3000 (number)

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Natural number

| <- 2999  | 3000 |  3001 ->

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* List of numbers
* Integers

← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →

Cardinal| three thousand
Ordinal| 3000th
(three thousandth)
Factorization| 23 × 3 × 53
Greek numeral| ,Γ´
Roman numeral| MMM, mmm
Unicode symbol(s)| MMM, mmm
Binary| 1011101110002
Ternary| 110100103
Senary| 215206
Octal| 56708
Duodecimal| 18A012
Hexadecimal| BB816
Armenian| Վ
Egyptian hieroglyph| 𓆾

3000 (three thousand) is the natural number following 2999 and preceding 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

[edit]

### 3001 to 3099

[edit]

* 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 prime
* 3023 – 84th Sophie Germain prime, 51st safe prime
* 3025 = 552, sum of the cubes of the first ten integers, centered octagonal number,[1] dodecagonal number[2]
* 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[3]
* 3052 – decagonal number[4]
* 3059 – centered cube number[5]
* 3061 – prime of the form 2p-1
* 3063 – perfect totient number[6]
* 3067 – super-prime
* 3071 – Thabit number
* 3072 – 3-smooth number (210×3)
* 3075 – nonagonal number[7]
* 3078 – 18th pentagonal pyramidal number[8]
* 3080 – pronic number
* 3081 – triangular number, 497th sphenic number
* 3087 – sum of first 40 primes

### 3100 to 3199

[edit]

* 3109 – super-prime
* 3119 – safe prime
* 3121 – centered square number,[9] emirp, largest minimal prime in quinary.
* 3125 – a solution to the expression  n n {\displaystyle n^{n}} , where  n = 5 {\displaystyle n=5} ( 3125 = 5 5 {\displaystyle 3125=5^{5}} ).
* 3136 = 562, palindromic in ternary (110220113), tribonacci number[10]
* 3137 – Proth prime,[11] both a left- and right-truncatable prime
* 3149 – highly cototient number[12]
* 3150 = 153 \- 152
* 3155 – member of the Mian–Chowla sequence[13]
* 3159 = number of trees with 14 unlabeled nodes[14]
* 3160 – triangular number
* 3167 – safe prime
* 3169 – super-prime, Cuban prime of the form  x = y + 1 {\displaystyle x=y+1} .[15]
* 3192 – pronic number

### 3200 to 3299

[edit]

* 3203 – safe prime
* 3207 – number of compositions of 14 whose run-lengths are either weakly increasing or weakly decreasing[16]
* 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,[1] 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[3]
* 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[17]
* 3266 – sum of first 41 primes, 523rd sphenic number
* 3276 – tetrahedral number[18]
* 3277 – 5th super-Poulet number,[19] decagonal number[4]
* 3279 – first composite Wieferich number
* 3281 – octahedral number,[20] centered square number[9]
* 3286 – nonagonal number[7]
* 3299 – 85th Sophie Germain prime, super-prime

### 3300 to 3399

[edit]

* 3306 – pronic number
* 3307 – balanced prime[21]
* 3313 – balanced prime, star number[21]
* 3319 – super-prime, happy number
* 3321 – triangular number
* 3329 – 86th Sophie Germain prime, Proth prime,[11] member of the Padovan sequence[22]
* 3354 – member of the Mian–Chowla sequence[13]
* 3358 – sum of the squares of the first eleven primes
* 3359 – 87th Sophie Germain prime, highly cototient number[12]
* 3360 – largely composite number[23]
* 3363/2378 ≈ √2
* 3364 = 582
* 3367 = 153 \- 23 = 163 \- 93 = 343 \- 333[importance?]
* 3375 = 153, palindromic in base 14 (133114), 15th cube
* 3389 – 88th Sophie Germain prime

### 3400 to 3499

[edit]

* 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 n-queens problem for n = 19.
* 3445 – centered square number[9]
* 3447 – sum of first 42 primes
* 3449 – 90th Sophie Germain prime
* 3456 – 3-smooth number (27×33)
* 3457 – Proth prime[11]
* 3463 – happy number
* 3467 – safe prime
* 3469 – super-prime, Cuban prime of the form x = y \+ 2, completes the tenth prime quadruplet set[24]
* 3473 – centered heptagonal number[3]
* 3481 = 592, centered octagonal number[1]
* 3486 – triangular number
* 3491 – 91st Sophie Germain prime

### 3500 to 3599

[edit]

