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...	8000 eight 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...	8000th eight 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	MMM
Roman numeral (Unicode)	MMM, mmm
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...	1111101000000
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...	17500
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'...	4768
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...	1F40

Selected numbers in the range 8001–8999

• 8001 – 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...
  
  
• 8002 – Mertens function zero
• 8011 – Mertens function zero
• 8012 – Mertens function zero
• 8017 – Mertens function zero
• 8021 – Mertens function zero
• 8039 – 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...
  
  
• 8069 – 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...
  
  
• 8093 – Sophie Germain prime
• 8100 –
• 8111 – Sophie Germain prime
• 8117 – balanced prime
• 8119 – 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...
  
  
• 8125 – 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....
  
  
• 8128 – perfect number
  Perfect number
  In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...
  
  , harmonic divisor number
  Harmonic divisor number
  In mathematics, a harmonic divisor number, or Ore number , is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are...
  
  , 127th 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...
  
  , 64th hexagonal number
  Hexagonal number
  A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
  
  , eighth 292-gonal number, fourth 1356-gonal number
• 8147 – safe prime
• 8189 – 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...
  
  
• 8190 – harmonic divisor number
• 8191 – Mersenne prime
  Mersenne prime
  In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
  
  
• 8192 – power of two
  Power of two
  In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....
  
  
• 8233 – 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...
  
  
• 8243 – Sophie Germain prime
• 8256 – triangular number
• 8257 – sum of the squares of the first fourteen primes
• 8269 – cuban prime of the form x = y + 1
• 8273 – Sophie Germain prime
• 8281 – , sum of the cubes of the first thirteen integers, nonagonal number, 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...
  
  
• 8321 – super-Poulet number
• 8326 – 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:...
  
  
• 8361 – 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...
  
  
• 8385 – triangular number
• 8423 – safe prime
• 8436 – 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...
  
  
• 8464 –
• 8513 – Sophie Germain prime
• 8515 – triangular number
• 8543 – safe prime
• 8555 – 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...
  
  
• 8576 – centered heptagonal number
• 8625 – enneagonal number
• 8646 – triangular number
• 8649 – , centered octagonal number
• 8663 – Sophie Germain prime
• 8693 – Sophie Germain prime
• 8695 – decagonal number
• 8699 – safe prime
• 8712 – smallest number that is divisible by its reverse: 8712 = 4×2178 (excluding palindromes and numbers with trailing zeros)
• 8713 – balanced prime
• 8741 – Sophie Germain prime
• 8747 – safe prime, balanced prime
• 8751 – 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;...
  
  
• 8778 – triangular number
• 8783 – safe prime
• 8801 – 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 = 26.
• 8819 – safe prime
• 8833 –
• 8836 –
• 8851 – Son G. constant
• 8855 – member of a Ruth-Aaron pair
  Ruth-Aaron pair
  In mathematics, a Ruth–Aaron pair consists of two consecutive integers for which the sums of the prime factors of each integer are equal:andIf only distinct prime factors are counted, the first few Ruth–Aaron pairs are:...
  
   (first definition) with 8856
• 8856 – member of a Ruth-Aaron pair (first definition) with 8855
• 8911 – Carmichael number, triangular number
• 8926 – centered heptagonal number
• 8944 – sum of the cubes of the first seven primes
• 8951 – Sophie Germain prime
• 8963 – safe prime
• 8969 – Sophie Germain prime
• 8976 – enneagonal number