4000 (number)

"4,000" redirects here. For other uses, see 4000 (disambiguation).

Natural number

| <- 3999  | 4000 |  4001 ->

|
|

* List of numbers
* Integers

← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →

Cardinal| four thousand
Ordinal| 4000th
(four thousandth)
Factorization| 25 × 53
Greek numeral| ,Δ´
Roman numeral| MV, or IV
Unicode symbol(s)| MV, mv, IV, iv
Binary| 1111101000002
Ternary| 121110113
Senary| 303046
Octal| 76408
Duodecimal| 239412
Hexadecimal| FA016
Armenian| Տ
Egyptian hieroglyph| 𓆿

4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number.[1]

## Selected numbers in the range 4001–4999

[edit]

### 4001 to 4099

[edit]

* 4005 – triangular number[2]
* 4007 – safe prime
* 4010 – magic constant of n × n normal magic square and n-queens problem for n = 20
* 4013 – balanced prime[3]
* 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[4]
* 4031 – sum of the cubes of the first six primes
* 4032 – pronic number[5]
* 4033 – sixth super-Poulet number;[6] strong pseudoprime in base 2[7]
* 4057 – prime of the form 2p-1
* 4060 – tetrahedral number[8]
* 4073 – Sophie Germain prime
* 4079 – safe prime
* 4091 – super-prime
* 4095 – triangular number[2] and odd abundant number;[9] number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form  2 n − 1 {\displaystyle 2^{n}-1} [10]
* 4096 = 642 = 163 = 84 = 46 = 212, smallest number with exactly 13 factors, a superperfect number[11]

### 4100 to 4199

[edit]

* 4104 = 23 \+ 163 = 93 \+ 153
* 4127 – safe prime
* 4133 – super-prime
* 4139 – safe prime
* 4140 – Bell number[12]
* 4141 – centered square number[13]
* 4147 – smallest cyclic number in duodecimal represented in base-12 notation as 249712
2×4147dez = 497212
3×4147dez = 724912
4×4147dez = 972412
* 4153 – super-prime
* 4160 – pronic number[5]
* 4166 – centered heptagonal number[14]
* 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14[15]
* 4169 – a number of points of norm <= 10 in cubic lattice[16]
* 4177 – prime of the form 2p-1
* 4181 – Fibonacci number,[17] Markov number[18]
* 4186 – triangular number[2]
* 4187 – factor of R13, the record number of wickets taken in first-class cricket by Wilfred Rhodes
* 4199 – highly cototient number,[19] product of three consecutive primes

### 4200 to 4299

[edit]

* 4200 – nonagonal number,[20] pentagonal pyramidal number,[21] largely composite number[22]
* 4210 – 11th semi-meandric number[23]
* 4211 – Sophie Germain prime
* 4213 – Riordan number
* 4217 – super-prime, happy number
* 4219 – cuban prime of the form x = y \+ 1,[24] centered hexagonal number
* 4225 = 652, centered octagonal number[25]
* 4227 – sum of the first 46 primes
* 4240 – Leyland number[26]
* 4257 – decagonal number[1]
* 4259 – safe prime
* 4261 – prime of the form 2p-1
* 4271 – Sophie Germain prime
* 4273 – super-prime, number of non-isomorphic set-systems of weight 11
* 4278 – triangular number[2]
* 4279 – little Schroeder number
* 4283 – safe prime
* 4289 – highly cototient number[19]
* 4290 – pronic number[5]

### 4300 to 4399

[edit]

* 4320 – largely composite number[22]
* 4324 – 23rd square pyramidal number[27]
* 4325 – centered square number[13]
* 4339 – super-prime, twin prime
* 4349 – Sophie Germain prime
* 4356 = 662, sum of the cubes of the first eleven integers
* 4357 – prime of the form 2p-1
* 4359 – perfect totient number[28]
* 4369 – seventh super-Poulet number[6]
* 4371 – triangular number[2]
* 4373 – Sophie Germain prime
* 4374 – The largest number such that both it and the next number (4375) are 7-smooth
* 4375 – perfect totient number (the smallest not divisible by 3)[28]
* 4391 – Sophie Germain prime
* 4397 – Year of Comet Hale–Bopp's return, super-prime

### 4400 to 4499

[edit]

* 4400 – the number of missing persons in the sci-fi show The 4400
* 4409 – Sophie Germain prime, highly cototient number,[19] balanced prime,[3] 600th prime number
* 4410 – member of the Padovan sequence[29]
* 4411 – centered heptagonal number[14]
* 4421 – super-prime, alternating factorial[30]
* 4422 – pronic number[5]
* 4425 = 15 \+ 25 \+ 35 \+ 45 \+ 55[31]
* 4438 – sum of the first 47 primes
* 4444 \- repdigit
* 4446 – nonagonal number[20]
* 4447 – cuban prime of the form x = y \+ 1[24]
* 4457 – balanced prime[3]
* 4463 – super-prime
* 4465 – triangular number[2]
* 4481 – Sophie Germain prime
* 4489 = 672, centered octagonal number[25]
* 4495 – tetrahedral number[8]

### 4500 to 4599

[edit]

* 4503 – largest number not the sum of four or fewer squares of composites
* 4505 – fifth Zeisel number[32]
* 4513 – centered square number
* 4516 – centered pentagonal number
* 4517 – super-prime, happy number
* 4522 – decagonal number[1]
* 4547 – safe prime
* 4549 – super-prime
* 4556 – pronic number[5]
* 4560 – triangular number[2]
* 4567 – super-prime
* 4579 – octahedral number[33]
* 4597 – balanced prime[3]

