4000 (number)

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title: "4000 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/4000_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::data[format=table title="Infobox number"]

Field	Value
number	4000
roman	M, or
unicode	M, m, ,
lang1	Armenian
::

| number = 4000 | roman = M, or | unicode = M, m, , |lang1=Armenian|lang1 symbol=Տ|lang2=Egyptian hieroglyph|lang2 symbol=𓆿}} 4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number.

Selected numbers in the range 4001–4999

4001 to 4099

• 4005 – triangular number
• 4007 – safe prime
• 4010 – magic constant of n × n normal magic square and n-queens problem for n = 20
• 4013 – balanced prime
• 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
• 4031 – sum of the cubes of the first six primes
• 4032 – pronic number
• 4033 – sixth super-Poulet number; strong pseudoprime in base 2
• 4057 – prime of the form 2p-1
• 4060 – tetrahedral number
• 4073 – Sophie Germain prime
• 4079 – safe prime
• 4091 – super-prime
• 4095 – triangular number 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
• 4096 = 642 = 163 = 84 = 46 = 212, smallest number with exactly 13 factors, a superperfect number

4100 to 4199

• 4104 = 23 + 163 = 93 + 153
• 4127 – safe prime
• 4133 – super-prime
• 4139 – safe prime
• 4140 – Bell number
• 4141 – centered square number
• 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
• 4166 – centered heptagonal number
• 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14
• 4169 – a number of points of norm
• 4177 – prime of the form 2p-1
• 4181 – Fibonacci number, Markov number
• 4186 – triangular number
• 4187 – factor of R13, the record number of wickets taken in first-class cricket by Wilfred Rhodes
• 4199 – highly cototient number, product of three consecutive primes

4200 to 4299

• 4200 – nonagonal number, pentagonal pyramidal number, largely composite number
• 4210 – 11th semi-meandric number
• 4211 – Sophie Germain prime
• 4213 – Riordan number
• 4217 – super-prime, happy number
• 4219 – cuban prime of the form x = y + 1, centered hexagonal number
• 4225 = 652, centered octagonal number
• 4227 – sum of the first 46 primes
• 4240 – Leyland number
• 4257 – decagonal number
• 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
• 4279 – little Schroeder number
• 4283 – safe prime
• 4289 – highly cototient number
• 4290 – pronic number

4300 to 4399

• 4320 – largely composite number
• 4324 – 23rd square pyramidal number
• 4325 – centered square number
• 4339 – super-prime, twin prime
• 4349 – Sophie Germain prime
• 4351 – Normalized total height of all rooted trees on 6 labeled nodes
• 4356 = 662, sum of the cubes of the first eleven integers
• 4357 – prime of the form 2p-1
• 4359 – perfect totient number
• 4369 – seventh super-Poulet number
• 4371 – triangular number
• 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)
• 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, balanced prime, 600th prime number
• 4410 – member of the Padovan sequence
• 4411 – centered heptagonal number
• 4421 – super-prime, alternating factorial
• 4422 – pronic number
• 4425 = 15 + 25 + 35 + 45 + 55
• 4438 – sum of the first 47 primes
• 4444 - repdigit
• 4446 – nonagonal number
• 4447 – cuban prime of the form x = y + 1
• 4457 – balanced prime
• 4463 – super-prime
• 4465 – triangular number
• 4481 – Sophie Germain prime
• 4489 = 672, centered octagonal number
• 4495 – tetrahedral number

4500 to 4599

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

4600 to 4699

• 4604 – sum of the only two known Wieferich primes, 1093 and 3511
• 4607 – Woodall number
• 4608 – 3-smooth number (29×32)
• 4619 – highly cototient number
• 4620 – largely composite number
• 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
• 4657 – balanced prime
• 4661 – sum of the first 48 primes
• 4663 – super-prime, centered heptagonal number
• 4679 – safe prime
• 4680 – largely composite number
• 4681 – eighth super-Poulet number
• 4688 – 2-automorphic number
• 4689 – sum of divisors and number of divisors are both triangular numbers
• 4691 – balanced prime
• 4692 – pronic number
• 4699 – nonagonal number

