4000 (number)

• 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[2]
• 4019 – Sophie Germain prime
• 4027 – super-prime
• 4028 – sum of the first 45 primes
• 4030 – third weird number[3]
• 4031 – sum of the cubes of the first six primes
• 4032 – pronic number
• 4033 – sixth super-Poulet number;[4] strong pseudoprime in base 2[5]
• 4060 – tetrahedral number[6]
• 4073 – Sophie Germain prime
• 4079 – safe prime
• 4091 – super-prime
• 4092 – an occasional glitch in the game The Legend of Zelda: Ocarina of Time causes the Gossip Stones to say this number
• 4095 – triangular number and odd abundant number;[7] number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form ${\displaystyle 2^{n}-1}$.[8]
• 4096 = 64² = 16³ = 8⁴ = 4⁶ = 2¹², the smallest number with exactly 13 divisors, a superperfect number[9]

• 4104 = 2³ + 16³ = 9³ + 15³
• 4127 – safe prime
• 4133 – super-prime
• 4139 – safe prime
• 4140 – Bell number[10]
• 4141 – centered square number[11]
• 4147 – smallest cyclic number in duodecimal represented in base-12 notation as 2497₁₂.
  2×4147_dez = 4972₁₂
  3×4147_dez = 7249₁₂
  4×4147_dez = 9724₁₂
• 4153 – super-prime
• 4160 – pronic number
• 4166 – centered heptagonal number,[12]
• 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14[13]
• 4169 – a number of points of norm n </= n in cubic lattice [14]
• 4177 – prime of the form 2p-1
• 4181 – Fibonacci number,[15] Markov number[16]
• 4186 – triangular number
• 4187 – factor of R₁₃, also the record number of wickets taken in first-class cricket by Wilfred Rhodes.
• 4199 – highly cototient number,[17] product of three consecutive primes

• 4200 – nonagonal number,[18] pentagonal pyramidal number,[19]
• 4210 – 11th semi-meandric number[20]
• 4211 – Sophie Germain prime
• 4213 – Riordan number
• 4217 – super-prime, happy number
• 4219 – cuban prime of the form x = y + 1,[21] centered hexagonal number
• 4225 = 65², centered octagonal number[22]
• 4227 – sum of the first 46 primes
• 4240 – Leyland number[23]
• 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
• 4279 – little Schroeder number
• 4283 – safe prime
• 4289 – highly cototient number[17]
• 4290 – pronic number

• 4324 – 23rd square pyramidal number[24]
• 4325 – centered square number[11]
• 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[25]
• 4369 – seventh super-Poulet number[4]
• 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)[25]
• 4391 – Sophie Germain prime
• 4397 – Year of Comet Hale–Bopp's return, super-prime

• 4400 – the number of missing persons in the sci-fi show The 4400
• 4409 – Sophie Germain prime, highly cototient number,[17] balanced prime,[2] 600th prime number
• 4410 – member of the Padovan sequence[26]
• 4411 – centered heptagonal number[12]
• 4421 – super-prime, alternating factorial[27]
• 4422 – pronic number
• 4425 = 1⁵ + 2⁵ + 3⁵ + 4⁵ + 5⁵[28]
• 4438 – sum of the first 47 primes
• 4446 – nonagonal number[18]
• 4447 – cuban prime of the form x = y + 1[21]
• 4457 – balanced prime[2]
• 4463 – super-prime
• 4465 – triangular number
• 4481 – Sophie Germain prime
• 4489 = 67², centered octagonal number[22]
• 4495 – tetrahedral number[6]

• 4503 – largest number not the sum of four or fewer squares of composites
• 4505 – fifth Zeisel number[29]
• 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
• 4560 – triangular number
• 4567 – super-prime
• 4579 – octahedral number[30]
• 4597 – balanced prime[2]

• 4607 – Woodall number[31]
• 4608 – 3-smooth number (2⁹×3²)
• 4619 – highly cototient number[17]
• 4621 – prime of the form 2p-1
• 4624 = 68²
• 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[2]
• 4661 – sum of the first 48 primes
• 4663 – super-prime, centered heptagonal number[12]
• 4679 – safe prime
• 4681 – eighth super-Poulet number[4]
• 4688 – 2-automorphic number[32]
• 4689 – sum of divisors and number of divisors are both triangular numbers[33]
• 4691 – balanced prime[2]
• 4692 – pronic number
• 4699 – nonagonal number[18]

• 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[22]
• 4769 = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1.[34]
• 4787 – safe prime, super-prime
• 4788 – 14th Keith number[35]
• 4793 – Sophie Germain prime
• 4795 – decagonal number[1]
• 4799 – safe prime

• 4801 – super-prime, cuban prime of the form x = y + 2,[36] 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[19]
• 4862 – Catalan number[37]
• 4871 – Sophie Germain prime
• 4877 – super-prime
• 4879 – 11th Kaprekar number[38]
• 4888 – sum of the first 49 primes

• 4900 = 70², the only square-pyramidal square other than 1 ()
• 4901 – centered square number
• 4913 = 17³
• 4919 – Sophie Germain prime, safe prime
• 4922 – centered heptagonal number[12]
• 4933 – super-prime
• 4941 – centered cube number[39]
• 4943 – Sophie Germain prime, super-prime
• 4950 – triangular number, 12th Kaprekar number[38]
• 4951 – centered pentagonal number
• 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
• 4959 – nonagonal number[18]
• 4960 – tetrahedral number;[6] greater of fourth pair of Smith brothers
• 4970 – pronic number
• 4973 – the 666th prime
• 4991 – Lucas–Carmichael number
• 4993 – balanced prime[2]
• 4999 – prime of the form ${\displaystyle 2n^{2}-1}$[40]

There are 119 prime numbers between 4000 and 5000:[41][42]

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