149.50.163.173: /* 9500 to 9599 */

2025-03-07T21:44:25Z

9500 to 9599

New page

{{Redirect|9,000|other uses|9000 (disambiguation)}}
{{Infobox number
| number = 9000
| roman = M{{overline|X}}, or {{overline|IX}}
| unicode = M{{overline|X}}, m{{overline|x}}, {{overline|IX}}, {{overline|ix}}
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ք}}
'''9000''' ('''nine thousand''') is the natural number following [[8000 (number)#890 to 8999|
8999]] and preceding 9001.

== Selected numbers in the range 9001–9999==


===9001 to 9099===
* '''9001''' – [[sexy prime]] with 9007
* '''9007''' – sexy prime with 9001
* '''9009''' – [[centered cube number]]<ref>{{cite OEIS|A005898|Centered cube numbers: n^3 + (n+1)^3.}}</ref>
* '''9025''' = [[95 (number)|95]]2, [[centered octagonal number]]
* '''9029''' – [[Sophie Germain prime]]
* '''9041''' – [[super-prime]]
* '''9045''' – [[triangular number]]
* '''9059''' – Sophie Germain prime
* '''9072''' – [[decagonal number]]
* '''9077''' – [[Markov number]]<ref>{{cite OEIS|A002559| Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.}}</ref>
* '''9091''' – [[unique prime]]<ref>{{cite OEIS|A040017| Prime 3 followed by unique period primes (the period r of 1/p is not shared with any other prime) of the form A019328(r)/gcd(A019328(r),r) in order (periods r are given in A051627).}}</ref>

===9100 to 9199===
* '''9103''' – [[super-prime]]
* '''9126''' – [[pentagonal pyramidal number]]<ref>{{cite OEIS|A002411|Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.}}</ref>
* '''9139''' – [[tetrahedral number]]<ref>{{cite OEIS|A000292|Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.}}</ref>
* '''9175''' – smallest (provable) generalized [[Sierpiński number]] in [[decimal|base 10]]: {{math|9175*10''n''+1}} is always divisible by [[covering set|one of the prime numbers]] {{math|{7, 11, 13, 73}}}.<ref>{{Cite journal |url=https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1639-08.pdf |title=GENERALIZED SIERPIŃSKI NUMBERS TO BASE b |author1=Brunner, Amy |author2=Caldwell, Chris K. |author3=Krywaruczenko, Daniel |author4=Lownsdale, Chris |journal=数理解析研究所講究録 [Notes from the Institute of Mathematical Analysis (in, New Aspects of Analytic Number Theory)] |publisher=[[Research Institute for Mathematical Sciences|RIMS]] |location=Kyoto |volume=1639 |year=2009 |pages=69–79 |hdl=2433/140555 |s2cid=38654417 }}</ref>
* '''9180''' – triangular number

===9200 to 9299===
* '''9216''' = [[96 (number)|96]]2
* '''9221''' – Sophie Germain prime
* '''9224''' – [[octahedral number]]<ref>{{cite OEIS|A005900|Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.}}</ref>
* '''9241''' – [[cuban prime]] of the form ''x'' = ''y'' + 1<ref>{{cite OEIS|A002407|Cuban primes: primes which are the difference of two consecutive cubes.}}</ref>
* '''9261''' = 213, largest 4 digit [[perfect cube]]
* '''9272''' – [[weird number]]<ref>{{cite OEIS|A006037|Weird numbers: abundant (A005101) but not pseudoperfect (A005835).}}</ref>
* '''9283''' – [[centered heptagonal number]]
* '''9293''' – Sophie Germain prime, [[super-prime]]

===9300 to 9399===
* '''9316''' – triangular number
* '''9319''' – [[super-prime]]
* '''9334''' – [[nonagonal number]]
* '''9349''' – [[Lucas prime]],<ref>{{cite OEIS|A005479|Prime Lucas numbers (cf. A000032).}}</ref> [[Fibonacci number]]
* '''9361''' - [[star number]]
* '''9371''' – Sophie Germain prime
* '''9376''' – 1-[[automorphic number]]
* '''9397''' – [[balanced prime]]

