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...	4000 four 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...	4000th four 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	M
Roman numeral (Unicode)	M, m
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...	111110100000
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...	7640
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'...	2394
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...	FA0

Selected numbers in the range 4001–4999

• 4005 – 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...
  
  
• 4007 – 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...
  
  
• 4010 – 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 = 20.
• 4013 – balanced prime
• 4019 – 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...
  
  
• 4028 – sum of the first 45 primes
• 4030 – third weird number
  Weird number
  In number theory, a weird number is a natural number that is abundant but not semiperfect.In other words, the sum of the proper divisors of the number is greater than the number, but no subset of those divisors sums to the number itself.- Examples :The smallest weird number is 70...
  
  
• 4031 – sum of the cubes of the first six primes
• 4032 – pronic number
  Pronic number
  A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...
  
  
• 4033 – sixth super-Poulet number; strong pseudoprime
  Strong pseudoprime
  In number theory, a strong pseudoprime is a composite number that passes a primality test. All primes pass this test, but a small fraction of composites pass as well, making them "false primes"...
  
   in base 2
• 4060 – 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...
  
  
• 4073 – Sophie Germain prime
• 4079 – safe prime
• 4095 – triangular number, the largest one of the form
• 4096 – 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....
  
   ; ; 16th cube
  Cube (arithmetic)
  In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplying by itself three times:...
  
  ; smallest number with exactly 13 divisors; a superperfect number
  Superperfect number
  In mathematics a superperfect number is a positive integer n that satisfies\sigma^2=\sigma=2n\, ,where σ is the divisor function...
  
  
• 4104
  4104 (number)
  4104 is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729, is called the "Ramanujan-Hardy number"....
  
  – (taxicab number
  Taxicab number
  In mathematics, the nth taxicab number, typically denoted Ta or Taxicab, is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways. The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th...
  
  )
• 4127 – safe prime
• 4139 – safe prime
• 4140 – Bell number
  Bell number
  In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it...
  
  
• 4141 – centered square number
  Centered square number
  In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...
  
  
• 4160 – pronic number
• 4166 – 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...
  
  , 7! − 6! − 5! − 4! − 3! − 2! − 1! − 0!
• 4167 – 7! − 6! − 5! − 4! − 3! − 2! − 1!
• 4168 – 7! − 6! − 5! − 4! − 3! − 2!
• 4170 – 7! − 6! − 5! − 4! − 3!
• 4176 – 7! − 6! − 5! − 4!
• 4181 – Fibonacci number
  Fibonacci number
  In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
  
  , 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...
  
  
• 4186 – triangular number
• 4187 – factor of R
  Repunit
  In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler...
  
  ₁₃. Also record number of wickets taken in first-class cricket
  First-class cricket
  First-class cricket is a class of cricket that consists of matches of three or more days' scheduled duration, that are between two sides of eleven players and are officially adjudged first-class by virtue of the standard of the competing teams...
  
   by Wilfred Rhodes
  Wilfred Rhodes
  Wilfred Rhodes was an English professional cricketer who played 58 Test matches for England between 1899 and 1930. In Tests, Rhodes took 127 wickets in and scored 2,325 runs, becoming the first Englishman to complete the double of 1,000 runs and 100 wickets in Test matches...
  
  .
• 4199 – 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...
  
  
• 4200 – nonagonal number, 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....
  
  , 7! − 6! − 5!
• 4210 – 11th semi-meandric number
• 4211 – Sophie Germain prime
• 4219 – cuban prime of the form x = y + 1
• 4223 – Kynea number
• 4225 – , 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...
  
  
• 4227 – sum of the first 46 primes
• 4240 – 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...
  
  
• 4257 – decagonal number
• 4259 – safe prime
• 4271 – Sophie Germain prime
• 4278 – triangular number
• 4283 – safe prime
• 4289 – highly cototient number
• 4290 – pronic number
• 4320 – 7! − 6!
• 4324 – 23rd 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...
  
