Selected numbers in the range 4001–4999
4001 to 4099
- 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 [10]
- 4096 = 642 = 163 = 84 = 46 = 212, smallest number with exactly 13 factors, a superperfect number [11]
4100 to 4199
- 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 R 13, 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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 [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 [43]
Prime numbers
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