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

• 5003 – Sophie 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...
  
  
• 5020 – amicable 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
• 5039 – factorial 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...
  
  
• 5050 – triangular 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
• 5076 – decagonal 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
• 5087 – safe 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
• 5107 – balanced prime
• 5113 – balanced prime
• 5151 – triangular number
• 5167 – cuban 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...
  
  
• 5226 – nonagonal number
• 5231 – Sophie Germain prime
• 5244 –
• 5249 – highly 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
  • 5335 – magic 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.
  • 5340 – octahedral 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
  • 5392 – Leyland 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
  • 5456 – tetrahedral 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
  • 5461 – super-Poulet number, centered heptagonal number
  • 5476 –
  • 5483 – safe prime
  • 5500 – nonagonal number
  • 5501 – Sophie Germain prime
  • 5507 – safe prime
  • 5525 – square 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
  • 5566 – pentagonal 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....
    
    
  • 5571 – perfect 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
  • 5719 – Zeisel 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
  • 5798 – Motzkin 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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