  
• 4325 – centered square number
• 4349 – Sophie Germain prime
• 4356 – , sum of the cubes of the first eleven integers
• 4359 – 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;...
  
  
• 4369 – seventh super-Poulet number
• 4371 – triangular number
• 4373 – Sophie Germain prime
• 4375 – perfect totient number (the smallest not divisible by 3)
• 4391 – Sophie Germain prime
• 4397 – Year of Comet Hale–Bopp's return, a prime number
• 4400 – the number of missing persons in the sci-fi show The 4400
  The 4400
  The 4400 is a science fiction TV series produced by CBS Paramount Network Television in association with Sky Television, Renegade 83, and American Zoetrope for USA Network. The show was created and written by Scott Peters and René Echevarria, and it stars Joel Gretsch and Jacqueline McKenzie...
  
  
• 4409 – Sophie Germain prime, highly cototient number, balanced prime
• 4411 – centered heptagonal number
• 4421 – alternating factorial
  Alternating factorial
  In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials.This is the same as their sum, with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an...
  
  
• 4422 – pronic number
• 4438 – sum of the first 47 primes
• 4446 – nonagonal number
• 4447 – cuban prime of the form x = y + 1
• 4457 – balanced prime
• 4465 – triangular number
• 4481 – Sophie Germain prime
• 4489 – , centered octagonal number
• 4495 – 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...
  
  
• 4503 – largest number not the sum of four or fewer squares of composites
• 4505 – fifth Zeisel number
• 4513 – centered square number
• 4522 – decagonal number
• 4547 – safe prime
• 4556 – pronic number
• 4560 – triangular number
• 4579 – 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...
  
  
• 4597 – balanced prime
• 4607 – Woodall number
  Woodall number
  In number theory, a Woodall number is any natural number of the formfor some natural number n. The first few Woodall numbers are:Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers...
  
  
• 4619 – highly cototient number
• 4624 –
• 4641 – 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 = 21.
• 4656 – triangular number
• 4657 – balanced prime
• 4661 – sum of the first 48 primes
• 4663 – centered heptagonal number
• 4679 – safe prime
• 4681 – eighth super-Poulet number
• 4691 – balanced prime
• 4692 – pronic number
• 4699 – nonagonal number
• 4703 – safe prime
• 4705 – , centered square number
• 4727 – sum of the squares of the first twelve primes
• 4733 – Sophie Germain prime
• 4753 – triangular number
• 4761 – , centered octagonal number
• 4787 – safe prime
• 4788 – 14th Keith number
• 4793 – Sophie Germain prime
• 4795 – decagonal number
• 4799 – safe prime
• 4801 – cuban prime of the form x = y + 2, smallest prime with a composite sum of digits in base 7
• 4830 – pronic number
• 4851 – triangular number, 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....
  
  
• 4862 – Catalan number
  Catalan number
  In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involvingrecursively defined objects...
  
  
• 4871 – Sophie Germain prime
• 4879 – 11th 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...
  
  
• 4888 – sum of the first 49 primes
• 4900 – , the only square-pyramidal
  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...
  
   square
  Square number
  In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
  
   other than 1http://mathworld.wolfram.com/CannonballProblem.html
• 4901 – centered square number
• 4913 – 17th cube
  Cube (arithmetic)
  In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplying by itself three times:...
  
  
• 4919 – Sophie Germain prime, safe prime
• 4922 – centered heptagonal number
• 4941 – centered cube number
  Centered cube number
  A centered cube number is a centered figurate number that represents a cube. The centered cube number for n is given byn^3 + ^3.The first few centered cube numbers are...
  
  
• 4943 – Sophie Germain prime
• 4950 – triangular number, 12th 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...
  
  
• 4959 – nonagonal number
• 4960 – 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...
  
  ; greater of fourth pair of Smith brothers
  Smith number
  A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...
  
  
• 4970 – pronic number
• 4991 – Lucas–Carmichael number
• 4993 – balanced prime