View source for 4000 (number)

{{Redirect|4,000|other uses|4000 (disambiguation)}}
{{Infobox number
| number = 4000
| roman = M{{Overline|V}}, or {{Overline|IV}}
| unicode = M{{Overline|V}}, m{{Overline|v}}, {{Overline|IV}}, {{Overline|iv}}
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Տ|lang2=[[Egyptian numerals|Egyptian hieroglyph]]|lang2 symbol=<span style="font-size:200%;">𓆿</span>}}
'''4000''' ('''four thousand''') is the [[natural number]] following [[3000 (number)#3900 to 3999|3999]] and preceding 4001. It is a [[decagonal number]].<ref name=":0">{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref>

== Selected numbers in the range 4001–4999 ==

===4001 to 4099===
* '''4005''' – [[triangular number]]<ref name=A000217>{{Cite OEIS|A000217|2=Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n}}</ref>
* '''4007''' – [[safe prime]]
* '''4010''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 20
* '''4013''' – [[balanced prime]]<ref name=A006562>{{Cite OEIS|A006562|Balanced primes}}</ref>
* '''4019''' – [[Sophie Germain prime]]
* '''4021''' – prime of the form 2p-1
* '''4027''' – [[super-prime]]
* '''4028''' – sum of the first 45 primes
* '''4030''' – third [[weird number]]<ref>{{Cite OEIS|A006037|Weird numbers}}</ref>
* '''4031''' – sum of the cubes of the first six primes
* '''4032''' – [[pronic number]]<ref name=A002378>{{Cite OEIS|A002378|2=Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1)}}</ref>
* '''4033''' – sixth [[super-Poulet number]];<ref name=A050217>{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> [[strong pseudoprime]] in base 2<ref>{{Cite OEIS|A001262|Strong pseudoprimes to base 2}}</ref>
* '''4057''' – prime of the form 2p-1
* '''4060''' – [[tetrahedral number]]<ref name=A000292>{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
* '''4073''' – Sophie Germain prime
* '''4079''' – safe prime
* '''4091''' – super-prime
* '''4095''' – triangular number<ref name=A000217/> and odd [[abundant number]];<ref>{{Cite OEIS|A005231|Odd abundant numbers}}</ref> number of divisors in the sum of the fifth and largest known [[unitary perfect number]], largest [[Ramanujan–Nagell equation#Triangular Mersenne numbers|Ramanujan–Nagell number]] of the form <math>2^{n} - 1</math><ref>{{Cite OEIS|A076046|Ramanujan-Nagell numbers}}</ref>
* '''4096''' = 64<sup>2</sup> = 16<sup>3</sup> = 8<sup>4</sup> = 4<sup>6</sup> = [[power of two|2<sup>12</sup>]], smallest number with exactly 13 factors, a [[superperfect number]]<ref>{{Cite OEIS|A019279|Superperfect numbers}}</ref>

===4100 to 4199===
* '''[[4104 (number)|4104]]''' = 2<sup>3</sup> + 16<sup>3</sup> = 9<sup>3</sup> + 15<sup>3</sup>
* '''4127''' – [[safe prime]]
* '''4133''' – [[super-prime]]
* '''4139''' – safe prime
* '''4140''' – [[Bell number]]<ref>{{Cite OEIS|A000110|Bell or exponential numbers}}</ref>
* '''4141''' – [[centered square number]]<ref name=A001844>{{Cite OEIS|A001844|Centered square numbers}}</ref>
* '''4147''' – smallest [[cyclic number]] in [[duodecimal]] represented in [[base-12]] notation as 2497<sub>12</sub><br />2&times;4147<sub>dez</sub> = 4972<sub>12</sub><br />3&times;4147<sub>dez</sub> = 7249<sub>12</sub><br />4&times;4147<sub>dez</sub> = 9724<sub>12</sub>
* '''4153''' – super-prime
* '''4160''' – pronic number<ref name=A002378/>
* '''4166''' – [[centered heptagonal number]]<ref name=A069099>{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref>
* '''4167''' = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14<ref>{{cite OEIS|A000219|name=Number of planar partitions (or plane partitions) of n}}</ref>
* '''4169''' – a number of points of norm <= 10 in cubic lattice<ref>{{cite OEIS|A000605|2=Number of points of norm <= n in cubic lattice}}</ref>
* '''4177''' – prime of the form 2p-1
* '''4181''' – [[Fibonacci number]],<ref>{{Cite OEIS|A000045|Fibonacci numbers}}</ref> [[Markov number]]<ref>{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref>
* '''4186''' – triangular number<ref name=A000217/>
* '''4187''' – factor of [[repunit|R]]<sub>13</sub>, the record number of wickets taken in [[first-class cricket]] by [[Wilfred Rhodes]]
* '''4199''' – [[highly cototient number]],<ref name=A100827>{{Cite OEIS|A100827|Highly cototient numbers}}</ref> product of three consecutive primes