4700 to 4799

• 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
• 4759 – super-prime
• 4761 = 692, centered octagonal number
• 4769 = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1
• 4787 – safe prime, super-prime
• 4788 – 14th Keith number
• 4793 – Sophie Germain prime
• 4795 – decagonal number
• 4799 – safe prime

4800 to 4899

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

4900 to 4999

• 4900 = 702, the only square-pyramidal square other than 1 (http://mathworld.wolfram.com/CannonballProblem.html)
• 4901 – centered square number
• 4913 = 173
• 4919 – Sophie Germain prime, safe prime
• 4922 – centered heptagonal number
• 4933 – super-prime
• 4941 – centered cube number
• 4943 – Sophie Germain prime, super-prime
• 4950 – triangular number, 12th Kaprekar number
• 4951 – centered pentagonal number
• 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
• 4959 – nonagonal number
• 4960 – tetrahedral number; greater of fourth pair of Smith brothers
• 4970 – pronic number
• 4973 – the 666th prime
• 4991 – Lucas–Carmichael number
• 4993 – balanced prime
• 4999 – prime of the form 2n^2-1

Prime numbers

There are 119 prime numbers between 4000 and 5000: :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

References

1. {{Cite OEIS. A001107. 10-gonal (or decagonal) numbers
2. {{Cite OEIS. A000217
3. {{Cite OEIS. A006562. Balanced primes
4. {{Cite OEIS. A006037. Weird numbers
5. {{Cite OEIS. A002378
6. {{Cite OEIS. A050217. Super-Poulet numbers
7. {{Cite OEIS. A001262. Strong pseudoprimes to base 2
8. {{Cite OEIS. A000292. Tetrahedral numbers
9. and odd [[abundant number]];{{Cite OEIS. A005231. Odd abundant numbers
10. {{Cite OEIS. A076046. Ramanujan-Nagell numbers
11. {{Cite OEIS. A019279. Superperfect numbers
12. {{Cite OEIS. A000110. Bell or exponential numbers
13. {{Cite OEIS. A001844. Centered square numbers
14. {{Cite OEIS. A069099. Centered heptagonal numbers
15. {{cite OEIS. A000219
16. {{cite OEIS. A000605
17. {{Cite OEIS. A000045. Fibonacci numbers
18. {{Cite OEIS. A002559. Markoff (or Markov) numbers
19. {{Cite OEIS. A100827. Highly cototient numbers
20. {{Cite OEIS. A001106. 9-gonal (or enneagonal or nonagonal) numbers
21. {{Cite OEIS. A002411. Pentagonal pyramidal numbers
22. {{Cite OEIS. A067128. Ramanujan's largely composite numbers
23. {{Cite OEIS. A000682. Semimeanders
24. {{Cite OEIS. A002407. Cuban primes
25. {{Cite OEIS. A016754
26. {{Cite OEIS. A076980. Leyland numbers
27. {{Cite OEIS. A000330. Square pyramidal numbers
28. {{cite OEIS. A234953. Normalized total height of all rooted trees on n labeled nodes
29. {{Cite OEIS. A082897. Perfect totient numbers
30. {{Cite OEIS. A000931. Padovan sequence
31. {{Cite OEIS. A005165. Alternating factorials
32. {{cite OEIS. A031971
33. {{Cite OEIS. A051015. Zeisel numbers
34. {{Cite OEIS. A005900. Octahedral numbers
35. {{Cite OEIS. A003261. Woodall numbers
36. {{Cite OEIS. A030984
37. {{cite OEIS. A070996. Numbers n whose sum of divisors and number of divisors are both triangular numbers
38. {{cite OEIS. A122400. Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1
39. {{Cite OEIS. A007629. Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)
40. {{Cite OEIS. A002648. A variant of the cuban primes
41. {{Cite OEIS. A000108. Catalan numbers
42. {{Cite OEIS. A006886. Kaprekar numbers
43. {{Cite OEIS. A005898. Centered cube numbers
44. {{Cite OEIS. A066436. Primes of the form 2*n^2 - 1
45. {{Cite OEIS. A038823. Number of primes between n*1000 and (n+1)*1000
46. Stein, William A.. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture".

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