1.
59 (getal)
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59 is the natural number following 58 and preceding 60. Fifty-nine is the 17th smallest prime number, the next is sixty-one, with which it comprises a twin prime. 59 is an prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no part and real part of the form 3n −1. +1 is divisible by 59 but 59 is not one more than a multiple of 15,59 is a Pillai prime and it is also a highly cototient number. There are 59 stellations of the icosahedron,59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13# +1 =2 ×3 ×5 ×7 ×11 ×13 +1 =59 ×509, the duration of Saros series 59 was 1280.1 years, and it contained 72 solar eclipses. The Saros number of the lunar eclipse series began in March,729 BC

2.
60 (getal)
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60 is the natural number following 59 and preceding 61. Being three times 20, it is called three score in older literature. It is a number, with divisors 1,2,3,4,5,6,10,12,15,20,30. Because it is the sum of its divisors, it is a unitary perfect number. Being ten times a number, it is a semiperfect number. It is the smallest number divisible by the numbers 1 to 6 and it is the smallest number with exactly 12 divisors. It is the sum of a pair of twin primes and the sum of four consecutive primes and it is adjacent to two primes. It is the smallest number that is the sum of two odd primes in six ways, the smallest non-solvable group has order 60. There are four Archimedean solids with 60 vertices, the icosahedron, the rhombicosidodecahedron, the snub dodecahedron. The skeletons of these polyhedra form 60-node vertex-transitive graphs, there are also two Archimedean solids with 60 edges, the snub cube and the icosidodecahedron. The skeleton of the forms a 60-edge symmetric graph. There are 60 one-sided hexominoes, the polyominoes made from six squares, in geometry, it is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the three angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees. Because it is divisible by the sum of its digits in base 10, a number system with base 60 is called sexagesimal. It is the smallest positive integer that is written only the smallest. The first fullerene to be discovered was buckminsterfullerene C60, an allotrope of carbon with 60 atoms in each molecule and this ball is known as a buckyball, and looks like a soccer ball. The atomic number of neodymium is 60, and cobalt-60 is an isotope of cobalt. The electrical utility frequency in western Japan, South Korea, Taiwan, the Philippines, Saudi Arabia, the United States, and several other countries in the Americas is 60 Hz

3.
64 (getal)
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64 is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube of 4, and it is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime,64 is the sum of Eulers totient function for the first fourteen integers. It is also a number and a centered triangular number. 64 is also the first whole number that is both a square and a perfect cube. Since it is possible to find sequences of 64 consecutive integers such that each member shares a factor with either the first or the last member,64 is an Erdős–Woods number. In base 10, no integer added up to its own digits yields 64,64 is a superperfect number—a number such that σ = 2n. The New General Catalogue object NGC64, a spiral galaxy in the constellation Cetus. The Saros number of the solar eclipse series began on -832 April 11. The duration of Saros series 64 was 1262.1 years, the Saros number of the lunar eclipse series which began on -801 August 9 and ended on 714 February. The duration of Saros series 64 was 1514.5 years, route 64, a highway from Arizona to North Carolina The subject of the Beatles song When Im Sixty-Four The registry of the U. S. They include, singing, dancing, painting, poetry, playing cards, making arguments, making flower garlands, the number of the French department Pyrénées-Atlantiques The number of crayons in the popular Crayola 64 pack Base 64 is used for example with Base64 encoding. Maximum stack size in the video game Minecraft, in non-command situations,64 is a character in the Donald Duck comics universe. Number of codons in the RNA codon table under genetic code, number of golden disks in the myth of the Tower of Hanoi. A number referring to Tiananmen Square protests of 1989 in Chinese 64 is the title of a song by the hip-hop group Mellowhype from their album Blackenedwhite The 64,000 Dollar Question

4.
66 (getal)
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66 is the natural number following 65 and preceding 67. Usages of this include,66 is, a sphenic number. A semiperfect number, being a multiple of a perfect number, an Erdős–Woods number, since it is possible to find sequences of 66 consecutive integers such that each inner member shares a factor with either the first or the last member. Palindromic and a repdigit in bases 10,21 and 32 a Harshad number in bases 2,4,5,6,7,8,11,12,13 and 16. Messier object Spiral Galaxy M66, a magnitude 10.0 galaxy in the constellation Leo, the New General Catalogue object NGC66, a peculiar barred spiral galaxy in the constellation Cetus. The Saros number of the solar eclipse series began on 12 March -756. The duration of Saros series 66 was 1298.1 years, the Saros number of the lunar eclipse series which began on 12 August -671 and ended on 27 January 826. The duration of Saros series 66 was 1496.5 years, the atomic number of dysprosium, a lanthanide. 66 megahertz is a common divisor for the front side bus speed, overall central processing unit speed, and base bus speed. On a Core 2 CPU, and a Core 2 motherboard, the FSB is 1066 MHz, the speed is usually 666.67 MHz. The designation of the historic U. S. Route 66, the designation of US Interstate 66, a freeway that runs from Virginia to Washington, D. C. The designation of 36 US state and 2 territorial highways, phillips 66, a brand of gasoline and service station in the United States. The total number of chapters in the Bible book of Isaiah, the number of verses in Chapter 3 of the book of Lamentations in the Old Testament. The total number of books in the Protestant edition of the Bible combined, in Abjad numerals, The Name Of Allah numeric value is 66. The Green Bay Packers of the National Football League retired jersey number 66 for linebacker Ray Nitschke, the last Packer to wear number 66 before it was retired in 1983 to honor Nitschke was offensive tackle Larry Pfohl, who is better known to professional wrestling fans as Lex Luger. Jersey number 66 was retired by the Pittsburgh Penguins of the National Hockey League in honor of Mario Lemieux, sixty Six is a 2006 British movie about a bar mitzvah in London on the day of the 1966 World Cup final. In the Star Wars movie series, Order 66 is an order to the clone troopers to kill the Jedi commanding them. Route 66 was a popular US television series on CBS from 1960 to 1964, in the video game Fullmetal Alchemist, elusive villain Barry the Chopper is imprisoned in cell number 66, which later becomes his alias when battling the brothers at Laboratory Five

