900 (number)

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For the year 900, see 900 BC and 900 AD.
← 899 900 901 →
Cardinal nine hundred
Ordinal 900th
(nine hundredth)
Factorization 22× 32× 52
Divisors 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
Roman numeral CM
Unicode symbol(s) CM, cm
Binary 11100001002
Ternary 10201003
Quaternary 320104
Quinary 121005
Senary 41006
Octal 16048
Duodecimal 63012
Hexadecimal 38416
Vigesimal 25020
Base 36 P036

900 (nine hundred) is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 integers. In base 10 it is a Harshad number.

Nine hundred is also:

901 = 17 × 53, happy number

902 = 2 × 11 × 41, sphenic number, nontotient, Harshad number

903 = 3 × 7 × 43, sphenic number, triangular number,[1] Schröder–Hipparchus number, Mertens function (903) returns 0

904 = 23 × 113 or 113 × 8, Mertens function(904) returns 0

905 = 5 × 181, sum of seven consecutive primes (109 + 113 + 127 + 131 + 137 + 139 + 149)

906 = 2 × 3 × 151, sphenic number, Mertens function(906) returns 0

907 prime number

908 = 22 × 227, nontotient

909 = 32 × 101

910 = 2 × 5 × 7 × 13, Mertens function(910) returns 0, Harshad number, happy number

911 = prime number, has its own page

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

913 = 11 × 83, Smith number,[2] Mertens function(913) returns 0.

  • After escaping the Jedi purge, Obi-Wan Kenobi transmitted a 913 emergency transmission.

914 = 2 × 457, nontotient

915 = 3 × 5 × 61, sphenic number, Smith number,[2] Mertens function(915) returns 0, Harshad number

916 = 22 × 229, Mertens function(916) returns 0, nontotient, member of the Mian–Chowla sequence[3]

917 = 7 × 131, sum of five consecutive primes (173 + 179 + 181 + 191 + 193)

918 = 2 × 33 × 17, Harshad number

919 prime number, cuban prime,[4] Chen prime, palindromic prime, centered hexagonal number,[5] happy number, Mertens function(919) returns 0

920 = 23 × 5 × 23, Mertens function(920) returns 0

921 = 3 × 307

922 = 2 × 461, nontotient, Smith number[2]

923 = 13 × 71

924 = 22 × 3 × 7 × 11, sum of a twin prime (461 + 463), central binomial coefficient [6]

925 = 52 × 37, pentagonal number,[7] centered square number[8]

926 = 2 × 463, sum of six consecutive primes (139 + 149 + 151 + 157 + 163 + 167), nontotient

927 = 32 × 103, tribonacci number[9]

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

929 prime number, Proth prime,[10] palindromic prime, sum of nine consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127), Eisenstein prime with no imaginary part

930 = 2 × 3 × 5 × 31, pronic number[11]

931 = 72 × 19; sum of three consecutive primes (307 + 311 + 313); double repdigit, 11130 and 77711

932 = 22 × 233

933 = 3 × 311

934 = 2 × 467, nontotient

935 = 5 × 11 × 17, sphenic number, Lucas–Carmichael number,[12] Harshad number

936 = 23 × 32 × 13, pentagonal pyramidal number,[13] Harshad number

937 prime number, Chen prime, star number,[14] happy number

938 = 2 × 7 × 67, sphenic number, nontotient

939 = 3 × 313

940 = 22 × 5 × 47, totient sum for first 55 integers

941 prime number, sum of three consecutive primes (311 + 313 + 317), sum of five consecutive primes (179 + 181 + 191 + 193 + 197), Chen prime, Eisenstein prime with no imaginary part

942 = 2 × 3 × 157, sphenic number, sum of four consecutive primes (229 + 233 + 239 + 241), nontotient

943 = 23 × 41

944 = 24 × 59, nontotient

945 = 33 × 5 × 7, double factorial of 9,[15] smallest odd abundant number (divisors less than itself add up to 975);[16] smallest odd primitive abundant number;[17] smallest odd primitive semiperfect number;[18] Leyland number[19]

