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{{Redirect|3,000|other uses|3000 (disambiguation)}}
{{More citations needed|date=June 2016}}
{{Infobox number
| number = 3000
| unicode = MMM, mmm
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Վ|lang3=[[Egyptian numerals|Egyptian hieroglyph]]|lang3 symbol=𓆾}}

'''3000''' ('''three thousand''') is the [[natural number]] following [[2000 (number)#2900 to 2999|2999]] and preceding [[#3001 to 3099|3001]]. It is the smallest number requiring thirteen letters in English (when "and" is required from 101 forward).

==Selected numbers in the range 3001–3999==

===3001 to 3099===
* '''3001''' – [[super-prime]]; divides the [[Euclid number]] 2999# + 1
* '''3003''' – [[triangular number]], only number known to appear eight times in [[Pascal's triangle]]; no number is known to appear more than eight times other than 1. (see [[Singmaster's conjecture]])
* '''3019''' – [[super-prime]], [[happy number|happy prime]]
* '''3023''' – 84th [[Sophie Germain prime]], 51st [[safe prime]]
* '''3025''' = 552, sum of the cubes of the first ten integers, [[centered octagonal number]],<ref name=":0">{{Cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref> [[dodecagonal number]]<ref>{{Cite OEIS|A051624|12-gonal (or dodecagonal) numbers}}</ref>
* '''3037''' – [[star number]], [[cousin prime]] with 3041
* '''3045''' – sum of the integers 196 to 210 ''and'' sum of the integers 211 to 224
* '''3046''' – [[centered heptagonal number]]<ref name=":1">{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref>
* '''3052''' – [[decagonal number]]<ref name=":2">{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref>
* '''3059''' – [[centered cube number]]<ref name=":3">{{Cite OEIS|A005898|Centered cube numbers}}</ref>
* '''3061''' – prime of the form 2p-1
* '''3063''' – [[perfect totient number]]<ref>{{Cite OEIS|A082897|Perfect totient numbers}}</ref>
* '''3067''' – [[super-prime]]
* '''3071''' – [[Thabit number]]
* '''3072''' – [[3-smooth]] number (210×3)
* '''3075''' – [[nonagonal number]]<ref name=":4">{{Cite OEIS|A001106|9-gonal (or enneagonal or nonagonal) numbers}}</ref>
* '''3078''' – 18th [[pentagonal pyramidal number]]<ref name=":5">{{Cite OEIS|A002411|Pentagonal pyramidal numbers}}</ref>
* '''3080''' – [[pronic number]]
* '''3081''' – triangular number, 497th [[sphenic number]]
* '''3087''' – sum of first 40 primes

===3100 to 3199===
* '''3109''' – [[super-prime]]
* '''3119''' – [[safe prime]]
* '''3121''' – [[centered square number]],<ref name=":6">{{Cite OEIS|A001844|Centered square numbers}}</ref> [[emirp]], largest [[Minimal prime (recreational mathematics)|minimal prime]] in [[quinary]].
* '''3125''' – a solution to the expression <math>n^n</math>, where <math>n=5</math> (<math>3125=5^5</math>).
* '''3136''' = 562, palindromic in [[ternary numeral system|ternary]] (110220113), [[tribonacci number]]<ref>{{Cite OEIS|A000073|Tribonacci numbers}}</ref>
* '''3137''' – [[Proth prime]],<ref name=":7">{{Cite OEIS|A080076|Proth primes}}</ref> both a left- and right-[[truncatable prime]]
* '''3149''' – [[highly cototient number]]<ref name=":8">{{Cite OEIS|A100827|Highly cototient numbers}}</ref>
* '''3150''' = 153 - 152
* '''3155''' – member of the [[Mian–Chowla sequence]]<ref name=":9">{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref>
* '''3159''' = number of trees with 14 unlabeled nodes<ref>{{cite OEIS|A000055|Number of trees with n unlabeled nodes}}</ref>
* '''3160''' – [[triangular number]]
* '''3167''' – safe prime
* '''3169''' – [[super-prime]], [[Cuban prime]] of the form <math>x=y+1</math>.<ref name=":10">{{Cite OEIS|A002407|Cuban primes}}</ref>
*'''3192''' – [[pronic number]]

