900 (number)

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.


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


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


952 = 23 × 7 × 17


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


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


956 = 22 × 239


957 = 3 × 11 × 29, sphenic number


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


959 = 7 × 137, Carol number[25]


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


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]


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


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


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


965 = 5 × 193


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


967 prime number


968 = 23 × 112, nontotient


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


970 = 2 × 5 × 97, sphenic number


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


972 = 22 × 35, Harshad number


973 = 7 × 139, happy number


974 = 2 × 487, nontotient


975 = 3 × 52 × 13


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]


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


979 = 11 × 89


980 = 22 × 5 × 72


981 = 32 × 109


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]


984 = 23 × 3 × 41


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


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


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


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


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


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]


993 = 3 × 331


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


995 = 5 × 199


996 = 22 × 3 × 83


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


998 = 2 × 499, nontotient


999 = 33 × 37, Kaprekar number, Harshad number


See also

1000 (number)

References

Wikimedia Commons has media related to 900 (number).
  1. 1 2 3 "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  2. 1 2 3 4 5 "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. 1 2 "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. 1 2 "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. 1 2 3 "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.
This article is issued from Wikipedia - version of the 11/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.