5000 (five thousand) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the

English language English is a West Germanic language of the Indo-European language family, with its earliest forms spoken by the inhabitants of early medieval England. It is named after the Angles, one of the ancient Germanic peoples that migrated to the is ...

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 A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

with 5023 * 5023 – twin prime with 5021 * 5039 –

factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! +&n ...

, 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 A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

, 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 A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns inv ...

* 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,

with 5281, 700th prime number * 5280 is the number of

feet The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...

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 William Thomas Kinkade III (January 19, 1958 – April 6, 2012) was an American painter of popular realistic, pastoral, and idyllic subjects. He is notable for achieving success during his lifetime with the mass marketing of his work as ...

* 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 In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, ...

* 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 In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: :714 = 2 × 3 × 7 × 17, :715 = 5 × 11 × 13, and : 2 + 3 + 7 + 17 = 5 + 11 + 13 = ...

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,

with 5503 * 5503 –

, twin prime with 5501,

cousin prime In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences and in OE ...

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 In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...

* 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,

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 In mathematics, the Fibonacci numbers form a sequence defined recursion, 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 Fibo ...

* 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 In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5 ...

* 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 number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s 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