>Meters: Reverted edit by 2001:1A10:195B:4701:244C:8FF7:626D:BD64 (talk) to last version by Joyous!

2025-03-10T04:32:44Z

Reverted edit by 2001:1A10:195B:4701:244C:8FF7:626D:BD64 (talk) to last version by Joyous!

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{{Redirect|5,000|other uses|5000 (disambiguation){{!}}5000}}
{{Infobox number
| number = 5000
| unicode = {{Overline|V}}, {{Overline|v}}, ↁ
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ր}}
'''5000''' ('''five thousand''') is the [[natural number]] following 4999 and preceding 5001. Five thousand is, at the same time, the largest [[Heterogram (literature)|isogrammic]] numeral, and the smallest number that contains every one of the five [[vowel]]s (a, e, i, o, u) in the [[English language]].

{{Wiktionary|five thousand}}

==Selected numbers in the range 5001–5999==

===5001 to 5099===
* '''5003''' – [[Sophie Germain prime]]
* '''5020''' – [[amicable number]] with 5564
* '''5021''' – [[super-prime]], [[twin prime]] with 5023
* '''5023''' – twin prime with 5021
* '''5039''' – [[factorial prime]],<ref>{{Cite web|url=https://oeis.org/A088054|title=Sloane's A088054 : Factorial primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> Sophie Germain prime
* '''[[5040 (number)|5040]]''' = 7!, [[superior highly composite number]]
* '''5041''' = 712, [[centered octagonal number]]<ref name=":0">{{Cite web|url=https://oeis.org/A016754|title=Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5050''' – [[triangular number]], [[Kaprekar number]],<ref name=":1">{{Cite web|url=https://oeis.org/A006886|title=Sloane's A006886 : Kaprekar numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> sum of first 100 integers
* '''5051''' – Sophie Germain prime
* '''5059''' – [[super-prime]]
* '''5076''' – [[decagonal number]]<ref name=":2">{{Cite web|url=https://oeis.org/A001107|title=Sloane's A001107 : 10-gonal (or decagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5077''' – prime of the form 2p-1
* '''5081''' – Sophie Germain prime
* '''5087''' – [[safe prime]]
* '''5099''' – safe prime

===5100 to 5199===
* '''5101''' – prime of the form 2p-1
* '''5107''' – [[super-prime]], [[balanced prime]]<ref name=":3">{{Cite web|url=https://oeis.org/A006562|title=Sloane's A006562 : Balanced primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5113''' – balanced prime,<ref name=":3" /> prime of the form 2p-1
* '''5117''' – sum of the first 50 primes
* '''5151''' – triangular number
* '''5167''' – [[Leonardo prime]], [[cuban prime]] of the form ''x'' = ''y'' + 1<ref name=":4">{{Cite web|url=https://oeis.org/A002407|title=Sloane's A002407 : Cuban primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5171''' – Sophie Germain prime
* '''5184''' = 722
* '''5186''' – φ(5186) = 2592
* '''5187''' – φ(5187) = 2592
* '''5188''' – φ(5189) = 2592, [[centered heptagonal number]]<ref name=":5">{{Cite web|url=https://oeis.org/A069099|title=Sloane's A069099 : Centered heptagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5189''' – [[super-prime]]

