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,^[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

5100 to 5199

• 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

5200 to 5299

• 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][better source needed]}
• 5292 – Kaprekar number^[3]

5300 to 5399

• 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

5400 to 5499

• 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 to 5599

• 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]
• 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

5600 to 5699

• 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

5700 to 5799

• 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]

5800 to 5899

• 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

5900 to 5999

• 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]
• 5984 – tetrahedral number^[15]
• 5995 – triangular number

Prime numbers

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