946 = 2 × 11 × 43, sphenic number, triangular number,[1] hexagonal number,[20] happy number

947 prime number, sum of seven consecutive primes (113 + 127 + 131 + 137 + 139 + 149 + 151), balanced prime,[21] Chen prime, Eisenstein prime with no imaginary part

948 = 22 × 3 × 79, nontotient, forms a Ruth–Aaron pair with 949 under second definition

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

950 = 2 × 52 × 19, nontotient

  • one of two ISBN Group Identifiers for books published in Argentina

951 = 3 × 317, centered pentagonal number[22]

  • one of two ISBN Group Identifiers for books published in Finland

952 = 23 × 7 × 17

953 prime number, Sophie Germain prime,[23] Chen prime, Eisenstein prime with no imaginary part, centered heptagonal number[24]

  • ISBN Group Identifier for books published in Croatia

954 = 2 × 32 × 53, sum of ten consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, Harshad number

955 = 5 × 191

  • ISBN Group Identifier for books published in Sri Lanka

956 = 22 × 239

  • ISBN Group Identifier for books published in Chile

957 = 3 × 11 × 29, sphenic number

  • one of two ISBN Group Identifiers for books published in Taiwan and China

958 = 2 × 479, nontotient, Smith number[2]

959 = 7 × 137, Carol number[25]

  • ISBN Group Identifier for books published in Cuba

960 = 26 × 3 × 5, sum of six consecutive primes (149 + 151 + 157 + 163 + 167 + 173), Harshad number

  • country calling code for Maldives, ISBN Group Identifier for books published in Greece
  • The number of possible starting positions for the chess variant Chess960
    • Chess960 also got its name from the number itself

961 = 312, the largest 3-digit perfect square, sum of three consecutive primes (313 + 317 + 331), sum of five consecutive primes (181 + 191 + 193 + 197 + 199), centered octagonal number[26]

  • country calling code for Lebanon, ISBN Group Identifier for books published in Slovenia

962 = 2 × 13 × 37, sphenic number, nontotient

  • country calling code for Jordan, one of two ISBN Group Identifiers for books published in Hong Kong

963 = 32 × 107, sum of the first twenty-four primes

  • country calling code for Syria, ISBN Group Identifier for books published in Hungary

964 = 22 × 241, sum of four consecutive primes (233 + 239 + 241 + 251), nontotient, totient sum for first 56 integers

  • country calling code for Iraq, ISBN Group Identifier for books published in Iran, happy number

965 = 5 × 193

  • country calling code for Kuwait, ISBN Group Identifier for books published in Israel

966 = 2 × 3 × 7 × 23, sum of eight consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137 + 139), Harshad number

  • country calling code for Saudi Arabia, one of two ISBN Group Identifiers for books published in Ukraine

967 prime number

  • country calling code for Yemen, one of two ISBN Group Identifiers for books published in Malaysia

968 = 23 × 112, nontotient

  • country calling code for Oman, one of two ISBN Group Identifiers for books published in Mexico

969 = 3 × 17 × 19, sphenic number, nonagonal number,[27] tetrahedral number[28]

970 = 2 × 5 × 97, sphenic number

  • country calling code for Palestinian territories, one of two ISBN Group Identifiers for books published in Mexico

971 prime number, Chen prime, Eisenstein prime with no imaginary part

  • country calling code for United Arab Emirates, ISBN Group Identifier for books published in the Philippines

972 = 22 × 35, Harshad number

  • country calling code for Israel, one of two ISBN Group Identifiers for books published in Portugal

973 = 7 × 139, happy number

  • country calling code for Bahrain, ISBN Group Identifier for books published in Romania,

974 = 2 × 487, nontotient

  • country calling code for Qatar, ISBN Group Identifier for books published in Thailand

975 = 3 × 52 × 13

  • country calling code for Bhutan, ISBN Group Identifier for books published in Turkey

976 = 24 × 61, decagonal number[29]

977 prime number, sum of nine consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), balanced prime,[21] Chen prime, Eisenstein prime with no imaginary part, Stern prime,[30] strictly non-palindromic number[31]