### 4600 to 4699

[edit]

* 4604 – sum of the only two known Wieferich primes, 1093 and 3511
* 4607 – Woodall number[34]
* 4608 – 3-smooth number (29×32)
* 4619 – highly cototient number[19]
* 4620 – largely composite number[22]
* 4621 – prime of the form 2p-1
* 4624 = 682, 173 – 172
* 4641 – magic constant of n × n normal magic square and n-queens problem for n = 21
* 4655 – number of free decominoes
* 4656 – triangular number[2]
* 4657 – balanced prime[3]
* 4661 – sum of the first 48 primes
* 4663 – super-prime, centered heptagonal number[14]
* 4679 – safe prime
* 4680 – largely composite number[22]
* 4681 – eighth super-Poulet number[6]
* 4688 – 2-automorphic number[35]
* 4689 – sum of divisors and number of divisors are both triangular numbers[36]
* 4691 – balanced prime[3]
* 4692 – pronic number[5]
* 4699 – nonagonal number[20]

### 4700 to 4799

[edit]

* 4703 – safe prime
* 4705 = 482 \+ 492 = 172 \+ 182 \+ … + 262, centered square number
* 4727 – sum of the squares of the first twelve primes
* 4731 – centered pentagonal number
* 4733 – Sophie Germain prime
* 4753 – triangular number[2]
* 4759 – super-prime
* 4761 = 692, centered octagonal number[25]
* 4769 = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1[37]
* 4787 – safe prime, super-prime
* 4788 – 14th Keith number[38]
* 4793 – Sophie Germain prime
* 4795 – decagonal number[1]
* 4799 – safe prime

### 4800 to 4899

[edit]

* 4801 – super-prime, cuban prime of the form x = y \+ 2,[39] smallest prime with a composite sum of digits in base 7
* 4830 – pronic number[5]
* 4840 \- square yards in an acre
* 4851 – triangular number,[2] pentagonal pyramidal number[21]
* 4862 – Catalan number[40]
* 4871 – Sophie Germain prime
* 4877 – super-prime
* 4879 – 11th Kaprekar number[41]
* 4888 – sum of the first 49 primes

### 4900 to 4999

[edit]

* 4900 = 702, the only square-pyramidal square other than 1 ([1])
* 4901 – centered square number
* 4913 = 173
* 4919 – Sophie Germain prime, safe prime
* 4922 – centered heptagonal number[14]
* 4933 – super-prime
* 4941 – centered cube number[42]
* 4943 – Sophie Germain prime, super-prime
* 4950 – triangular number,[2] 12th Kaprekar number[41]
* 4951 – centered pentagonal number
* 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
* 4959 – nonagonal number[20]
* 4960 – tetrahedral number;[8] greater of fourth pair of Smith brothers
* 4970 – pronic number[5]
* 4973 – the 666th prime
* 4991 – Lucas–Carmichael number
* 4993 – balanced prime[3]
* 4999 – prime of the form  2 n 2 − 1 {\displaystyle 2n^{2}-1} [43]

### Prime numbers

[edit]

There are 119 prime numbers between 4000 and 5000:[44][45]

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

[edit]

1. ^ 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.
2. ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A006037 (Weird numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ a b c Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^ Sloane, N. J. A. (ed.). "Sequence A001262 (Strong pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
8. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. ^ Sloane, N. J. A. (ed.). "Sequence A005231 (Odd abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
10. ^ Sloane, N. J. A. (ed.). "Sequence A076046 (Ramanujan-Nagell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
11. ^ Sloane, N. J. A. (ed.). "Sequence A019279 (Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
12. ^ Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ a b Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
14. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
16. ^ Sloane, N. J. A. (ed.). "Sequence A000605 (Number of points of norm <= n in cubic lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
17. ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
18. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
19. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
20. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
21. ^ a b Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
22. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
23. ^ Sloane, N. J. A. (ed.). "Sequence A000682 (Semimeanders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
24. ^ a b Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
25. ^ a b c 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.
26. ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
27. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
28. ^ a b Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
29. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
30. ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
31. ^ Sloane, N. J. A. (ed.). "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
32. ^ Sloane, N. J. A. (ed.). "Sequence A051015 (Zeisel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
33. ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
34. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
35. ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-01.
36. ^ Sloane, N. J. A. (ed.). "Sequence A070996 (Numbers n whose sum of divisors and number of divisors are both triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
37. ^ Sloane, N. J. A. (ed.). "Sequence A122400 (Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
38. ^ 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.
39. ^ Sloane, N. J. A. (ed.). "Sequence A002648 (A variant of the cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
40. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
41. ^ a b Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
42. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
43. ^ Sloane, N. J. A. (ed.). "Sequence A066436 (Primes of the form 2*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
44. ^ 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.
45. ^ 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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* 654
* 655
* 656
* 657
* 658
* 659

* 660
* 661
* 662
* 663
* 664
* 665
* 666
* 667
* 668
* 669

* 670
* 671
* 672
* 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
* 2000
* 3000
* 4000
* 5000
* 6000
* 7000
* 8000
* 9000

* 10,000
* 20,000
* 30,000
* 40,000
* 50,000
* 60,000
* 70,000
* 80,000
* 90,000

* 100,000
* 1,000,000
* 10,000,000
* 100,000,000
* 1,000,000,000

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