5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number 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 Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins :3, 5, 11, 17, 31, ...

, twin prime with 5023 * 5023 – twin prime with 5021 * 5039 – factorial prime, Sophie Germain prime * 5040 = 7!,

superior highly composite number In mathematics, a superior highly composite number is a natural number which has the highest ratio of its number of divisors to ''some'' positive power of itself than any other number. It is a stronger restriction than that of a highly composite ...

* 5041 = 71², centered octagonal number * 5050 – triangular number, Kaprekar number, sum of first 100 integers * 5051 – Sophie Germain prime * 5059 –

* 5076 – decagonal number * 5081 – Sophie Germain prime * 5087 – safe prime * 5099 – safe prime

5100 to 5199

* 5107 –

balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...

* 5113 – balanced prime * 5117 – sum of the first 50 primes * 5151 – triangular number * 5167 –

Leonardo prime The Leonardo numbers are a sequence of numbers given by the recurrence: : L(n) = \begin 1 & \mbox n = 0 \\ 1 & \mbox n = 1 \\ L(n - 1) + L(n - 2) + 1 & \mbox n > 1 \\ \end Edsger W ...

, cuban prime of the form ''x'' = ''y'' + 1 * 5171 – Sophie Germain prime * 5184 = 72² * 5186 – φ(5186) = 2592 * 5187 – φ(5187) = 2592 * 5188 – φ(5189) = 2592, centered heptagonal number * 5189 –

5200 to 5299

* 5209 - largest minimal prime in base 6 * 5226 – nonagonal number * 5231 – Sophie Germain prime * 5244 = 22² + 23² + … + 29² = 20² + 21² + … + 28² * 5249 –

highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient fun ...

* 5253 – triangular number * 5279 – Sophie Germain prime, twin prime with 5281, 700th prime number * 5280 is the number of feet in a

mile The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of distance; both are based on the older English unit of length equal to 5,280 English ...

. 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 number In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factoriza ...

s. Specifically: :

5280 = -\sqrt

* 5281 –

, twin prime with 5279 * 5282 - used in various paintings by Thomas Kinkade * 5292 – Kaprekar number

5300 to 5399

* 5303 – Sophie Germain prime, balanced prime * 5329 = 73², centered octagonal number * 5333 – Sophie Germain prime * 5335 –

magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...

of ''n'' × ''n'' normal

magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...

and ''n''-queens problem for ''n'' = 22. * 5340 – octahedral number * 5356 – triangular number * 5365 – decagonal number * 5381 –

* 5387 – safe prime, balanced prime * 5392 – Leyland number * 5393 – balanced prime * 5399 – Sophie Germain prime, safe prime

5400 to 5499

* 5402 – number of ways in which one million can be expressed as the sum of two prime numbers * 5405 – member of a Ruth–Aaron pair with 5406 (either definition) * 5406 – member of a Ruth–Aaron pair with 5405 (either definition) * 5419 – Cuban prime of the form ''x'' = ''y'' + 1 * 5441 – Sophie Germain prime,

* 5456 – tetrahedral number * 5459 – highly cototient number * 5460 – triangular number * 5461 – super-Poulet number, centered heptagonal number * 5476 = 74² * 5483 – safe prime

5500 to 5599

* 5500 – nonagonal number * 5501 – Sophie Germain prime, twin prime with 5503 * 5503 –

, twin prime with 5501, cousin prime with 5507 * 5507 – safe prime, cousin prime with 5503 * 5525 –

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broa ...

* 5527 – happy prime * 5536 –

tetranacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequ ...

* 5557 – super-prime * 5563 – balanced prime * 5564 – amicable number with 5020 * 5565 – triangular number * 5566 – pentagonal pyramidal number * 5569 – happy prime * 5571 –

perfect totient number In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is reached, ...

* 5581 – prime of the form 2p-1

5600 to 5699

* 5623 –

* 5625 = 75², centered octagonal number * 5631 – number of compositions of 15 whose run-lengths are either weakly increasing or weakly decreasing * 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 –

* 5711 – Sophie Germain prime * 5719 – Zeisel number,

Lucas–Carmichael number In mathematics, a Lucas–Carmichael number is a positive composite integer ''n'' such that # if ''p'' is a prime factor of ''n'', then ''p'' + 1 is a factor of ''n'' + 1; # ''n'' is odd and square-free. The first condition resembles the Korselt's ...

* 5741 – Sophie Germain prime,

Pell prime In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , a ...

Markov prime A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are : 1, 2, 5, 13, 29, 34, 89 ...

, centered heptagonal number * 5749 – super-prime * 5768 – tribonacci number * 5776 = 76² * 5777 – smallest counterexample to the conjecture that all odd numbers are of the form ''p'' + 2''a''² * 5778 – triangular number * 5781 – nonagonal number * 5798 – Motzkin number

5800 to 5899

* 5801 –

* 5807 – safe prime, balanced prime * 5832 = 18³ * 5842 – member of the Padovan sequence * 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 * 5984 – tetrahedral number * 5995 – triangular number

Prime numbers

There are 114 prime numbers between 5000 and 6000: :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

References

{{Integers, 10 Integers