5000 (number) explained

Number:	5000
Unicode:	,, ↁ
Lang1:	Armenian
Lang1 Symbol:	Ր

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 everyone of the five vowels (a, e, i, o, u) 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,^[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, 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:

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

• 5281 – super-prime, twin prime with 5279
• 5282 - used in various paintings by Thomas Kinkade^[11]
• 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^[12]
• 5356 – triangular number
• 5365 – decagonal number
• 5381 – super-prime
• 5387 – safe prime, balanced prime
• 5392 – Leyland number^[13]
• 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^[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
• 5437 – prime of the form 2p-1
• 5441 – Sophie Germain prime, super-prime
• 5456 – tetrahedral number^[15]
• 5459 – highly cototient number
• 5460 – triangular number
• 5461 – super-Poulet number,^[16] 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^[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

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^[21]
• 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, 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
• 5743 = number of signed trees with 9 nodes
• 5749 – super-prime
• 5768 – tribonacci number^[26]
• 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^[27]

5800 to 5899

• 5801 – super-prime
• 5807 – safe prime, balanced prime
• 5832 = 18³
• 5842 – member of the Padovan sequence^[28]
• 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
• 5971 – first composite Wilson number
• 5984 – tetrahedral number
• 5995 – triangular number

Prime numbers

There are 114 prime numbers between 5000 and 6000:^[29]

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

Notes and References

1. Web site: Sloane's A088054 : Factorial primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
2. Web site: Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
3. Web site: Sloane's A006886 : Kaprekar numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
4. Web site: Sloane's A001107 : 10-gonal (or decagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
5. Web site: Sloane's A006562 : Balanced primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
6. Web site: Sloane's A002407 : Cuban primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
7. Web site: Sloane's A069099 : Centered heptagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
8. Web site: Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
9. Web site: Sloane's A100827 : Highly cototient numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
10. Web site: Weights and measures. Merriam-Webster. www.merriam-webster.com. 11 March 2021.
11. Web site: My 14-Hour Search for the End of TGI Friday's Endless Appetizers . 18 July 2014 .
12. Web site: Sloane's A005900 : Octahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
13. Web site: Sloane's A076980 : Leyland numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
14. A065577. Number of Goldbach partitions of 10^n. 2023-08-31.
15. Web site: Sloane's A000292 : Tetrahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
16. Web site: Sloane's A050217 : Super-Poulet numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
17. Web site: Sloane's A000330 : Square pyramidal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
18. Web site: Sloane's A000078 : Tetranacci numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
19. Web site: Sloane's A002411 : Pentagonal pyramidal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
20. Web site: Sloane's A082897 : Perfect totient numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
21. 2022-06-02.
22. Web site: Sloane's A051015 : Zeisel numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
23. Web site: Sloane's A006972 : Lucas-Carmichael numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
24. Web site: Sloane's A000129 : Pell numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
25. Web site: Sloane's A002559 : Markoff (or Markov) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
26. Web site: Sloane's A000073 : Tribonacci numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
27. Web site: Sloane's A001006 : Motzkin numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-13.
28. Web site: Sloane's A000931 : Padovan sequence. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-11.
29. Web site: Stein . William A. . William A. Stein . The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture . wstein.org . 10 February 2017 . 6 February 2021.