4000 (number)

Short description: Natural number

← 3999 4000 4001 →
List of numbers — Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	four thousand
Ordinal	4000th (four thousandth)
Factorization	25 × 53
Greek numeral	,Δ´
Roman numeral	MV, or IV
Unicode symbol(s)	MV, mv, IV, iv
Binary	1111101000002
Ternary	121110113
Quaternary	3322004
Quinary	1120005
Senary	303046
Octal	76408
Duodecimal	239412
Hexadecimal	FA016
Vigesimal	A0020
Base 36	33436

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 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 [math]\displaystyle{ 2^{n} - 1 }[/math].
• 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.
  2×4147_dez = 4972₁₂
  3×4147_dez = 7249₁₂
  4×4147_dez = 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

• 4604 – sum of the only two known Wieferich primes, 1093 and 3511
• 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 ([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 [math]\displaystyle{ 2n^2-1 }[/math]

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