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 certain dialects of the English language (i.e. those that do not include the word “and” when writing out 230, 250, 260, 602, and 640).

• 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 number²
• 5050 – triangular number, Kaprekar number,³ sum of first 100 integers
• 5051 – Sophie Germain prime
• 5059 – super-prime
• 5076 – decagonal number⁴
• 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 prime⁵
• 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 + 1⁶
• 5171 – Sophie Germain prime
• 5184 = 72²
• 5186 – φ(5186) = 2592
• 5187 – φ(5187) = 2592
• 5188 – φ(5189) = 2592, centered heptagonal number⁷
• 5189 – super-prime

• 5209 – largest minimal prime in base 6
• 5226 – nonagonal number⁸
• 5231 – Sophie Germain prime
• 5233 – prime of the form 2p-1
• 5244 = 22² + 23² + ... + 29² = 20² + 21² + ... + 28²
• 5249 – highly cototient number⁹
• 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.
  • a number 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 Kinkade¹¹
• 5292 – Kaprekar number³

• 5303 – Sophie Germain prime, balanced prime⁵
• 5329 = 73², centered octagonal number²
• 5333 – Sophie Germain prime
• 5335 – magic constant of n × n normal magic square and n-queens problem for n = 22.
• 5340 – octahedral number¹²
• 5350 - sum of the first 51 primes
• 5356 – triangular number
• 5365 – decagonal number⁴
• 5381 – super-prime
• 5387 – safe prime, balanced prime⁵
• 5392 – Leyland number¹³
• 5393 – balanced prime⁵
• 5399 – Sophie Germain prime, safe prime

• 5402 – number of non-equivalent ways of expressing 1,000,000 as the sum of two prime numbers¹⁴
• 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 + 1⁶
• 5437 – prime of the form 2p-1
• 5441 – Sophie Germain prime, super-prime
• 5456 – tetrahedral number¹⁵
• 5459 – highly cototient number⁹
• 5460 – triangular number
• 5461 – super-Poulet number,¹⁶ centered heptagonal number⁷
• 5476 = 74²
• 5483 – safe prime

• 5500 – nonagonal number⁸
• 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
• 5508 = 18³ – 18²
• 5525 – square pyramidal number¹⁷
• 5527 – happy prime
• 5536 – tetranacci number¹⁸
• 5555 – repdigit
• 5557 – super-prime
• 5563 – balanced prime
• 5564 – amicable number with 5020
• 5565 – triangular number
• 5566 – pentagonal pyramidal number¹⁹
• 5569 – happy prime
• 5571 – perfect totient number²⁰
• 5581 – prime of the form 2p-1
• 5589 - sum of the first 52 primes

• 5623 – super-prime
• 5625 = 75², centered octagonal number²
• 5631 – number of compositions of 15 whose run-lengths are either weakly increasing or weakly decreasing²¹
• 5639 – Sophie Germain prime, safe prime
• 5651 – super-prime
• 5659 – happy prime, completes the eleventh prime quadruplet set
• 5662 – decagonal number⁴
• 5671 – triangular number

• 5701 – super-prime, prime of the form 2p-1
• 5711 – Sophie Germain prime
• 5719 – Zeisel number,²² Lucas–Carmichael number²³
• 5741 – Sophie Germain prime, Pell prime,²⁴ Markov prime,²⁵ centered heptagonal number⁷
• 5743 = number of signed trees with 9 nodes²⁶
• 5749 – super-prime
• 5768 – tribonacci number²⁷
• 5776 = 76²
• 5777 – smallest counterexample to the conjecture that all odd numbers are of the form p + 2a²
• 5778 – triangular number
• 5781 – nonagonal number⁸
• 5798 – Motzkin number²⁸

• 5801 – super-prime
• 5807 – safe prime, balanced prime
• 5830 - sum of the first 53 primes
• 5832 = 18³
• 5842 – member of the Padovan sequence²⁹
• 5849 – Sophie Germain prime
• 5869 – super-prime
• 5879 – safe prime, highly cototient number⁹
• 5886 – triangular number

• 5903 – Sophie Germain prime
• 5913 – sum of the first seven factorials
• 5927 – safe prime
• 5929 = 77², centered octagonal number²
• 5939 – safe prime
• 5967 – decagonal number⁴
• 5971 – first composite Wilson number
• 5984 – tetrahedral number¹⁵
• 5995 – triangular number

There are 114 prime numbers between 5000 and 6000:³⁰³¹

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