===4200 to 4299===
* '''4200''' – [[nonagonal number]],<ref name=":7">{{Cite OEIS|A001106|9-gonal (or enneagonal or nonagonal) numbers}}</ref> [[pentagonal pyramidal number]],<ref name=":8">{{Cite OEIS|A002411|Pentagonal pyramidal numbers}}</ref> largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''4210''' – 11th [[semi-meandric number]]<ref>{{Cite OEIS|A000682|Semimeanders}}</ref>
* '''4211''' – [[Sophie Germain prime]]
* '''4213''' – [[oeis:A005043|Riordan number]]
* '''4217''' – [[super-prime]], [[happy number]]
* '''4219''' – [[cuban prime]] of the form ''x'' = ''y'' + 1,<ref name=":9">{{Cite OEIS|A002407|Cuban primes}}</ref> [[centered hexagonal number]]
* '''4225''' = 65<sup>2</sup>, [[centered octagonal number]]<ref name=":10">{{Cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref>
* '''4227''' – sum of the first 46 primes
* '''4240''' – [[Leyland number]]<ref>{{Cite OEIS|A076980|Leyland numbers}}</ref>
* '''4257''' – [[decagonal number]]<ref name=":0" />
* '''4259''' – safe prime
* '''4261''' – prime of the form 2p-1
* '''4271''' – Sophie Germain prime
* '''4273''' – [[super-prime]], [[oeis:A283877|number of non-isomorphic set-systems of weight 11]]
* '''4278''' – triangular number<ref name=A000217/>
* '''4279''' – [[oeis:A001003|little Schroeder number]]
* '''4283''' – safe prime
* '''4289''' – highly cototient number<ref name=A100827/>
* '''4290''' – pronic number<ref name=A002378/>

===4300 to 4399===
* '''4320''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''4324''' – 23rd [[square pyramidal number]]<ref>{{Cite OEIS|A000330|Square pyramidal numbers}}</ref>
* '''4325''' – centered square number<ref name=A001844/>
* '''4339''' – [[super-prime]], [[twin prime]]
* '''4349''' – Sophie Germain prime
* '''4351''' – Normalized total height of all rooted trees on 6 labeled nodes<ref>{{cite OEIS|A234953|Normalized total height of all rooted trees on n labeled nodes}}</ref>
* '''4356''' = 66<sup>2</sup>, sum of the cubes of the first eleven integers
* '''4357''' – prime of the form 2p-1
* '''4359''' – [[perfect totient number]]<ref name=":11">{{Cite OEIS|A082897|Perfect totient numbers}}</ref>
* '''4369''' – seventh [[super-Poulet number]]<ref name=A050217/>
* '''4371''' – triangular number<ref name=A000217/>
* '''4373''' – Sophie Germain prime
* '''4374''' – The largest number such that both it and the next number (4375) are [[Smooth number|7-smooth]]
* '''4375''' – perfect totient number (the smallest not divisible by 3)<ref name=":11" />
* '''4391''' – Sophie Germain prime
* '''4397''' – Year of [[Comet Hale–Bopp]]'s return, [[super-prime]]

