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 number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form <math>2^{n} - 1</math>
• 4096 = 64² = 16³ = 8⁴ = 4⁶ = 2¹², smallest number with exactly 13 factors, a superperfect number
• 4098 – the fifth maximum-score busy beaver 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<br />2&times;4147_dez = 4972₁₂<br />3&times;4147_dez = 7249₁₂<br />4&times;4147_dez = 9724₁₂
• 4153 – super-prime
• 4160 – pronic 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 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
• 4324 – 23rd square pyramidal number
• 4325 – centered square number
• 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
• 4411 – centered heptagonal number
• 4422 – pronic number
• 4438 – sum of the first 47 primes
• 4444 - repdigit
• 4446 – nonagonal number
• 4513 – centered square number
• 4516 – centered pentagonal number
• 4517 – super-prime, happy number
• 4522 – decagonal number
• 4597 – balanced prime
• 4608 – 3-smooth number (2⁹×3²)
• 4619 – highly cototient number
• 4621 – prime of the form 2p-1
• 4624 = 68², 17³ – 17²
• 4641 – magic constant of n&nbsp;×&nbsp;n normal magic square and n-queens problem for n = 21
• 4655 – number of free decominoes
• 4656 – triangular number
• 4681 – eighth super-Poulet number
• 4689 – sum of divisors and number of divisors are both triangular numbers
• 4691 – balanced prime
• 4787 – safe prime, super-prime
• 4788 – 14th Keith number
• 4793 – Sophie Germain prime
• 4795 – decagonal number smallest prime with a composite sum of digits in base 7
• 4830 – pronic 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
• 4943 – Sophie Germain prime, super-prime
• 4950 – triangular number,

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