=== 5200 to 5299 ===

* '''5209''' - largest [[Minimal prime (recreational mathematics)|minimal prime]] in base 6
* '''5226''' – [[nonagonal number]]<ref name=":6">{{Cite web|url=https://oeis.org/A001106|title=Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5231''' – Sophie Germain prime
* '''5233''' – prime of the form 2p-1
* '''5244''' = 222 + 232 + … + 292 = 202 + 212 + … + 282
* '''5249''' – [[highly cototient number]]<ref name=":7">{{Cite web|url=https://oeis.org/A100827|title=Sloane's A100827 : Highly cototient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5253''' – triangular number
* '''5279''' – Sophie Germain prime, [[twin prime]] with 5281, 700th prime number
* '''5280''' is the number of [[foot (unit)|feet]] in a [[mile]].<ref>{{cite web|url=https://www.merriam-webster.com/dictionary/weight#table|title=Weights and measures|publisher=[[Merriam-Webster]]|website=www.merriam-webster.com|accessdate=11 March 2021}}</ref> It is divisible by three, yielding 1760 [[yard]]s per mile and by 16.5, yielding 320 [[Rod (unit)|rods]] per mile. Also, 5280 is connected with both Klein's [[J-invariant]] and the [[Heegner number]]s. Specifically:
:<math>
5280 = -\sqrt[3]{j\left( {\scriptstyle\frac{1}{2}} \left( 1 + i\sqrt{67}\, \right)\right) }.
</math>
* '''5281''' – [[super-prime]], twin prime with 5279
* '''5282''' - used in various paintings by [[Thomas Kinkade]]<ref>{{Cite web |last=Cullum|first=Paul|url=https://www.vanityfair.com/news/2008/11/thomas-kincades-16-guidelines-for-making-stuff-suck? | title=Thomas Kinkade's 16 Guidelines for Making Stuff Suck | date=14 November 2008 |via=Vanity Fair }}</ref>
* '''5292''' – Kaprekar number<ref name=":1" />

===5300 to 5399===
* '''5303''' – Sophie Germain prime, balanced prime<ref name=":3" />
* '''5329''' = 732, centered octagonal number<ref name=":0" />
* '''5333''' – Sophie Germain prime
* '''5335''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 22.
* '''5340''' – [[octahedral number]]<ref>{{Cite web|url=https://oeis.org/A005900|title=Sloane's A005900 : Octahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5350''' - sum of the first 51 primes
* '''5356''' – triangular number
* '''5365''' – decagonal number<ref name=":2" />
* '''5381''' – [[super-prime]]
* '''5387''' – safe prime, balanced prime<ref name=":3" />
* '''5392''' – [[Leyland number]]<ref>{{Cite web|url=https://oeis.org/A076980|title=Sloane's A076980 : Leyland numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5393''' – balanced prime<ref name=":3" />
* '''5399''' – Sophie Germain prime, safe prime

===5400 to 5499===
* '''5402''' – number of non-equivalent ways of expressing 1,000,000 as the sum of two prime numbers<ref>{{Cite OEIS|1=A065577|2=Number of Goldbach partitions of 10^n|access-date=2023-08-31}}</ref>
* '''5405''' – member of a [[Ruth–Aaron pair]] with 5406 (either definition)
* '''5406''' – member of a Ruth–Aaron pair with 5405 (either definition)
* '''5413''' – prime of the form 2p-1
* '''5419''' – Cuban prime of the form ''x'' = ''y'' + 1<ref name=":4" />
* '''5437''' – prime of the form 2p-1
* '''5441''' – Sophie Germain prime, [[super-prime]]
* '''5456''' – [[tetrahedral number]]<ref name=":8">{{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=2016-06-13}}</ref>
* '''5459''' – highly cototient number<ref name=":7" />
* '''5460''' – triangular number
* '''5461''' – [[super-Poulet number]],<ref>{{Cite web|url=https://oeis.org/A050217|title=Sloane's A050217 : Super-Poulet numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> centered heptagonal number<ref name=":5" />
* '''5476''' = 742
* '''5483''' – safe prime

===5500 to 5599===
* '''5500''' – nonagonal number<ref name=":6" />
* '''5501''' – Sophie Germain prime, [[twin prime]] with 5503
* '''5503''' – [[super-prime]], twin prime with 5501, [[cousin prime]] with 5507
* '''5507''' – safe prime, cousin prime with 5503
* '''5508''' = 183 – 182
* '''5525''' – [[square pyramidal number]]<ref>{{Cite web|url=https://oeis.org/A000330|title=Sloane's A000330 : Square pyramidal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5527''' – [[happy prime]]
* '''5536''' – [[tetranacci number]]<ref>{{Cite web|url=https://oeis.org/A000078|title=Sloane's A000078 : Tetranacci numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5555''' – repdigit
* '''5557''' – super-prime
* '''5563''' – balanced prime
* '''5564''' – amicable number with 5020
* '''5565''' – triangular number
* '''5566''' – [[pentagonal pyramidal number]]<ref>{{Cite web|url=https://oeis.org/A002411|title=Sloane's A002411 : Pentagonal pyramidal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5569''' – happy prime
* '''5571''' – [[perfect totient number]]<ref>{{Cite web|url=https://oeis.org/A082897|title=Sloane's A082897 : Perfect totient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5581''' – prime of the form 2p-1
* '''5589''' - sum of the first 52 primes