===4400 to 4499===
* '''4400''' – the number of missing persons in the sci-fi show ''[[The 4400]]''
* '''4409''' – Sophie Germain prime, highly cototient number,<ref name=A100827/> balanced prime,<ref name=A006562/> 600th prime number
* '''4410''' – member of the [[Padovan sequence]]<ref>{{Cite OEIS|A000931|Padovan sequence}}</ref>
* '''4411''' – centered heptagonal number<ref name=A069099/>
* '''4421''' – [[super-prime]], [[alternating factorial]]<ref>{{Cite OEIS|A005165|Alternating factorials}}</ref>
* '''4422''' – pronic number<ref name=A002378/>
* '''4425''' = 1<sup>5</sup> + 2<sup>5</sup> + 3<sup>5</sup> + 4<sup>5</sup> + 5<sup>5</sup><ref>{{cite OEIS|A031971|2=a(n) = Sum_{k=1..n} k^n}}</ref>
* '''4438''' – sum of the first 47 primes
* '''4444''' - [[repdigit]]
* '''4446''' – nonagonal number<ref name=":7" />
* '''4447''' – [[cuban prime]] of the form ''x'' = ''y'' + 1<ref name=":9" />
* '''4457''' – balanced prime<ref name=A006562/>
* '''4463''' – [[super-prime]]
* '''4465''' – triangular number<ref name=A000217/>
* '''4481''' – Sophie Germain prime
* '''4489''' = 67<sup>2</sup>, centered octagonal number<ref name=":10" />
* '''4495''' – [[tetrahedral number]]<ref name=A000292/>

===4500 to 4599===
* '''4503''' – largest number not the sum of four or fewer squares of [[Composite number|composites]]
* '''4505''' – fifth Zeisel number<ref>{{Cite OEIS|A051015|Zeisel numbers}}</ref>
* '''4513''' – centered square number
* '''4516''' – [[centered pentagonal number]]
* '''4517''' – [[super-prime]], [[happy number]]
* '''4522''' – decagonal number<ref name=":0" />
* '''4547''' – safe prime
* '''4549''' – [[super-prime]]
* '''4556''' – pronic number<ref name=A002378/>
* '''4560''' – triangular number<ref name=A000217/>
* '''4567''' – super-prime
* '''4579''' – [[octahedral number]]<ref>{{Cite OEIS|A005900|Octahedral numbers}}</ref>
* '''4597''' – balanced prime<ref name=A006562/>

===4600 to 4699===
* '''4604''' – sum of the only two known [[Wieferich prime]]s, 1093 and 3511
* '''4607''' – [[Woodall number]]<ref>{{Cite OEIS|A003261|Woodall numbers}}</ref>
* '''4608''' – [[3-smooth]] number (2<sup>9</sup>×3<sup>2</sup>)
* '''4619''' – highly [[cototient number]]<ref name=A100827/>
* '''4620''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''4621''' – prime of the form 2p-1
* '''4624''' = 68<sup>2</sup>, 17<sup>3</sup> – 17<sup>2</sup>
* '''4641''' – [[magic constant]] of ''n''&nbsp;×&nbsp;''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 21
* '''4655''' – number of free [[decomino]]es
* '''4656''' – triangular number<ref name=A000217/>
* '''4657''' – balanced prime<ref name=A006562/>
* '''4661''' – sum of the first 48 primes
* '''4663''' – [[super-prime]], centered heptagonal number<ref name=A069099/>
* '''4679''' – safe prime
* '''4680''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''4681''' – eighth [[super-Poulet number]]<ref name=A050217/>
* '''4688''' – 2-[[automorphic number]]<ref>{{Cite OEIS|A030984|2=2-automorphic numbers|access-date=2021-09-01}}</ref>
* '''4689''' – sum of divisors and number of divisors are both triangular numbers<ref>{{cite OEIS|A070996|Numbers n whose sum of divisors and number of divisors are both triangular numbers}}</ref>
* '''4691''' – balanced prime<ref name=A006562/>
* '''4692''' – pronic number<ref name=A002378/>
* '''4699''' – nonagonal number<ref name=":7" />