  • country calling code for Nepal
  • EAN prefix for ISSNs
  • ISBN Group Identifier for books published in Egypt

978 = 2 × 3 × 163, sphenic number, nontotient,

  • First EAN prefix for ISBNs
  • ISBN Group Identifier for books published in Nigeria

979 = 11 × 89

  • Second EAN prefix for ISBNs. Also for ISMNs
  • ISBN Group Identifier for books published in Indonesia

980 = 22 × 5 × 72

  • ISBN Group Identifier for books published in Venezuela

981 = 32 × 109

  • one of two ISBN Group Identifiers for books published in Singapore

982 = 2 × 491, happy number

983 prime number, safe prime,[32] Chen prime, Eisenstein prime with no imaginary part, Wedderburn–Etherington number,[33] strictly non-palindromic number[31]

  • One of two ISBN Group Identifiers for books published in Malaysia

984 = 23 × 3 × 41

  • ISBN Group Identifier for books published in Bangladesh

985 = 5 × 197, sum of three consecutive primes (317 + 331 + 337), Markov number,[34] Pell number,[35] Smith number[2]

  • one of two ISBN Group Identifiers for books published in Belarus

986 = 2 × 17 × 29, sphenic number, nontotient

  • one of two ISBN Group Identifiers for books published in Taiwan and China

987 = 3 × 7 × 47, Fibonacci number[36]

  • one of two ISBN Group Identifiers for books published in Argentina

988 = 22 × 13 × 19, nontotient. sum of four consecutive primes (239 + 241 + 251 + 257)

  • one of two ISBN Group Identifiers for books published in Hong Kong

989 = 23 × 43, Extra strong Lucas pseudoprime[37]

  • one of two ISBN Group Identifiers for books published in Portugal

990 = 2 × 32 × 5 × 11, sum of six consecutive primes (151 + 157 + 163 + 167 + 173 + 179), triangular number,[1] Harshad number

991 prime number, sum of five consecutive primes (191 + 193 + 197 + 199 + 211), sum of seven consecutive primes (127 + 131 + 137 + 139 + 149 + 151 + 157), Chen prime

992 = 25 × 31, pronic number,[11] nontotient; number of eleven-dimensional exotic spheres.[38]

  • country calling code for Tajikistan

993 = 3 × 331

  • country calling code for Turkmenistan

994 = 2 × 7 × 71, sphenic number, nontotient

  • country calling code for Azerbaijan

995 = 5 × 199

  • country calling code for Georgia
  • Singapore fire brigade and emergency ambulance services hotline

996 = 22 × 3 × 83

  • country calling code for Kyrgyzstan

997 is the largest three-digit prime number, strictly non-palindromic number[31]

998 = 2 × 499, nontotient

  • country calling code for Uzbekistan

999 = 33 × 37, Kaprekar number, Harshad number

See also[edit]

1000 (number)

References[edit]

  1. ^ a b c "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  2. ^ a b c d e "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  3. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  4. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  5. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  6. ^ "Sloane's A000984 : Central binomial coefficients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  7. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  8. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  9. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  10. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  11. ^ a b "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  12. ^ "Sloane's A006972 : Lucas-Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  13. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  14. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  15. ^ "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  16. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 13. ISBN 978-1-84800-000-1. 
  17. ^ "Sloane's A006038 : Odd primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  18. ^ "Sloane's A006036 : Primitive pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  19. ^ "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  20. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  21. ^ a b "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  22. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  23. ^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  24. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  25. ^ "Sloane's A093112 : a(n) = (2^n-1)^2 - 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  26. ^ "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  27. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  28. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  29. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  30. ^ "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  31. ^ a b c "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  32. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  33. ^ "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  34. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  35. ^ "Sloane's A000129 : Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  36. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  37. ^ "Sloane's A0217719 : Extra strong Lucas pseudoprimes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11. 
  38. ^ "week164". Math.ucr.edu. 2001-01-13. Retrieved 2014-05-12. 
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