5.
68 (getal)
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68 is the natural number following 67 and preceding 69. It is the largest known number to be the sum of two primes in exactly two different ways,68 =7 +61 =31 +37, because of the factorization of 68 as 22 ×, a 68-sided regular polygon may be constructed with compass and straightedge. The largest graceful graph on 13 nodes has exactly 68 edges, størmers theorem proves that, for every number p, there are a finite number of pairs of consecutive numbers that are both p-smooth. For p =13 this finite number is exactly 68, on an infinite chessboard, there are 68 squares three knights moves away from any cell. As a decimal number,68 is the last two-digit number to appear in the digits of pi. It is a number, meaning that repeatedly summing the squares of its digits eventually leads to 1,68 →62 +82 =100 →12 +02 +02 =1. 68 is the number of erbium, a lanthanide In the restaurant industry,68 may be used as a code meaning put back on the menu. 68 may also be used as slang for sex, based on a play on words involving the number 69

6.
Natuurlijk getal
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory

7.
Geheel getal
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain

8.
Ordinaalgetal
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In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another. Any finite collection of objects can be put in order just by the process of counting, labeling the objects with distinct whole numbers, Ordinal numbers are thus the labels needed to arrange collections of objects in order. An ordinal number is used to describe the type of a well ordered set. Whereas ordinals are useful for ordering the objects in a collection, they are distinct from cardinal numbers, although the distinction between ordinals and cardinals is not always apparent in finite sets, different infinite ordinals can describe the same cardinal. Like other kinds of numbers, ordinals can be added, multiplied, a natural number can be used for two purposes, to describe the size of a set, or to describe the position of an element in a sequence. When restricted to finite sets these two concepts coincide, there is one way to put a finite set into a linear sequence. This is because any set has only one size, there are many nonisomorphic well-orderings of any infinite set. Whereas the notion of number is associated with a set with no particular structure on it. A well-ordered set is an ordered set in which there is no infinite decreasing sequence, equivalently. Ordinals may be used to label the elements of any given well-ordered set and this length is called the order type of the set. Any ordinal is defined by the set of ordinals that precede it, in fact, the most common definition of ordinals identifies each ordinal as the set of ordinals that precede it. For example, the ordinal 42 is the type of the ordinals less than it, i. e. the ordinals from 0 to 41. Conversely, any set of ordinals that is downward-closed—meaning that for any ordinal α in S and any ordinal β < α, β is also in S—is an ordinal. There are infinite ordinals as well, the smallest infinite ordinal is ω, which is the type of the natural numbers. After all of these come ω·2, ω·2+1, ω·2+2, and so on, then ω·3, now the set of ordinals formed in this way must itself have an ordinal associated with it, and that is ω2. Further on, there will be ω3, then ω4, and so on, and ωω, then ωωω, then later ωωωω and this can be continued indefinitely far. The smallest uncountable ordinal is the set of all countable ordinals, in a well-ordered set, every non-empty subset contains a distinct smallest element. Given the axiom of dependent choice, this is equivalent to just saying that the set is ordered and there is no infinite decreasing sequence

9.
Priemfactor
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In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of an integer is a list of the integers prime factors, together with their multiplicities. The fundamental theorem of arithmetic says that every integer has a single unique prime factorization. To shorten prime factorizations, factors are expressed in powers. For example,360 =2 ×2 ×2 ×3 ×3 ×5 =23 ×32 ×5, in which the factors 2,3 and 5 have multiplicities of 3,2 and 1, respectively. For a prime factor p of n, the multiplicity of p is the largest exponent a for which pa divides n exactly. For a positive n, the number of prime factors of n. Perfect square numbers can be recognized by the fact all of their prime factors have even multiplicities. For example, the number 144 has the prime factors 144 =2 ×2 ×2 ×2 ×3 ×3 =24 ×32. These can be rearranged to make the more visible,144 =2 ×2 ×2 ×2 ×3 ×3 = × =2 =2. Because every prime factor appears a number of times, the original number can be expressed as the square of some smaller number. In the same way, perfect cube numbers will have prime factors whose multiplicities are multiples of three, and so on, positive integers with no prime factors in common are said to be coprime. Two integers a and b can also be defined as if their greatest common divisor gcd =1. Euclids algorithm can be used to determine whether two integers are coprime without knowing their prime factors, the runs in a time that is polynomial in the number of digits involved. The integer 1 is coprime to every integer, including itself. This is because it has no prime factors, it is the empty product and this implies that gcd =1 for any b ≥1. The function, ω, represents the number of prime factors of n, while the function, Ω. If n = ∏ i =1 ω p i α i, for example,24 =23 ×31, so ω =2 and Ω =3 +1 =4

10.
Deler
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number