* 3504 – nonagonal number[7]
* 3510 – decagonal number[4]
* 3511 – largest known Wieferich prime
* 3512 – number of primes  ≤ 2 15 {\displaystyle \leq 2^{15}} .[25]
* 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[12]
* 3570 – triangular number
* 3571 – 500th prime, Cuban prime of the form x = y \+ 1,[15] 17th Lucas number,[26] 4th balanced prime of order 4.[27]
* 3591 – member of the Mian–Chowla sequence[13]
* 3593 – 93rd Sophie Germain prime, super-prime

### 3600 to 3699

[edit]

* 3600 = 602, number of seconds in an hour, called šār or šāru in the sexagesimal system of Ancient Mesopotamia (cf. Saros), 1201-gonal number
* 3601 – star number
* 3610 – 19th pentagonal pyramidal number[8]
* 3613 – centered square number[9]
* 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[21]
* 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[18]
* 3655 – triangular number, 601st sphenic number
* 3660 – pronic number
* 3684 – 13th Keith number[28]
* 3697 – centered heptagonal number[3]

### 3700 to 3799

[edit]

* 3721 = 612, centered octagonal number[1]
* 3729 – nonagonal number[7]
* 3733 – balanced prime, super-prime[21]
* 3741 – triangular number, 618th sphenic number
* 3751 – decagonal number[4]
* 3761 – 95th Sophie Germain prime, super-prime
* 3779 – 96th Sophie Germain prime, safe prime
* 3780 – largely composite number[23]
* 3782 – pronic number, 623rd sphenic number
* 3785 – centered square number[9]
* 3797 – member of the Mian–Chowla sequence,[13] both a left- and right- truncatable prime

### 3800 to 3899

[edit]

* 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[29]
* 3863 – 100th Sophie Germain prime
* 3865 – greater of third pair of Smith brothers
* 3888 – longest number when expressed in Roman numerals I, V, X, L, C, D, and M (MMMDCCCLXXXVIII), 3-smooth number (24×35)
* 3889 – Cuban prime of the form x = y \+ 2[24]
* 3894 – octahedral number[20]

### 3900 to 3999

[edit]

* 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[30]
* 3916 – triangular number
* 3925 – centered cube number[5]
* 3926 – 12th open meandric number, 654th sphenic number
* 3928 – centered heptagonal number[3]
* 3937 – product of distinct Mersenne primes,[31] repeated sum of divisors is prime,[32] denominator of conversion factor from meter to US survey foot[33]
* 3940 – there are 3940 distinct ways to arrange the 12 flat pentacubes (or 3-D pentominoes) into a 3x4x5 box (not counting rotations and reflections)
* 3943 – super-prime
* 3947 – safe prime
* 3960 – largely composite number[23]
* 3961 – nonagonal number,[7] centered square number[9]
* 3969 = 632, centered octagonal number[1]
* 3989 – highly cototient number[12]
* 3998 – member of the Mian–Chowla sequence[13]
* 3999 – largest number properly expressible using Roman numerals I, V, X, L, C, D, and M (MMMCMXCIX), ignoring vinculum

### Prime numbers

[edit]

There are 120 prime numbers between 3000 and 4000:[34][35]

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

[edit]

1. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A051624 (12-gonal (or dodecagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ a b Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
8. ^ a b Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
10. ^ Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
11. ^ a b c Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
12. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
14. ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ a b Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
16. ^ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
17. ^ Bashelor, Andrew; Ksir, Amy; Traves, Will (2008), "Enumerative algebraic geometry of conics." (PDF), Amer. Math. Monthly, 115 (8): 701–728, doi:10.1080/00029890.2008.11920584, JSTOR 27642583, MR 2456094, S2CID 16822027
18. ^ a b Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
19. ^ Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
20. ^ a b Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
21. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
22. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
23. ^ a b c Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
24. ^ a b Sloane, N. J. A. (ed.). "Sequence A002648 (A variant of the cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
25. ^ Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
26. ^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
27. ^ Sloane, N. J. A. (ed.). "Sequence A082079 (Balanced primes of order four)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
28. ^ Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
29. ^ Sloane, N. J. A. (ed.). "Sequence 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
30. ^ Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
31. ^ Sloane, N. J. A. (ed.). "Sequence A046528 (Numbers that are a product of distinct Mersenne primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
32. ^ Sloane, N. J. A. (ed.). "Sequence A247838 (Numbers n such that sigma(sigma(n)) is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
33. ^ Lamb, Evelyn (October 25, 2019), "Farewell to the Fractional Foot", Roots of Unity, Scientific American
34. ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
35. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.