===4700 to 4799===
* '''4703''' – [[safe prime]]
* '''4705''' = 48<sup>2</sup> + 49<sup>2</sup> = 17<sup>2</sup> + 18<sup>2</sup> + ... + 26<sup>2</sup>, [[centered square number]]
* '''4727''' – sum of the squares of the first twelve primes
* '''4731''' – [[centered pentagonal number]]
* '''4733''' – Sophie Germain prime
* '''4753''' – triangular number<ref name=A000217/>
* '''4759''' – [[super-prime]]
* '''4761''' = 69<sup>2</sup>, centered octagonal number<ref name=":10" />
* '''4769''' = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1<ref>{{cite OEIS|A122400|Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1}}</ref>
* '''4787''' – safe prime, [[super-prime]]
* '''4788''' – 14th [[Keith number]]<ref>{{Cite OEIS|A007629|Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)}}</ref>
* '''4793''' – Sophie Germain prime
* '''4795''' – decagonal number<ref name=":0" />
* '''4799''' – safe prime

===4800 to 4899===
* '''4801''' – [[super-prime]], [[cuban prime]] of the form ''x'' = ''y'' + 2,<ref>{{Cite OEIS|A002648|A variant of the cuban primes}}</ref> smallest prime with a composite sum of digits in base 7
* '''4830''' – pronic number<ref name=A002378/>
* '''4840''' - square yards in an [[acre]]
* '''4851''' – triangular number,<ref name=A000217/> [[pentagonal pyramidal number]]<ref name=":8" />
* '''4862''' – [[Catalan number]]<ref>{{Cite OEIS|A000108|Catalan numbers}}</ref>
* '''4871''' – Sophie Germain prime
* '''4877''' – [[super-prime]]
* '''4879''' – 11th [[Kaprekar number]]<ref name=":12">{{Cite OEIS|A006886|Kaprekar numbers}}</ref>
* '''4888''' – sum of the first 49 primes

===4900 to 4999===
* '''4900''' = 70<sup>2</sup>, the only [[square pyramidal number|square-pyramidal]] [[square number|square]] other than [[1 (number)|1]] ([http://mathworld.wolfram.com/CannonballProblem.html])
* '''4901''' – [[centered square number]]
* '''4913''' = 17<sup>3</sup>
* '''4919''' – Sophie Germain prime, safe prime
* '''4922''' – centered heptagonal number<ref name=A069099/>
* '''4933''' – [[super-prime]]
* '''4941''' – [[centered cube number]]<ref>{{Cite OEIS|A005898|Centered cube numbers}}</ref>
* '''4943''' – [[Sophie Germain prime]], [[super-prime]]
* '''4950''' – triangular number,<ref name=A000217/> 12th [[Kaprekar number]]<ref name=":12" />
* '''4951''' – [[centered pentagonal number]]
* '''4957''' – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
* '''4959''' – nonagonal number<ref name=":7" />
* '''4960''' – [[tetrahedral number]];<ref name=A000292/> greater of fourth pair of [[Smith number|Smith brothers]]
* '''4970''' – pronic number<ref name=A002378/>
* '''4973''' – the 666th prime
* '''4991''' – [[Lucas–Carmichael number]]
* '''4993''' – balanced prime<ref name=A006562/>
* '''4999''' – [[Prime number|prime]] of the form <math>2n^2-1</math><ref>{{Cite OEIS|A066436|Primes of the form 2*n^2 - 1}}</ref>

===Prime numbers===
There are 119 [[prime number]]s between 4000 and 5000:<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>
:4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999

==References==
{{Reflist}}

{{Integers|10}}

[[Category:Integers]]