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251 (number)
251 (two hundred ndfifty-one) is the natural number between 250 and 252. It is also a prime number. In mathematics 251 is: *a Sophie Germain prime. *the sum of three consecutive primes (79 + 83 + 89) and seven consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47). *a Chen prime. *an Eisenstein prime with no imaginary part. *a de Polignac number, meaning that it is odd and cannot be formed by adding a power of two to a prime number. *the smallest number that can be formed in more than one way by summing three positive cubes:251 = 2^3 + 3^3 + 6^3 = 1^3 + 5^3 + 5^3. Every 5 × 5 matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ... has exactly 251 square submatrices. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
250 (number)
250 (two hundred ndfifty) is the natural number following 249 and preceding 251. In mathematics 250 is a 5-smooth number, meaning that its divisors are all less than or equal to 5. In other fields * In Chinese slang, the number 250 means 'idiot' (spelled as èr bái wǔ/ㄦˋ ㄅㄞˇ ㄨˇ). The Gulfstream G280 was originally the G250, and was renamed for this reason. * The 250th anniversary is considered important in western culture; see United States Semiquincentennial The United States Semiquincentennial, also called the Bisesquicentennial, the Sestercentennial, America250 or the Quarter Millennium, will be the 250th anniversary of the United States Declaration of Independence. Festivities will mark various e .... References Integers {{Number-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
252 (number)
252 (two hundred ndfifty-two) is the natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ... following 251 and preceding 253. In mathematics 252 is: *the central binomial coefficient \tbinom, the largest one divisible by all coefficients in the previous line *\tau(3), where \tau is the Ramanujan tau function. *\sigma_3(6), where \sigma_3 is the function that sums the cubes of the divisors of its argument: :1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252. *a practical number, *a refactorable number, *a hexagonal pyramidal number. *a member of the Mian-Chowla sequence. There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice, 252 ways of writing the number 4 as a sum of six squares of integers, 252 ways of choosing four squa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of 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, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. 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 factorization, 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 primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophie Germain Prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat’s Last Theorem was to let ''p'' be a prime number of the form 8''k'' + 7 and to let ''n'' = ''p'' – 1. In this case, x^n + y^n = z^n is unsolvable. Germain’s proof, however, remained unfinished. Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Prime
In mathematics, a prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime. The first few Chen primes are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, … . The first few Chen primes that are not the lower member of a pair of twin primes are :2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, ... . The first few non-Chen primes are :43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, … . All of the supersingular primes are Chen primes. Rudolf Ondrejka discovered the following 3 × 3 m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eisenstein Prime
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form : z = a + b\omega , where and are integers and : \omega = \frac = e^ is a primitive (hence non-real) cube root of unity. The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex plane. The Eisenstein integers are a countably infinite set. Properties The Eisenstein integers form a commutative ring of algebraic integers in the algebraic number field – the third cyclotomic field. To see that the Eisenstein integers are algebraic integers note that each is a root of the monic polynomial : z^2 - (2a - b)\;\!z + \left(a^2 - ab + b^2\right)~. In particular, satisfies the equation : \omega^2 + \omega + 1 = 0~. The product of two Eisenstein integers and is given explicitly by : (a + b\;\!\omega) \;\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riesel Number
In mathematics, a Riesel number is an odd natural number ''k'' for which k\times2^n-1 is composite for all natural numbers ''n'' . In other words, when ''k'' is a Riesel number, all members of the following set are composite: :\left\. If the form is instead k\times2^n+1, then ''k'' is a Sierpiński number. Riesel problem In 1956, Hans Riesel showed that there are an infinite number of integers ''k'' such that k\times2^n-1 is not prime for any integer ''n''. He showed that the number 509203 has this property, as does 509203 plus any positive integer multiple of 11184810. The Riesel problem consists in determining the smallest Riesel number. Because no covering set has been found for any ''k'' less than 509203, it is conjectured to be the smallest Riesel number. To check if there are ''k'' ''k'') :2, 3, 3, 39, 4, 4, 4, 5, 6, 5, 5, 6, 5, 5, 5, 7, 6, 6, 11, 7, 6, 29, 6, 6, 7, 6, 6, 7, 6, 6, 6, 8, 8, 7, 7, 10, 9, 7, 8, 9, 7, 8, 7, 7, 8, 7, 8, 10, 7, 7, 26, 9, 7, 8, 7, 7, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hierarchy, is exactly equal to H_(1). Powers of two with Sign (mathematics)#Terminology for signs, non-negative exponents are integers: , , and is two multiplication, multiplied by itself times. The first ten powers of 2 for non-negative values of are: :1, 2, 4, 8, 16 (number), 16, 32 (number), 32, 64 (number), 64, 128 (number), 128, 256 (number), 256, 512 (number), 512, ... By comparison, powers of two with negative exponents are fractions: for positive integer , is one half multiplied by itself times. Thus the first few negative powers of 2 are , , , , etc. Sometimes these are called ''inverse powers of two'' because each is the multiplicative inverse of a positive power of two. Base of the binary numeral sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Submatrix
In mathematics, a matrix (: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly, or through their use in geometry and numerical analysis. '' Square matr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
