5000 (number)

5000 (number)
5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic numeral in the English language.
Selected numbers in the range 5001–5999
5001 to 5099
5003 – Sophie Germain prime
5020 – amicable number with 5564
5021 – super-prime, twin prime with 5023
5023 – twin prime with 5021
5039 – factorial prime, Sophie Germain prime
5040 = 7!, superior highly composite number
5041 = 712, centered octagonal number
5050 – triangular number, Kaprekar number, sum of first 100 integers
5051 – Sophie Germain prime
5059 – super-prime
5076 – decagonal number
5081 – Sophie Germain prime
5087 – safe prime
5099 – safe prime
5100 to 5199
5107 – super-prime, balanced prime
5113 – balanced prime
5117 – sum of the first 50 primes
5151 – triangular number
5167 – Leonardo prime, cuban prime of the form x = y + 1
5171 – Sophie Germain prime
5184 = 722
5186 – φ(5186) = 2592
5187 – φ(5187) = 2592
5188 – φ(5189) = 2592, centered heptagonal number
5189 – super-prime
5200 to 5299
5209 - largest minimal prime in base 6
5226 – nonagonal number
5231 – Sophie Germain prime
5244 = 222 + 232 + … + 292 = 202 + 212 + … + 282
5249 – highly cototient number
5253 – triangular number
5279 – Sophie Germain prime, twin prime with 5281, 700th prime number
5280 is the number of feet in a mile. It is divisible by three, yielding 1760 yards per mile and by 16.5, yielding 320 rods per mile. Also, 5280 is connected with both Klein's J-invariant and the Heegner numbers. Specifically:
5281 – super-prime, twin prime with 5279
5282 - used in various paintings by Thomas Kinkade
5292 – Kaprekar number
5300 to 5399
5303 – Sophie Germain prime, balanced prime
5329 = 732, centered octagonal number
5333 – Sophie Germain prime
5335 – magic constant of n × n normal magic square and n-queens problem for n = 22.
5340 – octahedral number
5356 – triangular number
5365 – decagonal number
5381 – super-prime
5387 – safe prime, balanced prime
5392 – Leyland number
5393 – balanced prime
5399 – Sophie Germain prime, safe prime
5400 to 5499
5402 – number of non-equivalent ways of expressing 1,000,000 as the sum of two prime numbers
5405 – member of a Ruth–Aaron pair with 5406 (either definition)
5406 – member of a Ruth–Aaron pair with 5405 (either definition)
5419 – Cuban prime of the form x = y + 1
5441 – Sophie Germain prime, super-prime
5456 – tetrahedral number
5459 – highly cototient number
5460 – triangular number
5461 – super-Poulet number, centered heptagonal number
5476 = 742
5483 – safe prime
5500 to 5599
5500 – nonagonal number
5501 – Sophie Germain prime, twin prime with 5503
5503 – super-prime, twin prime with 5501, cousin prime with 5507
5507 – safe prime, cousin prime with 5503
5525 – square pyramidal number
5527 – happy prime
5536 – tetranacci number
5557 – super-prime
5563 – balanced prime
5564 – amicable number with 5020
5565 – triangular number
5566 – pentagonal pyramidal number
5569 – happy prime
5571 – perfect totient number
5581 – prime of the form 2p-1
5600 to 5699
5623 – super-prime
5625 = 752, centered octagonal number
5631 – number of compositions of 15 whose run-lengths are either weakly increasing or weakly decreasing
5639 – Sophie Germain prime, safe prime
5651 – super-prime
5659 – happy prime, completes the eleventh prime quadruplet set
5662 – decagonal number
5671 – triangular number
5700 to 5799
5701 – super-prime
5711 – Sophie Germain prime
5719 – Zeisel number, Lucas–Carmichael number
5741 – Sophie Germain prime, Pell prime, Markov prime, centered heptagonal number
5749 – super-prime
5768 – tribonacci number
5776 = 762
5777 – smallest counterexample to the conjecture that all odd numbers are of the form p + 2a2
5778 – triangular number
5781 – nonagonal number
5798 – Motzkin number
5800 to 5899
5801 – super-prime
5807 – safe prime, balanced prime
5832 = 183
5842 – member of the Padovan sequence
5849 – Sophie Germain prime
5869 – super-prime
5879 – safe prime, highly cototient number
5886 – triangular number
5900 to 5999
5903 – Sophie Germain prime
5913 – sum of the first seven factorials
5927 – safe prime
5929 = 772, centered octagonal number
5939 – safe prime
5967 – decagonal number
5984 – tetrahedral number
5995 – triangular number
Prime numbers
There are 114 prime numbers between 5000 and 6000:
5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987
References
Integers