4000 (number)

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
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
4060 – tetrahedral number
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; number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form .
4096 = 642 = 163 = 84 = 46 = 212, the smallest number with exactly 13 divisors, 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 = 4972123×4147dez = 7249124×4147dez = 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 n </= n in cubic lattice
4177 – prime of the form 2p-1
4181 – Fibonacci number, Markov number
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, product of three consecutive primes
4200 to 4299
4200 – nonagonal number, pentagonal pyramidal 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
4324 – 23rd square pyramidal number
4325 – centered square number
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
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
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
4607 – Woodall number
4608 – 3-smooth number (29×32)
4619 – highly cototient number
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
4661 – sum of the first 48 primes
4663 – super-prime, centered heptagonal number
4679 – safe prime
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
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
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
Integers