936 = 23 × 32 × 13. It is a pentagonal pyramidal number[34] and a Harshad number.

937

937 is a prime number, a Chen prime, a star number,[35] and a happy number.

938

938 = 2 × 7 × 67. It is a sphenic number and a nontotient. There are 938 lines through at least 2 points of an 8 × 8 grid of points.[36]

939

939 = 3 × 313. There are 939 V-toothpicks after 31 rounds of the honeycomb sequence.[37]

940s

940

940 = 22 × 5 × 47. It is the totient sum for the first 55 integers.

941

941 is a prime number, a Chen prime, and an Eisenstein prime with no imaginary part. It is the sum of three consecutive primes (311 + 313 + 317) and the sum of five consecutive primes (179 + 181 + 191 + 193 + 197).

942

942 = 2 × 3 × 157. It is a sphenic number, a convolved Fibonacci number,[38] a nontotient, and the sum of four consecutive primes (229 + 233 + 239 + 241).

943

943 = 23 × 41.

944

944 = 24 × 59. It is a nontotient and a Lehmer-Comtet number.[39]

945

945 = 33 × 5 × 7. It is a Leyland number,[40] the smallest odd abundant number,[41] the smallest odd primitive abundant number,[42] and the smallest odd primitive semiperfect number.[43] 945 is the double factorial of 9: 945 = 9!!.[44]

946

946 = 2 × 11 × 43. It is a sphenic number, a hexagonal number,[45] a happy number, and the 43rd triangular number.[3]

947

947 is a prime number, a balanced prime,[46] a Chen prime, a lazy caterer number, an Eisenstein prime with no imaginary part, and the sum of seven consecutive primes (113 + 127 + 131 + 137 + 139 + 149 + 151).

948

948 = 22 × 3 × 79. It is a nontotient. It forms a Ruth–Aaron pair with 949 under the second definition. There are 948 combinatory separations of normal multisets of weight 6.[47]

949

949 = 13 × 73. It forms a Ruth–Aaron pair with 948 under the second definition.

950s

950

950 = 2 × 52 × 19. It is a nontotient and a generalized pentagonal number.[48]

951

951 = 3 × 317. It is a centered pentagonal number.[49]

952

Template:Redirect 952 = 23 × 7 × 17. There are 952 reduced words of length 3 in the Weyl group D_17.[50] There are 952 regions in regular tetradecagon with all diagonals drawn.[51]

953

953 is a prime number, a Sophie Germain prime,[52] a Chen prime, an Eisenstein prime with no imaginary part, and a centered heptagonal number.[53]

954

954 = 2 × 32 × 53. It is a nontotient, a Harshad number, and the sum of ten consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113). It is sixth derivative of x^(x^x) evaluated at x=1.[54]

955

955 = 5 × 191. There are 955 transitive rooted trees with 17 nodes.

956

956 = 22 × 239. There are 956 compositions of 13 into powers of 2.[55]

957

957 = 3 × 11 × 29 = antisigma(45).[56] It is a sphenic number.

958

958 = 2 × 479. It is a nontotient and a Smith number.[15]

It is the millesimal fineness number for Britannia silver

959

959 = 7 × 137. It is a composite de Polignac number.[57]

960s

960

960 = 26 × 3 × 5. It is aHarshad number and the sum of six consecutive primes (149 + 151 + 157 + 163 + 167 + 173).

There are 960 possible starting positions for the chess variant Chess960.

961

961 = 312. It is the largest 3-digit perfect square and a centered octagonal number.[58] It is the sum of three consecutive primes (313 + 317 + 331) and the sum of five consecutive primes (181 + 191 + 193 + 197 + 199).

962

962 = 2 × 13 × 37. It is a sphenic number and a nontotient.

963

963 = 32 × 107. It is the sum of the first 24 primes.

964

964 = 22 × 241. It is a happy number, a nontotient, the totient sum of the first 56 integers, and the sum of four consecutive primes (233 + 239 + 241 + 251).

965

965 = 5 × 193.

966

966 = 2 × 3 × 7 × 23 = {83}. It is a Harshad number and the sum of eight consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137 + 139).

967

967 is a prime number and a prime index prime.

