# 4000 (number)

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 and odd abundant 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 = 64$^2$ = 16$^3$ = 8$^4$ = 4$^6$ = 2$^{12}$, smallest number with exactly 13 factors, a superperfect number

### 4100 to 4199

* 4104 = 2$^3$ + 16$^3$ = 9$^3$ + 15$^3$
* 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 2497$_{12}$ 2×4147$_{dez}$ = 4972$_{12}$ 3×4147$_{dez}$ = 7249$_{12}$ 4×4147$_{dez}$ = 9724$_{12}$
* 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 <= 10 in cubic lattice
* 4177 – prime of the form 2p-1
* 4181 – Fibonacci number, Markov number
* 4186 – triangular number
* 4187 – factor of R$_{13}$, 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 = 65$^2$, 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
* 4356 = 66$^2$, 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 = 1$^5$ + 2$^5$ + 3$^5$ + 4$^5$ + 5$^5$
* 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 = 67$^2$, 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 (2$^9$×3$^2$)
* 4619 – highly cototient number
* 4620 – largely composite number
* 4621 – prime of the form 2p-1
* 4624 = 68$^2$, 17$^3$ – 17$^2$
* 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 = 48$^2$ + 49$^2$ = 17$^2$ + 18$^2$ + … + 26$^2$, 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 = 69$^2$, 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 = 70$^2$, the only square-pyramidal square other than 1
* 4901 – centered square number
* 4913 = 17$^3$
* 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