===9400 to 9499===
* '''9403''' – [[super-prime]]
* '''9409''' = [[97 (number)|97]]2, centered octagonal number
* '''9419''' – Sophie Germain prime
* '''9439''' – completes the twelfth [[prime quadruplet]] set
* '''9453''' – triangular number
* '''9455''' – [[square pyramidal number]]<ref>{{cite OEIS|A000330|Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.}}</ref>
* '''9457''' – decagonal number
* '''9461''' – [[super-prime]], [[twin prime]]
* '''9467''' – [[safe prime]]
* '''9473''' – Sophie Germain prime, balanced prime, [[Proth prime]]
* '''9474''' – [[Narcissistic number]] in base 10
* '''9479''' – Sophie Germain prime
* '''9496''' – [[Telephone number (mathematics)|Telephone/involution number]]

===9500 to 9599===
* '''9511''' - prime number
* '''9521''' - prime number
* '''9533''' - prime number
* '''9539''' – Sophie Germain prime, [[super-prime]]
* '''9551''' – first prime followed by as many as 35 consecutive [[composite number]]s
* '''9587''' – safe prime, follows 35 consecutive composite numbers
* '''9591''' – triangular number
* '''9592''' - the number of primes under 100,000

===9600 to 9699===
* '''9601''' – [[Proth prime]]
* '''9604''' = [[98 (number)|98]]2
* '''9619''' – [[super-prime]]
* '''9629''' – Sophie Germain prime
* '''9647''' – centered heptagonal number
* '''9661''' – super-prime, sum of nine consecutive primes (1049 + 1051 + 1061 + 1063 + 1069 + 1087 + 1091 + 1093 + 1097)
* '''9689''' – Sophie Germain prime
* '''9699''' – nonagonal number

===9700 to 9799===
* '''9721''' – prime of the form 2p-1
* '''9730''' – triangular number
* '''9739''' – [[super-prime]]
* '''9743''' – safe prime
* '''9791''' – Sophie Germain prime

===9800 to 9899===
* '''9800''' – member of a [[Ruth-Aaron pair]] (first definition) with 9801
* '''9801''' = [[99 (number)|99]]2, the largest 4 digit perfect square, centered octagonal number, square [[pentagonal number]], member of a Ruth-Aaron pair (first definition) with 9800
* '''9833''' – [[super-prime]]
* '''9839''' – safe prime
* '''9841''' - [[star number]]
* '''9850''' – decagonal number
* '''[[9855]]''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|n-Queens Problem]] for ''n'' = 27.
* '''9857''' – [[Proth prime]]
* '''9859''' – super-prime
* '''9870''' – triangular number
* '''9871''' – balanced prime
* '''9880''' – tetrahedral number<ref name=":1">{{Cite web|url=https://oeis.org/A000292|title=Sloane's A000292 : Tetrahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-14}}</ref>
* '''9887''' – safe prime

===9900 to 9999===
* '''9901''' – unique prime, sum of seven consecutive primes (1381 + 1399 + 1409 + 1423 + 1427 + 1429 + 1433)<ref name=":0">{{Cite web|url=https://oeis.org/A040017|title=Sloane's A040017 : Unique period primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-14}}</ref>
* '''9905''' – number of compositions of 16 whose run-lengths are either weakly increasing or weakly decreasing<ref>{{cite OEIS|A332835|Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing|access-date=2022-06-02}}</ref>
* '''9923''' – [[super-prime]], probably smallest certainly executable [[prime number]] on [[x86 architecture|x86]] [[MS-DOS]]<ref name="9923_exe">{{citation |url=http://asdf.org/~fatphil/maths/illegal.html |title=An Executable Prime Number? |archive-url=https://web.archive.org/web/20100210085512/http://asdf.org/~fatphil/maths/illegal.html |archive-date=2010-02-10 }}</ref>
* '''9949''' – sum of nine consecutive primes (1087 + 1091 + 1093 + 1097 + 1103 + 1109 + 1117 + 1123 + 1129)
* '''9973''' – super-prime
* '''9988''' – number of [[prime knots]] with 13 crossings
* '''[[9999 (number)|9999]]''' – [[Kaprekar number]], [[repdigit]]

===Prime numbers===
There are 112 [[prime number]]s between 9000 and 10000:<ref>{{Cite OEIS|A038823|Number of primes between n*1000 and (n+1)*1000}}</ref><ref>{{cite web |last=Stein |first=William A. |author-link=William A. Stein |title=The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture |url=https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ |website=wstein.org |date=10 February 2017 |access-date=6 February 2021}}</ref>
:9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973

== References ==
{{Reflist}}

{{Integers|10}}

[[Category:Integers]]

9000 (number) - Revision history

149.50.163.173: /* 9500 to 9599 */