===3200 to 3299===
* '''3203''' – safe prime
* '''3207''' – number of compositions of 14 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}}</ref>
* '''3229''' – [[super-prime]]
* '''3240''' – [[triangular number]]
* '''3248''' – member of a [[Ruth-Aaron pair]] with 3249 under second definition, largest number whose [[factorial]] is less than 1010000 – hence its factorial is the largest certain advanced computer programs can handle.
*'''3249''' = 572, palindromic in base 7 (123217), centered octagonal number,<ref name=":0" /> member of a Ruth–Aaron pair with 3248 under second definition
* '''3253''' – sum of eleven consecutive primes (269 + 271 + 277 + 281 + 283 + 293 + 307 + 311 + 313 + 317 + 331)
* '''3256''' – centered heptagonal number<ref name=":1" />
* '''3259''' – [[super-prime]], completes the ninth [[prime quadruplet]] set
* '''3264''' – solution to [[Steiner's conic problem]]: number of smooth conics tangent to 5 given conics in general position<ref>{{citation|mr=2456094
|last1=Bashelor|first1= Andrew|last2= Ksir|first2= Amy|last3= Traves|first3= Will|title=Enumerative algebraic geometry of conics.
|journal=Amer. Math. Monthly|volume= 115 |year=2008|number= 8|pages= 701–728|doi=10.1080/00029890.2008.11920584|jstor=27642583|s2cid=16822027|url=https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Bashelor.pdf}}</ref>
* '''3266''' – sum of first 41 primes, 523rd [[sphenic number]]
* '''3276''' – [[tetrahedral number]]<ref name=":11">{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
* '''3277''' – 5th [[super-Poulet number]],<ref>{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> decagonal number<ref name=":2" />
* '''3279''' – first composite [[Wieferich number]]
* '''3281''' – [[octahedral number]],<ref name=":12">{{Cite OEIS|A005900|Octahedral numbers}}</ref> centered square number<ref name=":6" />
* '''3286''' – nonagonal number<ref name=":4" />
* '''3299''' – 85th [[Sophie Germain prime]], super-prime

===3300 to 3399===
* '''3306''' – [[pronic number]]
* '''3307''' – [[balanced prime]]<ref name=":13">{{Cite OEIS|A006562|Balanced primes}}</ref>
* '''3313''' – balanced prime, [[star number]]<ref name=":13" />
* '''3319''' – [[super-prime]], [[happy number]]
* '''3321''' – [[triangular number]]
* '''3329''' – 86th [[Sophie Germain prime]], Proth prime,<ref name=":7" /> member of the [[Padovan sequence]]<ref>{{Cite OEIS|A000931|Padovan sequence}}</ref>
* '''3354''' – member of the Mian–Chowla sequence<ref name=":9" />
* '''3358''' – sum of the squares of the first eleven primes
* '''3359''' – 87th [[Sophie Germain prime]], [[highly cototient number]]<ref name=":8" />
* '''3360''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''3363'''/2378 ≈ [[square root of 2|√2]]
* '''3364''' = 582
* '''3367''' = 153 - 23 = 163 - 93 = 343 - 333{{importance inline}}
* '''3375''' = 153, palindromic in base 14 (133114), 15th [[Cube (arithmetic)|cube]]
* '''3389''' – 88th [[Sophie Germain prime]]

