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{{Infobox number | |||
| number = 5000 | |||
| unicode = {{Overline|V}}, {{Overline|v}}, {{unicode|ↁ}} | |||
}} | |||
'''5000''' ('''five thousand''') is the [[natural number]] following 4999 and preceding 5001. Five thousand is the largest [[isogram]]mic number in the [[English language]]. | |||
{{Wiktionary|five thousand}} | |||
==Selected numbers in the range 5001–5999== | |||
* '''5003''' – [[Sophie Germain prime]] | |||
* '''5020''' – [[amicable number]] with 5564 | |||
* '''5039''' – [[factorial prime]], Sophie Germain prime | |||
* '''[[5040 (number)|5040]]''' – 7!, [[superior highly composite number]] | |||
* '''5041''' – <math>71^2</math>, [[centered octagonal number]] | |||
* '''5050''' – [[triangular number]], [[Kaprekar number]], sum of first 100 integers | |||
* '''5051''' – Sophie Germain prime | |||
* '''5076''' – [[decagonal number]] | |||
* '''5081''' – Sophie Germain prime | |||
* '''5087''' – [[safe prime]] | |||
* '''5099''' – safe prime | |||
* '''5107''' – [[balanced prime]] | |||
* '''5113''' – balanced prime | |||
* '''5151''' – triangular number | |||
* '''5167''' – [[cuban prime]] of the form ''x'' = ''y'' + 1 | |||
* '''5171''' – Sophie Germain prime | |||
* '''5184''' – <math>72^2</math> | |||
* '''5186''' – φ(5186) = 2592 | |||
* '''5187''' – φ(5187) = 2592 | |||
* '''5188''' – φ(5189) = 2592, [[centered heptagonal number]] | |||
* '''5226''' – [[nonagonal number]] | |||
* '''5231''' – Sophie Germain prime | |||
* '''5244''' – <math>22^2 + 23^2 + \cdots + 29^2 = 20^2 + 21^2 + \cdots + 28^2</math> | |||
* '''5249''' – [[highly cototient number]] | |||
* '''5253''' – triangular number | |||
* '''5279''' – Sophie Germain prime | |||
* '''5280''' is the number of feet in a mile. It is evenly divisible by three, yielding exactly 1760 [[yard]]s per mile and by 16.5, yielding exactly 320 [[Rod (unit)|rods]] per mile. | |||
* '''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> | |||
* '''5292''' – Kaprekar number | |||
* '''5303''' – Sophie Germain prime, balanced prime | |||
* '''5329''' – <math>73^2</math>, centered octagonal number | |||
* '''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]] | |||
* '''5356''' – triangular number | |||
* '''5365''' – decagonal number | |||
* '''5387''' – safe prime, balanced prime | |||
* '''5392''' – [[Leyland number]] | |||
* '''5393''' – balanced prime | |||
* '''5399''' – Sophie Germain prime, safe prime | |||
* '''5405''' – member of a [[Ruth–Aaron pair]] with 5406 (either definition) | |||
* '''5406''' – member of a [[Ruth–Aaron pair]] with 5405 (either definition) | |||
* '''5419''' – Cuban prime of the form ''x'' = ''y'' + 1 | |||
* '''5441''' – Sophie Germain prime | |||
* '''5456''' – [[tetrahedral number]] | |||
* '''5459''' – highly cototient number | |||
* '''5460''' – triangular number | |||
* '''5461''' – [[super-Poulet number]], centered heptagonal number | |||
* '''5476''' – <math>74^2</math> | |||
* '''5483''' – safe prime | |||
* '''5500''' – nonagonal number | |||
* '''5501''' – Sophie Germain prime | |||
* '''5507''' – safe prime | |||
* '''5525''' – [[square pyramidal number]] | |||
* '''5536''' – [[tetranacci number]] | |||
* '''5563''' – balanced prime | |||
* '''5564''' – amicable number with 5020 | |||
* '''5565''' – triangular number | |||
* '''5566''' – [[pentagonal pyramidal number]] | |||
* '''5571''' – [[perfect totient number]] | |||
* '''5625''' – <math>75^2</math>, centered octagonal number | |||
* '''5639''' – Sophie Germain prime, safe prime | |||
* '''5662''' – decagonal number | |||
* '''5671''' – triangular number | |||
* '''5711''' – Sophie Germain prime | |||
* '''5719''' – [[Zeisel number]], [[Lucas–Carmichael number]] | |||
* '''5741''' – Sophie Germain prime, [[Pell number]], [[Markov number]], centered heptagonal number | |||
* '''5768''' – [[tribonacci number]] | |||
* '''5776''' – <math>76^2</math> | |||
* '''5777''' – smallest counterexample to the conjecture that all odd numbers are of the form <math>p + 2a^2</math> | |||
* '''5778''' – triangular number | |||
* '''5781''' – nonagonal number | |||
* '''5798''' – [[Motzkin number]] | |||
* '''5807''' – safe prime, balanced prime | |||
* '''5832''' – 18<sup>3</sup> | |||
* '''5849''' – Sophie Germain prime | |||
* '''5879''' – safe prime, highly cototient number | |||
* '''5886''' – triangular number | |||
* '''5903''' – Sophie Germain prime | |||
* '''5913''' – sum of the first seven factorials | |||
* '''5927''' – safe prime | |||
* '''5929''' – <math>77^2</math>, centered octagonal number | |||
* '''5939''' – safe prime | |||
* '''5967''' – decagonal number | |||
* '''5984''' – tetrahedral number | |||
* '''5995''' – triangular number | |||
{{DEFAULTSORT:5000 (Number)}} | |||
[[Category:Integers|59e03 5000]] |
Revision as of 22:25, 29 January 2014
Template:Infobox number 5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the English language.
