5000 (number)

5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is, at the same time, the largest isogrammic numeral, and the smallest number that contains every one of the five vowels (a, e, i, o, u) in the English language.

Look up five thousand in Wiktionary, the free dictionary.

• 5003 – Sophie Germain prime
• 5020 – amicable number with 5564
• 5021 – super-prime, twin prime with 5023
• 5023 – twin prime with 5021
• 5039 – factorial prime,^[1] Sophie Germain prime
• 5040 = 7!, superior highly composite number
• 5041 = 71², centered octagonal number^[2]
• 5050 – triangular number, Kaprekar number,^[3] sum of first 100 integers
• 5051 – Sophie Germain prime
• 5059 – super-prime
• 5076 – decagonal number^[4]
• 5077 – prime of the form 2p-1
• 5081 – Sophie Germain prime
• 5087 – safe prime
• 5099 – safe prime

• 5101 – prime of the form 2p-1
• 5107 – super-prime, balanced prime^[5]
• 5113 – balanced prime,^[5] prime of the form 2p-1
• 5117 – sum of the first 50 primes
• 5151 – triangular number
• 5167 – Leonardo prime, cuban prime of the form x = y + 1^[6]
• 5171 – Sophie Germain prime
• 5184 = 72²
• 5186 – φ(5186) = 2592
• 5187 – φ(5187) = 2592
• 5188 – φ(5189) = 2592, centered heptagonal number^[7]
• 5189 – super-prime

• 5209 - largest minimal prime in base 6
• 5226 – nonagonal number^[8]
• 5231 – Sophie Germain prime
• 5233 – prime of the form 2p-1
• 5244 = 22² + 23² + … + 29² = 20² + 21² + … + 28²
• 5249 – highly cototient number^[9]
• 5253 – triangular number
• 5279 – Sophie Germain prime, twin prime with 5281, 700th prime number
• 5280 is the number of feet in a mile.^[10] 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:

${\displaystyle 5280=-{\sqrt[{3}]{j\left({\scriptstyle {\frac {1}{2}}}\left(1+i{\sqrt {67}}\,\right)\right)}}.}$

• 5281 – super-prime, twin prime with 5279
• 5282 - used in various paintings by Thomas Kinkade^[11]
• 5292 – Kaprekar number^[3]

• 5303 – Sophie Germain prime, balanced prime^[5]
• 5329 = 73², centered octagonal number^[2]
• 5333 – Sophie Germain prime
• 5335 – magic constant of n × n normal magic square and n-queens problem for n = 22.
• 5340 – octahedral number^[12]
• 5356 – triangular number
• 5365 – decagonal number^[4]
• 5381 – super-prime
• 5387 – safe prime, balanced prime^[5]
• 5392 – Leyland number^[13]
• 5393 – balanced prime^[5]
• 5399 – Sophie Germain prime, safe prime

• 5402 – number of non-equivalent ways of expressing 1,000,000 as the sum of two prime numbers^[14]
• 5405 – member of a Ruth–Aaron pair with 5406 (either definition)
• 5406 – member of a Ruth–Aaron pair with 5405 (either definition)
• 5413 – prime of the form 2p-1
• 5419 – Cuban prime of the form x = y + 1^[6]
• 5437 – prime of the form 2p-1
• 5441 – Sophie Germain prime, super-prime
• 5456 – tetrahedral number^[15]
• 5459 – highly cototient number^[9]
• 5460 – triangular number
• 5461 – super-Poulet number,^[16] centered heptagonal number^[7]
• 5476 = 74²
• 5483 – safe prime

• 5500 – nonagonal number^[8]
• 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^[17]
• 5527 – happy prime
• 5536 – tetranacci number^[18]
• 5555 – repdigit
• 5557 – super-prime
• 5563 – balanced prime
• 5564 – amicable number with 5020
• 5565 – triangular number
• 5566 – pentagonal pyramidal number^[19]
• 5569 – happy prime
• 5571 – perfect totient number^[20]
• 5581 – prime of the form 2p-1

• 5623 – super-prime
• 5625 = 75², centered octagonal number^[2]
• 5631 – number of compositions of 15 whose run-lengths are either weakly increasing or weakly decreasing^[21]
• 5639 – Sophie Germain prime, safe prime
• 5651 – super-prime
• 5659 – happy prime, completes the eleventh prime quadruplet set
• 5662 – decagonal number^[4]
• 5671 – triangular number

• 5701 – super-prime, prime of the form 2p-1
• 5711 – Sophie Germain prime
• 5719 – Zeisel number,^[22] Lucas–Carmichael number^[23]
• 5741 – Sophie Germain prime, Pell prime,^[24] Markov prime,^[25] centered heptagonal number^[7]
• 5743 = number of signed trees with 9 nodes^[26]
• 5749 – super-prime
• 5768 – tribonacci number^[27]
• 5776 = 76²
• 5777 – smallest counterexample to the conjecture that all odd numbers are of the form p + 2a²
• 5778 – triangular number
• 5781 – nonagonal number^[8]
• 5798 – Motzkin number^[28]

• 5801 – super-prime
• 5807 – safe prime, balanced prime
• 5832 = 18³
• 5842 – member of the Padovan sequence^[29]
• 5849 – Sophie Germain prime
• 5869 – super-prime
• 5879 – safe prime, highly cototient number^[9]
• 5886 – triangular number

• 5903 – Sophie Germain prime
• 5913 – sum of the first seven factorials
• 5927 – safe prime
• 5929 = 77², centered octagonal number^[2]
• 5939 – safe prime
• 5967 – decagonal number^[4]
• 5971 – first composite Wilson number
• 5984 – tetrahedral number^[15]
• 5995 – triangular number

There are 114 prime numbers between 5000 and 6000:^[30][31]

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