===3400 to 3499===
* '''3403''' – [[triangular number]]
* '''3407''' – [[super-prime]]
* '''3413''' – 89th [[Sophie Germain prime]], sum of the first 5 nn: 3413 = 11 + 22 + 33 + 44 + 55
* '''3422''' – [[pronic number]], 553rd [[sphenic number]], [[melting point]] of [[tungsten]] in [[degrees Celsius]]
* '''3435''' – a [[perfect digit-to-digit invariant]], equal to the sum of its digits to their own powers (33 + 44 + 33 + 55 = 3435)
* '''3439''' – [[magic constant]] of ''n''×''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 19.
* '''3445''' – [[centered square number]]<ref name=":6" />
* '''3447''' – sum of first 42 primes
* '''3449''' – 90th [[Sophie Germain prime]]
* '''3456''' – [[3-smooth]] number (27×33)
* '''3457''' – Proth prime<ref name=":7" />
* '''3463''' – [[happy number]]
* '''3467''' – safe prime
* '''3469''' – [[super-prime]], [[Cuban prime]] of the form ''x'' = ''y'' + 2, completes the tenth [[prime quadruplet]] set<ref name=":14">{{Cite OEIS|A002648|A variant of the cuban primes}}</ref>
* '''3473''' – centered heptagonal number<ref name=":1" />
* '''3481''' = 592, centered octagonal number<ref name=":0" />
* '''3486''' – triangular number
* '''3491''' – 91st [[Sophie Germain prime]]

===3500 to 3599===
* '''3504''' – nonagonal number<ref name=":4" />
* '''3510''' – decagonal number<ref name=":2" />
* '''[[3511 (number)|3511]]''' – largest known [[Wieferich prime]]
* '''3512''' – number of primes <math>\leq 2^{15}</math>.<ref>{{cite OEIS|A007053|2=Number of primes <= 2^n}}</ref>
* '''3517''' – [[super-prime]], sum of nine consecutive primes (367 + 373 + 379 + 383 + 389 + 397 + 401 + 409 + 419)
* '''3539''' – 92nd [[Sophie Germain prime]]
* '''3540''' – [[pronic number]]
* '''3559''' – [[super-prime]]
* '''3569''' – [[highly cototient number]]<ref name=":8" />
* '''3570''' – [[triangular number]]
* '''3571''' – 500th prime, [[Cuban prime]] of the form ''x'' = ''y'' + 1,<ref name=":10" /> 17th [[Lucas number]],<ref>{{Cite OEIS|A000032|Lucas numbers}}</ref> 4th [[balanced prime]] of order 4.<ref>{{Cite OEIS|A082079|Balanced primes of order four}}</ref>
* '''3591''' – member of the Mian–Chowla sequence<ref name=":9" />
* '''3593''' – 93rd [[Sophie Germain prime]], super-prime

===3600 to 3699===
* '''3600''' = 602, number of [[seconds]] in an [[hour]], called ''šār'' or ''šāru'' in the [[sexagesimal]] system of [[Ancient Mesopotamia]] (''cf''. [[Saros (astronomy)|Saros]]), 1201-[[polygonal number|gonal number]]
* '''3601''' – [[star number]]
* '''3610''' – 19th [[pentagonal pyramidal number]]<ref name=":5" />
* '''3613''' – [[centered square number]]<ref name=":6" />
* '''3617''' – sum of eleven consecutive primes (293 + 307 + 311 + 313 + 317 + 331 + 337 + 347 + 349 + 353 + 359)
* '''3623''' – 94th [[Sophie Germain prime]], safe prime
* '''3637''' – balanced prime, [[super-prime]]<ref name=":13" />
* '''3638''' – sum of first 43 primes, 599th [[sphenic number]]
* '''3643''' – [[happy number]], sum of seven consecutive primes (499 + 503 + 509 + 521 + 523 + 541 + 547)
* '''3654''' – [[tetrahedral number]]<ref name=":11" />
* '''3655''' – [[triangular number]], 601st [[sphenic number]]
* '''3660''' – [[pronic number]]
* '''3684''' – 13th [[Keith number]]<ref>{{Cite OEIS|A007629|Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)}}</ref>
* '''3697''' – centered heptagonal number<ref name=":1" />