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Integers

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100s

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* 673
* 674
* 675
* 676
* 677
* 678
* 679

* 680
* 681
* 682
* 683
* 684
* 685
* 686
* 687
* 688
* 689

* 690
* 691
* 692
* 693
* 694
* 695
* 696
* 697
* 698
* 699

700s

* 700
* 701
* 702
* 703
* 704
* 705
* 706
* 707
* 708
* 709

* 710
* 711
* 712
* 713
* 714
* 715
* 716
* 717
* 718
* 719

* 720
* 721
* 722
* 723
* 724
* 725
* 726
* 727
* 728
* 729

* 730
* 731
* 732
* 733
* 734
* 735
* 736
* 737
* 738
* 739

* 740
* 741
* 742
* 743
* 744
* 745
* 746
* 747
* 748
* 749

* 750
* 751
* 752
* 753
* 754
* 755
* 756
* 757
* 758
* 759

* 760
* 761
* 762
* 763
* 764
* 765
* 766
* 767
* 768
* 769

* 770
* 771
* 772
* 773
* 774
* 775
* 776
* 777
* 778
* 779

* 780
* 781
* 782
* 783
* 784
* 785
* 786
* 787
* 788
* 789

* 790
* 791
* 792
* 793
* 794
* 795
* 796
* 797
* 798
* 799

800s

* 800
* 801
* 802
* 803
* 804
* 805
* 806
* 807
* 808
* 809

* 810
* 811
* 812
* 813
* 814
* 815
* 816
* 817
* 818
* 819

* 820
* 821
* 822
* 823
* 824
* 825
* 826
* 827
* 828
* 829

* 830
* 831
* 832
* 833
* 834
* 835
* 836
* 837
* 838
* 839

* 840
* 841
* 842
* 843
* 844
* 845
* 846
* 847
* 848
* 849

* 850
* 851
* 852
* 853
* 854
* 855
* 856
* 857
* 858
* 859

* 860
* 861
* 862
* 863
* 864
* 865
* 866
* 867
* 868
* 869

* 870
* 871
* 872
* 873
* 874
* 875
* 876
* 877
* 878
* 879

* 880
* 881
* 882
* 883
* 884
* 885
* 886
* 887
* 888
* 889

* 890
* 891
* 892
* 893
* 894
* 895
* 896
* 897
* 898
* 899

900s

* 900
* 901
* 902
* 903
* 904
* 905
* 906
* 907
* 908
* 909

* 910
* 911
* 912
* 913
* 914
* 915
* 916
* 917
* 918
* 919

* 920
* 921
* 922
* 923
* 924
* 925
* 926
* 927
* 928
* 929

* 930
* 931
* 932
* 933
* 934
* 935
* 936
* 937
* 938
* 939

* 940
* 941
* 942
* 943
* 944
* 945
* 946
* 947
* 948
* 949

* 950
* 951
* 952
* 953
* 954
* 955
* 956
* 957
* 958
* 959

* 960
* 961
* 962
* 963
* 964
* 965
* 966
* 967
* 968
* 969

* 970
* 971
* 972
* 973
* 974
* 975
* 976
* 977
* 978
* 979

* 980
* 981
* 982
* 983
* 984
* 985
* 986
* 987
* 988
* 989

* 990
* 991
* 992
* 993
* 994
* 995
* 996
* 997
* 998
* 999

1000s

* 1000
* 1001
* 1023
* 1024
* 1089
* 1093
* 1105
* 1234
* 1289
* 1458
* 1510
* 1728
* 1729
* 1980
* 1987

* 2000
* 2016
* 2520
* 3000
* 3511
* 4000
* 4104
* 5000
* 5040
* 6000
* 6174
* 7000
* 7744
* 7825
* 8000
* 8128
* 8192
* 9000
* 9855
* 9999

* 10,000
* 16,807
* 20,000
* 30,000
* 40,000
* 50,000
* 60,000
* 64,079
* 65,535
* 65,536
* 65,537
* 70,000
* 80,000
* 90,000

* 100,000
* 142,857
* 144,000
* 1,000,000
* 10,000,000
* 43,112,609
* 100,000,000
* 1,000,000,000
* 2,147,483,647
* 4,294,967,295
* 10,000,000,000
* 100,000,000,000

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