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Full Reptend Prime
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers (2 × 3) that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n displaystyle n , called trial division, tests whether n displaystyle n is a multiple of any integer between 2 and n displaystyle sqrt n
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Prime (other)
A prime is a natural number that has exactly two distinct natural number divisors: 1 and itself. Prime
Prime
or PRIME may also refer to:Contents1 Science and technology 2 Vehicles 3 Film and television 4 People 5 Other uses 6 See alsoScience and technology[edit]PRIME (PLC), a power line communication standard HP Prime, a graphing calculator model Prime
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Abstract Algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory
Category theory
is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects
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Prime Element
In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polynomials. Care should be taken to distinguish prime elements from irreducible elements, a concept which is the same in UFDs but not the same in general.Contents1 Definition 2 Connection with prime ideals 3 Irreducible elements 4 Examples 5 ReferencesDefinition[edit] An element p of a commutative ring R is said to be prime if it is not zero or a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b
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Prime Ideal
In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.[1][2] The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime.Contents1 Prime ideals for commutative rings1.1 Examples 1.2 Non-Examples 1.3 Properties 1.4 Uses2 Prime ideals for noncommutative rings2.1 Examples3 Important facts 4 Connection to maximality 5 References 6 Further readingPrime ideals for commutative rings[edit] An ideal P of a commutative ring R is prime if it has the following two properties:If a and b are two elements of R such that their product ab is an element of P, then a is in P or b is in P, P is not equal to R for the whole ring.This generalizes the following property of prime numbers: if p is a prime number and if p divides
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Cuisenaire Rods
Cuisenaire rods
Cuisenaire rods
are mathematics learning aids for students that provide an enactive, hands-on[1] way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors.[2][3] In the early 1950s, Caleb Gattegno
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Divisor
In mathematics, a divisor of an integer n displaystyle n , also called a factor of n displaystyle n , is an integer m displaystyle m that may be multiplied by some integer to produce n displaystyle n . In this case one says also that n displaystyle n is a multiple of m . displaystyle m
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13 (number)
13 (thirteen /θɜːrˈtiːn/) is the natural number following 12 and preceding 14. In English speech, the numbers 13 and 30 are sometimes confused, as they sound very similar. Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month)
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Public-key Cryptography
Public key cryptography, or asymmetrical cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. This accomplishes two functions: authentication, where the public key verifies that a holder of the paired private key sent the message, and encryption, where only the paired private key holder can decrypt the message encrypted with the public key. In a public key encryption system, any person can encrypt a message using the receiver's public key. That encrypted message can only be decrypted with the receiver's private key. To be practical, the generation of a public and private key -pair must be computationally economical. The strength of a public key cryptography system relies on the computational effort (work factor in cryptography) required to find the private key from its paired public key
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17 (number)
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. In English speech, the numbers 17 and 70 are sometimes confused, as they sound very similar. The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. Seventeen is the sum of the first four prime numbers.Contents1 In mathematics 2 In science 3 In languages3.1 Grammar4 Age 17 5 In culture5.1 Music5.1.1 Bands 5.1.2 Albums 5.1.3 Songs 5.1.4 Other5.2 Film 5.3 Anime and manga 5.4 Games 5.5 Print 5.6 Religion6 In sports 7 In other fields 8 References 9 External linksIn mathematics[edit] Seventeen is the seventh prime number
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19 (number)
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. In English speech, the numbers 19 and 90 are sometimes confused, as they sound very similar.Contents1 Mathematics 2 Science 3 Religion3.1 Islam 3.2 Baha'i faith4 Music 5 Literature 6 Games 7 Age 19 8 In sports 9 Other fields 10 References 11 External linksMathematics[edit]19 is a centered triangular number19 is a prime number. 19 is the seventh Mersenne prime
Mersenne prime
exponent.[1] 19 is the maximum number of fourth powers needed to sum up to any natural number. It is the fourth value of g(k). 19 is the lowest prime centered triangular number,[2] a centered hexagonal number[3] and a Heegner number.[4] The only non-trivial normal magic hexagon contains 19 hexagons (the other being 1). Science[edit]The atomic number of potassium. 19 years is very close to 235 lunations
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