5000 (number)

Template:Redirect Template:Infobox 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).

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,<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> Sophie Germain prime

• 5040 = 7!, superior highly composite number
• 5041 = 71², centered octagonal number<ref name=":0">{{#invoke:citation/CS1|citation

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• 5050 – triangular number, Kaprekar number,<ref name=":1">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> sum of first 100 integers

• 5051 – Sophie Germain prime
• 5059 – super-prime
• 5076 – decagonal number<ref name=":2">{{#invoke:citation/CS1|citation

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• 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<ref name=":3">{{#invoke:citation/CS1|citation

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• 5113 – balanced prime,<ref name=":3" /> 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<ref name=":4">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5171 – Sophie Germain prime
• 5184 = 72²
• 5186 – φ(5186) = 2592
• 5187 – φ(5187) = 2592
• 5188 – φ(5189) = 2592, centered heptagonal number<ref name=":5">{{#invoke:citation/CS1|citation

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• 5189 – super-prime

5200 to 5299

• 5209 - largest minimal prime in base 6
• 5226 – nonagonal number<ref name=":6">{{#invoke:citation/CS1|citation

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• 5231 – Sophie Germain prime
• 5233 – prime of the form 2p-1
• 5244 = 22² + 23² + … + 29² = 20² + 21² + … + 28²
• 5249 – highly cototient number<ref name=":7">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5253 – triangular number
• 5279 – Sophie Germain prime, twin prime with 5281, 700th prime number
• 5280 is the number of feet in a mile.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> 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:

<math>

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

• 5281 – super-prime, twin prime with 5279
• 5282 - used in various paintings by Thomas Kinkade<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5292 – Kaprekar number<ref name=":1" />

5300 to 5399

• 5303 – Sophie Germain prime, balanced prime<ref name=":3" />
• 5329 = 73², centered octagonal number<ref name=":0" />
• 5333 – Sophie Germain prime
• 5335 – magic constant of n × n normal magic square and n-queens problem for n = 22.
• 5340 – octahedral number<ref>{{#invoke:citation/CS1|citation

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• 5350 - sum of the first 51 primes
• 5356 – triangular number
• 5365 – decagonal number<ref name=":2" />
• 5381 – super-prime
• 5387 – safe prime, balanced prime<ref name=":3" />
• 5392 – Leyland number<ref>{{#invoke:citation/CS1|citation

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• 5393 – balanced prime<ref name=":3" />
• 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<ref>Template:Cite OEIS</ref>
• 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<ref name=":4" />
• 5437 – prime of the form 2p-1
• 5441 – Sophie Germain prime, super-prime
• 5456 – tetrahedral number<ref name=":8">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5459 – highly cototient number<ref name=":7" />
• 5460 – triangular number
• 5461 – super-Poulet number,<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> centered heptagonal number<ref name=":5" />

• 5476 = 74²
• 5483 – safe prime

5500 to 5599

• 5500 – nonagonal number<ref name=":6" />
• 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 number<ref>{{#invoke:citation/CS1|citation

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• 5527 – happy prime
• 5536 – tetranacci number<ref>{{#invoke:citation/CS1|citation

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• 5555 – repdigit
• 5557 – super-prime
• 5563 – balanced prime
• 5564 – amicable number with 5020
• 5565 – triangular number
• 5566 – pentagonal pyramidal number<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5569 – happy prime
• 5571 – perfect totient number<ref>{{#invoke:citation/CS1|citation

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• 5581 – prime of the form 2p-1
• 5589 - sum of the first 52 primes

5600 to 5699

• 5623 – super-prime
• 5625 = 75², centered octagonal number<ref name=":0" />
• 5631 – number of compositions of 15 whose run-lengths are either weakly increasing or weakly decreasing<ref>Template:Cite OEIS</ref>
• 5639 – Sophie Germain prime, safe prime
• 5651 – super-prime
• 5659 – happy prime, completes the eleventh prime quadruplet set
• 5662 – decagonal number<ref name=":2" />
• 5671 – triangular number

5700 to 5799

• 5701 – super-prime, prime of the form 2p-1
• 5711 – Sophie Germain prime
• 5719 – Zeisel number,<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> Lucas–Carmichael number<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

• 5741 – Sophie Germain prime, Pell prime,<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> Markov prime,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> centered heptagonal number<ref name=":5" />

• 5743 = number of signed trees with 9 nodes<ref>Template:Cite OEIS</ref>
• 5749 – super-prime
• 5768 – tribonacci number<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 5776 = 76²
• 5777 – smallest counterexample to the conjecture that all odd numbers are of the form p + 2a²
• 5778 – triangular number
• 5781 – nonagonal number<ref name=":6" />
• 5798 – Motzkin number<ref>{{#invoke:citation/CS1|citation

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5800 to 5899

• 5801 – super-prime
• 5807 – safe prime, balanced prime
• 5830 - sum of the first 53 primes
• 5832 = 18³
• 5842 – member of the Padovan sequence<ref>{{#invoke:citation/CS1|citation

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• 5849 – Sophie Germain prime
• 5869 – super-prime
• 5879 – safe prime, highly cototient number<ref name=":7" />
• 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<ref name=":0" />
• 5939 – safe prime
• 5967 – decagonal number<ref name=":2" />
• 5971 – first composite Wilson number
• 5984 – tetrahedral number<ref name=":8" />
• 5995 – triangular number

Prime numbers

There are 114 prime numbers between 5000 and 6000:<ref>Template:Cite OEIS</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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