===5600 to 5699===
* '''5623''' – [[super-prime]]
* '''5625''' = 752, centered octagonal number<ref name=":0" />
* '''5631''' – number of compositions of 15 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>
* '''5639''' – Sophie Germain prime, safe prime
* '''5651''' – super-prime
* '''5659''' – happy prime, completes the eleventh [[prime quadruplet]] set
* '''5662''' – decagonal number<ref name=":2" />
* '''5671''' – triangular number

===5700 to 5799===
* '''5701''' – [[super-prime]], prime of the form 2p-1
* '''5711''' – Sophie Germain prime
* '''5719''' – Zeisel number,<ref>{{Cite web|url=https://oeis.org/A051015|title=Sloane's A051015 : Zeisel numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> [[Lucas–Carmichael number]]<ref>{{Cite web|url=https://oeis.org/A006972|title=Sloane's A006972 : Lucas-Carmichael numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5741''' – Sophie Germain prime, [[Pell prime]],<ref>{{Cite web|url=https://oeis.org/A000129|title=Sloane's A000129 : Pell numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> [[Markov prime]],<ref>{{Cite web|url=https://oeis.org/A002559|title=Sloane's A002559 : Markoff (or Markov) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref> centered heptagonal number<ref name=":5" />
* '''5743''' = number of signed trees with 9 nodes<ref>{{cite OEIS|A000060|Number of signed trees with n nodes}}</ref>
* '''5749''' – super-prime
* '''5768''' – [[tribonacci number]]<ref>{{Cite web|url=https://oeis.org/A000073|title=Sloane's A000073 : Tribonacci numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>
* '''5776''' = 762
* '''5777''' – smallest counterexample to the conjecture that all odd numbers are of the form ''p'' + 2''a''2
* '''5778''' – triangular number
* '''5781''' – nonagonal number<ref name=":6" />
* '''5798''' – [[Motzkin number]]<ref>{{Cite web|url=https://oeis.org/A001006|title=Sloane's A001006 : Motzkin numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-13}}</ref>

===5800 to 5899===
* '''5801''' – [[super-prime]]
* '''5807''' – safe prime, balanced prime
* '''5830''' - sum of the first 53 primes
* '''5832''' = 183
* '''5842''' – member of the [[Padovan sequence]]<ref>{{Cite web|url=https://oeis.org/A000931|title=Sloane's A000931 : Padovan sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* '''5849''' – Sophie Germain prime
* '''5869''' – super-prime
* '''5879''' – safe prime, highly cototient number<ref name=":7" />
* '''5886''' – triangular number

===5900 to 5999===
* '''5903''' – Sophie Germain prime
* '''5913''' – sum of the first seven factorials
* '''5927''' – safe prime
* '''5929''' = 772, centered octagonal number<ref name=":0" />
* '''5939''' – safe prime
* '''5967''' – decagonal number<ref name=":2" />
* '''5971''' – first composite [[Wilson number]]
* '''5984''' – tetrahedral number<ref name=":8" />
* '''5995''' – triangular number

===Prime numbers===
There are 114 [[prime number]]s between 5000 and 6000:<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>
:5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987

==References==
{{Reflist}}

{{Integers|10}}

[[Category:Integers]]

5000 (number) - Revision history

>Meters: Reverted edit by 2001:1A10:195B:4701:244C:8FF7:626D:BD64 (talk) to last version by Joyous!