5000 (number)
Encyclopedia
5000 is the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 4999 and preceding 5001. Five thousand is the largest isogram
Isogram
An isogram is a logological term for a word or phrase without a repeating letter. It is also used by some to mean a word or phrase in which each letter appears the same number of times, not necessarily just once....

mic number in the English language
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

.
Cardinal
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...

5000
five thousand
Ordinal
Ordinal number
In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...

5000th
five thousandth
Factorization
Factorization
In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...

Roman numeral
Roman numeral (Unicode) , ,
Binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

1001110001000
Octal
Octal
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

11610
Duodecimal
Duodecimal
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...

2A88
Hexadecimal
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...

1388


Selected numbers in the range 5001–5999

  • 5003Sophie Germain prime
    Sophie Germain prime
    In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number...

  • 5020amicable number
    Amicable number
    Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. A pair of amicable numbers constitutes an aliquot sequence of period 2...

     with 5564
  • 5039factorial prime
    Factorial prime
    A factorial prime is a prime number that is one less or one more than a factorial . The first few factorial primes are:n! − 1 is prime for :n! + 1 is prime for :...

    , Sophie Germain prime
  • 5040
    5040 (number)
    5040 is a factorial , a highly composite number, a superior highly composite number, a colossally abundant number, and the number of permutations of 4 items out of 10 choices .-Philosophy:...

    – 7!, highly composite number
    Highly composite number
    A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....

  • 5041, centered octagonal number
    Centered octagonal number
    A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers...

  • 5050triangular number
    Triangular number
    A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

    , Kaprekar number
    Kaprekar number
    In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45. The Kaprekar numbers are...

    , sum of first 100 integers
  • 5051 – Sophie Germain prime
  • 5076decagonal number
    Decagonal number
    A decagonal number is a figurate number that represents a decagon. The n-th decagonal number is given by the formulaThe first few decagonal numbers are:...

  • 5081 – Sophie Germain prime
  • 5087safe prime
    Safe prime
    A safe prime is a prime number of the form 2p + 1, where p is also a prime. The first few safe primes are...

  • 5099 – safe prime
  • 5107balanced prime
  • 5113 – balanced prime
  • 5151 – triangular number
  • 5167cuban prime of the form x = y + 1
  • 5171 – Sophie Germain prime
  • 5184
  • 5186 – φ(5186) = 2592
  • 5187 – φ(5187) = 2592
  • 5188 – φ(5189) = 2592, centered heptagonal number
    Centered heptagonal number
    A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers...

  • 5226nonagonal number
  • 5231 – Sophie Germain prime
  • 5244
  • 5249highly cototient number
    Highly cototient number
    In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...

  • 5253 – triangular number
  • 5279 – Sophie Germain prime
  • 5280 is the number of feet in a mile. It is evenly divisible by three, yielding exactly 1760 yard
    Yard
    A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

    s per mile and by 16.5, yielding exactly 320 rods
    Rod (unit)
    The rod is a unit of length equal to 5.5 yards, 5.0292 metres, 16.5 feet, or of a statute mile. A rod is the same length as a perch or a pole. In old English, the term lug is also used.-History:...

     per mile.
  • 5280 is connected with both Klein's J-invariant
    J-invariant
    In mathematics, Klein's j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half-plane of complex numbers.We haveThe modular discriminant \Delta is defined as \Delta=g_2^3-27g_3^2...

     and the Heegner number
    Heegner number
    In number theory, a Heegner number is a square-free positive integer d such that the imaginary quadratic field Q has class number 1...

    s. Specifically
    • 5292 – Kaprekar number
    • 5303 – Sophie Germain prime, balanced prime
    • 5329, centered octagonal number
    • 5333 – Sophie Germain prime
    • 5335magic constant
      Magic constant
      The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....

       of n×n normal magic square
      Magic square
      In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...

       and n-queens problem
      Eight queens puzzle
      The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...

       for n = 22.
    • 5340octahedral number
      Octahedral number
      In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres...

    • 5356 – triangular number
    • 5365 – decagonal number
    • 5387 – safe prime, balanced prime
    • 5392Leyland number
      Leyland number
      In number theory, a Leyland number is a number of the form xy + yx, where x and y are integers greater than 1. The first few Leyland numbers are...

    • 5393 – balanced prime
    • 5399 – Sophie Germain prime, safe prime
    • 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
    • 5456tetrahedral number
      Tetrahedral number
      A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

    • 5459 – highly cototient number
    • 5460 – triangular number
    • 5461super-Poulet number, centered heptagonal number
    • 5476
    • 5483 – safe prime
    • 5500 – nonagonal number
    • 5501 – Sophie Germain prime
    • 5507 – safe prime
    • 5525square pyramidal number
      Square pyramidal number
      In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...

    • 5536 – tetranacci number
    • 5563 – balanced prime
    • 5564 – amicable number with 5020
    • 5565 – triangular number
    • 5566pentagonal pyramidal number
      Pentagonal pyramidal number
      A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base. The nth pentagonal pyramidal number is equal to the sum of the first n pentagonal numbers....

    • 5571perfect totient number
      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, and add together the resulting sequence of numbers;...

    • 5625, centered octagonal number
    • 5639 – Sophie Germain prime, safe prime
    • 5662 – decagonal number
    • 5671 – triangular number
    • 5711 – Sophie Germain prime
    • 5719Zeisel number, Lucas–Carmichael number
    • 5741 – Sophie Germain prime, Pell number
      Pell number
      In mathematics, the Pell numbers are an infinite sequence of integers that have been known since ancient times, the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers...

      , Markov number
      Markov number
      A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equationx^2 + y^2 + z^2 = 3xyz,\,studied by .The first few Markov numbers are...

      , centered heptagonal number
    • 5768 – tribonacci number
    • 5776
    • 5777 – smallest counterexample to the conjecture that all odd numbers are of the form
    • 5778 – triangular number
    • 5781 – nonagonal number
    • 5798Motzkin number
      Motzkin number
      In mathematics, a Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points. The Motzkin numbers have very diverse applications in geometry, combinatorics and number theory...

    • 5807 – safe prime, balanced prime
    • 5832 – 183
    • 5849 – Sophie Germain prime
    • 5879 – safe prime, highly cototient number
    • 5886 – triangular number
    • 5903 – Sophie Germain prime
    • 5913 – sum of the first seven factorials
    • 5927 – safe prime
    • 5929, centered octagonal number
    • 5939 – safe prime
    • 5967 – decagonal number
    • 5984 – tetrahedral number
    • 5995 – triangular number
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