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
4019 – Sophie Germain 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
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, odd abundant number, Mersenne number
4096 – power of two 2¹²; 64²; 16th cube; smallest number with exactly 13 divisors; a superperfect number
4104 – 2³ + 16³ = 9³ + 15³ (taxicab number)
4127 – safe prime
4139 – safe prime
4140 – Bell number
4141 – centered square number
4147 – smallest cyclic number in duodecimal
4160 – pronic number
4166 – centered heptagonal number, 7! − 6! − 5! − 4! − 3! − 2! − 1! − 0!
4167 – 7! − 6! − 5! − 4! − 3! − 2! − 1!
4168 – 7! − 6! − 5! − 4! − 3! − 2!
4170 – 7! − 6! − 5! − 4! − 3!
4176 – 7! − 6! − 5! − 4!
4181 – Fibonacci number, Markov number
4186 – triangular number
4187 – factor of R₁₃. Also record number of wickets taken in first-class cricket by Wilfred Rhodes.
4199 – highly cototient number, product of three consecutive primes
4200 – nonagonal number, pentagonal pyramidal number, 7! − 6! − 5!
4210 – 11th semi-meandric number
4211 – Sophie Germain prime
4219 – cuban prime of the form x = y + 1
4223 – Kynea number
4225 – 65², centered octagonal number
4227 – sum of the first 46 primes
4240 – Leyland number
4257 – decagonal number
4259 – safe prime
4271 – Sophie Germain prime
4278 – triangular number
4283 – safe prime
4289 – highly cototient number
4290 – pronic number
4320 – 7! − 6!
4324 – 23rd square pyramidal number
4325 – centered square number
4349 – Sophie Germain prime
4356 – 66², sum of the cubes of the first eleven integers
4359 – perfect totient number
4369 – seventh super-Poulet number
4371 – triangular number
4373 – Sophie Germain prime
4375 – perfect totient number (the smallest not divisible by 3)
4391 – Sophie Germain prime
4397 – Year of Comet Hale–Bopp's return, a prime number
4400 – the number of missing persons in the sci-fi show The 4400
4409 – Sophie Germain prime, highly cototient number, balanced prime
4411 – centered heptagonal number
4421 – alternating factorial
4422 – pronic number
4438 – sum of the first 47 primes
4446 – nonagonal number
4447 – cuban prime of the form x = y + 1
4457 – balanced prime
4465 – triangular number
4481 – Sophie Germain prime
4489 – 67², centered octagonal number
4495 – tetrahedral number
4503 – largest number not the sum of four or fewer squares of composites
4505 – fifth Zeisel number
4513 – centered square number
4522 – decagonal number
4547 – safe prime
4556 – pronic number
4560 – triangular number
4579 – octahedral number
4597 – balanced prime
4607 – Woodall number
4619 – highly cototient number
4624 – 68²
4641 – magic constant of n × n normal magic square and n-queens problem for n = 21.
4656 – triangular number
4657 – balanced prime
4661 – sum of the first 48 primes
4663 – centered heptagonal number
4679 – safe prime
4681 – eighth super-Poulet number
4691 – balanced prime
4692 – pronic number
4699 – nonagonal number
4703 – safe prime
4705 – 48² + 49² = 17² + 18² + … + 26², centered square number
4727 – sum of the squares of the first twelve primes
4733 – Sophie Germain prime
4753 – triangular number
4761 – 69², centered octagonal number
4787 – safe prime
4788 – 14th Keith number
4793 – Sophie Germain prime
4795 – decagonal number
4799 – safe prime
4801 – cuban prime of the form x = y + 2, smallest prime with a composite sum of digits in base 7
4830 – pronic number
4851 – triangular number, pentagonal pyramidal number
4862 – Catalan number
4871 – Sophie Germain prime
4879 – 11th Kaprekar number
4888 – sum of the first 49 primes
4900 – 70², the only square-pyramidal square other than 1
4901 – centered square number
4913 – 17th cube
4919 – Sophie Germain prime, safe prime
4922 – centered heptagonal number
4941 – centered cube number
4943 – Sophie Germain prime
4950 – triangular number, 12th Kaprekar number
4959 – nonagonal number
4960 – tetrahedral number; greater of fourth pair of Smith brothers
4970 – pronic number
4991 – Lucas–Carmichael number
4993 – balanced prime

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