968

968 = 23 × 112. It is a nontotient and an Achilles number.

969

969 = 3 × 17 × 19. It is a sphenic number, a nonagonal number,[59] and a tetrahedral number.[60]

970s

970

970 = 2 × 5 × 97. It is a sphenic number and a heptagonal number.

971

971 is a prime number, an emirp, a Chen prime, and an Eisenstein prime with no imaginary part.

972

972 = 22 × 35. It is a Harshad number[61] and an Achilles number.[62]

  • 972 has Anti-Factors = 5, 8, 24, 29, 67, 72, 216, 389, 648
  • The Sum of Anti-Factors of 972 = number * (n/2) where n is an Odd number. So, it is a Hemi-Anti-Perfect Number. Other such Numbers include 2692, etc.

Sum of Anti-Factors = 5 + 8 + 24 + 29 + 67 + 72 + 216 + 389 + 648 = 1458 = 972 * 3/2

973

973 = 7 × 139. It is a happy number.

974

974 = 2 × 487. It is a nontotient.

974! - 1 is prime.[63]

975

975 = 3 × 52 × 13.

976

Template:Redirect-distinguish976 = 24 × 61. It is a decagonal number.[64]

977

977 is a prime number, a balanced prime,[46] a Chen prime, an Eisenstein prime with no imaginary part, a Stern prime,[65] and the sum of nine consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131). It is a strictly non-palindromic number.[66]

978

978 = 2 × 3 × 163. It is a sphenic number and a nontotient.

There are 978 secondary structures of RNA molecules with 11 nucleotides.[67]

979

979 = 11 × 89. It is the sum of the five smallest fourth powers: 979=∑n=15n4.

980s

980

980 = 22 × 5 × 72. There are 980 ways to tile a hexagon of edge 3 with calissons of side 1.[68]

981

981 = 32 × 109.

982

982 = 2 × 491.

983

983 is a prime number, a safe prime,[69] a Chen prime, and an Eisenstein prime with no imaginary part. It is a Wedderburn–Etherington number[70] and a strictly non-palindromic number.[66]

984

984 = 23 × 3 × 41.

985

985 = 5 × 197. It is a Markov number,[71] a Pell number,[72] a Smith number,[15] and the sum of three consecutive primes (317 + 331 + 337).

986

986 = 2 × 17 × 29. It is a sphenic number, a strobogrammatic number, and a nontotient. There are 986 unimodal compositions of 14 where the maximal part appears once.[73]

987

987 = 3 × 7 × 47. It is a deficient number, a sphenic number, and the 16th number of the Fibonacci sequence.[74] There are 987 partitions of 52 into prime parts.

988

Template:Redirect 988 = 22 × 13 × 19. It is a nontotient, a cake number, and the sum of four consecutive primes (239 + 241 + 251 + 257).

989

989 = 23 × 43. It is an extra strong Lucas pseudoprime.[75]

990s

990

990 = 2 × 32 × 5 × 11. It is a Harshad number, the 44th triangular number,[3] and the sum of six consecutive primes (151 + 157 + 163 + 167 + 173 + 179).

The highest possible VantageScore credit score is 990.

991

991 is a prime number, a Chen prime, a lucky prime, and a prime index prime. It is the sum of five consecutive primes (191 + 193 + 197 + 199 + 211) and the sum of seven consecutive primes (127 + 131 + 137 + 139 + 149 + 151 + 157).

992

992 = 25 × 31. It is a pronic number[30] and a nontotient. There are 992 eleven-dimensional exotic spheres.[76]

993

993 = 3 × 331.

994

994 = 2 × 7 × 71. It is a sphenic number and a nontotient. There are 994 binary words of length 13 with all distinct runs.[77]

995

995 = 5 × 199.

996

996 = 22 × 3 × 83.

997

997 is the largest three-digit prime number, a lucky prime, and a strictly non-palindromic number.[66]

998

998 = 2 × 499. It is a nontotient. There are 998 7-node graphs with two connected components.[78]

999

Template:Redirect 999 = 33 × 37. It is a Kaprekar number[79] and a Harshad number.

In many video games, 999 is the maximum score that can be displayed.

References

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