===3700 to 3799===
* '''3721''' = 612, centered [[octagonal number]]<ref name=":0" />
* '''3729''' – nonagonal number<ref name=":4" />
* '''3733''' – balanced prime, [[super-prime]]<ref name=":13" />
* '''3741''' – [[triangular number]], 618th [[sphenic number]]
* '''3751''' – decagonal number<ref name=":2" />
* '''3761''' – 95th [[Sophie Germain prime]], super-prime
* '''3779''' – 96th [[Sophie Germain prime]], safe prime
* '''3780''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''3782''' – [[pronic number]], 623rd [[sphenic number]]
* '''3785''' – [[centered square number]]<ref name=":6" />
* '''3797''' – member of the Mian–Chowla sequence,<ref name=":9" /> both a left- and right- [[truncatable prime]]

===3800 to 3899===
* '''3803''' – 97th [[Sophie Germain prime]], [[safe prime]], the largest prime factor of 123,456,789
* '''3821''' – 98th [[Sophie Germain prime]]
* '''3828''' – [[triangular number]]
* '''3831''' – sum of first 44 primes
* '''3840''' = 163 - 162, [[double factorial]] of 10
* '''3844''' = 622
* '''3851''' – 99th [[Sophie Germain prime]]
* '''3856''' – number of 17-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref>{{cite OEIS|A000013|Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed}}</ref>
* '''3863''' – 100th [[Sophie Germain prime]]
* '''3865''' – greater of third pair of [[Smith number|Smith brothers]]
* '''3888''' – longest number when expressed in [[Roman numeral]]s I, V, X, L, C, D, and M (MMMDCCCLXXXVIII), [[3-smooth]] number (24×35)
* '''3889''' – [[Cuban prime]] of the form ''x'' = ''y'' + 2<ref name=":14" />
* '''3894''' – [[octahedral number]]<ref name=":12" />

===3900 to 3999===
* '''3901''' – [[star number]]
* '''3906''' – [[pronic number]]
* '''3911''' – 101st [[Sophie Germain prime]], [[super-prime]]
* '''3914''' – number of 18-bead necklaces (turning over is allowed) where complements are equivalent<ref>{{cite OEIS|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
* '''3916''' – [[triangular number]]
* '''3925''' – centered cube number<ref name=":3" />
* '''3926''' – 12th [[open meandric number]], 654th [[sphenic number]]
* '''3928''' – centered heptagonal number<ref name=":1" />
* '''3937''' – product of distinct Mersenne primes,<ref>{{cite OEIS|A046528|Numbers that are a product of distinct Mersenne primes}}</ref> repeated sum of divisors is prime,<ref>{{cite OEIS|A247838|Numbers n such that sigma(sigma(n)) is prime}}</ref> denominator of conversion factor from meter to [[US survey foot]]<ref>{{citation|url=https://blogs.scientificamerican.com/roots-of-unity/farewell-to-the-fractional-foot/|magazine=Scientific American|department=Roots of Unity|title=Farewell to the Fractional Foot|first=Evelyn|last=Lamb|date=October 25, 2019}}</ref>
* '''3940''' – there are 3940 distinct ways to arrange the 12 flat [[pentacube]]s (or 3-D [[pentomino]]es) into a 3x4x5 box (not counting rotations and reflections)
* '''3943''' – [[super-prime]]
* '''3947''' – safe prime
* '''3960''' – largely composite number<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
* '''3961''' – nonagonal number,<ref name=":4" /> centered square number<ref name=":6" />
* '''3969''' = 632, centered octagonal number<ref name=":0" />
* '''3989''' – [[highly cototient number]]<ref name=":8" />
* '''3998''' – member of the Mian–Chowla sequence<ref name=":9" />
* '''3999''' – largest number properly expressible using [[Roman numeral]]s I, V, X, L, C, D, and M (MMMCMXCIX), ignoring [[Vinculum (symbol)|vinculum]]

===Prime numbers===
There are 120 [[prime number]]s between 3000 and 4000:<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>
:3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989

==References==
{{Reflist}}

{{Integers|10}}

[[Category:Integers]]

3000 (number) - Revision history

>Bbb23: revert sock