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Selected numbers in the range 5001–5999
- 5003 – Sophie Germain prime
- 5020 – amicable number with 5564
- 5039 – factorial prime, Sophie Germain prime
- 5040 – 7!, superior highly composite number
- 5041 – , centered octagonal number
- 5050 – triangular number, Kaprekar number, sum of first 100 integers
- 5051 – Sophie Germain prime
- 5076 – decagonal number
- 5081 – Sophie Germain prime
- 5087 – safe prime
- 5099 – safe prime
- 5107 – balanced prime
- 5113 – balanced prime
- 5151 – triangular number
- 5167 – cuban prime of the form x = y + 1
- 5171 – Sophie Germain prime
- 5184 –
- 5186 – φ(5186) = 2592
- 5187 – φ(5187) = 2592
- 5188 – φ(5189) = 2592, centered heptagonal number
- 5226 – nonagonal number
- 5231 – Sophie Germain prime
- 5244 –
- 5249 – highly cototient number
- 5253 – triangular number
- 5279 – Sophie Germain prime
- 5280 is the number of feet in a mile. It is evenly divisible by three, yielding exactly 1760 yards per mile and by 16.5, yielding exactly 320 rods per mile.
- 5280 is connected with both Klein's J-invariant and the Heegner numbers. Specifically
- 5292 – Kaprekar number
- 5303 – Sophie Germain prime, balanced prime
- 5329 – , centered octagonal number
- 5333 – Sophie Germain prime
- 5335 – magic constant of n×n normal magic square and n-queens problem for n = 22.
- 5340 – octahedral number
- 5356 – triangular number
- 5365 – decagonal number
- 5387 – safe prime, balanced prime
- 5392 – Leyland number
- 5393 – balanced prime
- 5399 – Sophie Germain prime, safe prime
- 5405 – member of a Ruth–Aaron pair with 5406 (either definition)
- 5406 – member of a Ruth–Aaron pair with 5405 (either definition)
- 5419 – Cuban prime of the form x = y + 1
- 5441 – Sophie Germain prime
- 5456 – tetrahedral number
- 5459 – highly cototient number
- 5460 – triangular number
- 5461 – super-Poulet number, centered heptagonal number
- 5476 –
- 5483 – safe prime
- 5500 – nonagonal number
- 5501 – Sophie Germain prime
- 5507 – safe prime
- 5525 – square pyramidal number
- 5536 – tetranacci number
- 5563 – balanced prime
- 5564 – amicable number with 5020
- 5565 – triangular number
- 5566 – pentagonal pyramidal number
- 5571 – perfect totient number
- 5625 – , centered octagonal number
- 5639 – Sophie Germain prime, safe prime
- 5662 – decagonal number
- 5671 – triangular number
- 5711 – Sophie Germain prime
- 5719 – Zeisel number, Lucas–Carmichael number
- 5741 – Sophie Germain prime, Pell number, Markov number, centered heptagonal number
- 5768 – tribonacci number
- 5776 –
- 5777 – smallest counterexample to the conjecture that all odd numbers are of the form
- 5778 – triangular number
- 5781 – nonagonal number
- 5798 – Motzkin number
- 5807 – safe prime, balanced prime
- 5832 – 183
- 5849 – Sophie Germain prime
- 5879 – safe prime, highly cototient number
- 5886 – triangular number
- 5903 – Sophie Germain prime
- 5913 – sum of the first seven factorials
- 5927 – safe prime
- 5929 – , centered octagonal number
- 5939 – safe prime
- 5967 – decagonal number
- 5984 – tetrahedral number
- 5995 – triangular number