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19th Century In Jerusalem
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. Mathematics 19 is the eighth prime number, and forms a sexy prime with 13, a twin prime with 17, and a cousin prime with 23. It is the third full reptend prime, the fifth central trinomial coefficient, and the seventh Mersenne prime exponent. It is also the second Keith number, and more specifically the first Keith prime. * 19 is the maximum number of fourth powers needed to sum up to any natural number, and in the context of Waring's problem, 19 is the fourth value of g(k). * The sum of the squares of the first 19 primes is divisible by 19. *19 is the sixth Heegner number. 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total. * 19 is the third centered triangular number as well as the third centered hexagonal number. : The 19th triangular number is 190, equivalently the sum of the first 19 non-zero integers, that is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonadecimal
There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period By type of notation Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base. Standard positional numeral systems The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation. Non-standard positional numeral systems Bijective numeration Signed-digit representation Negative bases The common names of the negative base numeral systems are formed using the prefix ''nega-'', giving names such as: Complex bases Non-integer bases ''n''-adic number Mixed radix * Factorial number system * Even double factorial number system * Odd double factorial number system * Primorial number system * Fibonorial numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Number
In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factorization. The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–) Stark–Heegner theorem there are precisely nine Heegner numbers: This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated the gap in Heegner's proof was minor. Euler's prime-generating polynomial Euler's prime-generating polynomial n^2 + n + 41, which gives (distinct) primes for ''n'' = 0, ..., 39, is related to the Heegner number 163 = 4 · 41 − 1. Rabinowitz proved that n^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
