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66 (number)
66 (sixty-six) is the natural number following 65 and preceding 67. In mathematics 66 is a sphenic number, a semiperfect number, and a Erdős–Woods number. It is also the 11th triangular number and the 6th hexagonal number. In computing 66 (more specifically 66.667) megahertz (MHz) is a common divisor for the front side bus (FSB) speed, overall central processing unit (CPU) speed, and base bus speed. On a Core 2 CPU, and a Core 2 motherboard A motherboard, also called a mainboard, a system board, a logic board, and informally a mobo (see #Nomenclature, "Nomenclature" section), is the main printed circuit board (PCB) in general-purpose computers and other expandable systems. It ho ..., the FSB is 1066 MHz (~16 × 66 MHz), the memory speed is usually 666.67 MHz (~10 × 66 MHz), and the processor speed ranges from 1.86 gigahertz (GHz) (~66 MHz × 28) to 2.93 GHz (~66 MHz × 44), in 266 MHz (~66 MHz × 4) increments. In mot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
65 (number)
65 (sixty-five) is the natural number following 64 and preceding 66. In mathematics 65 is the nineteenth distinct semiprime, (5.13); and the third of the form (5.q), where q is a higher prime. 65 has a prime aliquot sum of 19 within an aliquot sequence of one composite numbers (65, 19, 1,0) to the prime; as the first member' of the 19-aliquot tree. It is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0. This number is the magic constant of a 5x5 normal magic square: \begin 17 & 24 & 1 & 8 & 15 \\ 23 & 5 & 7 & 14 & 16 \\ 4 & 6 & 13 & 20 & 22 \\ 10 & 12 & 19 & 21 & 3 \\ 11 & 18 & 25 & 2 & 9 \end. This number is also the magic constant of n-Queens Problem for n = 5. 65 is the smallest integer that can be expressed as a sum of two distinct positive squares in two (or more) ways, 65 = 82 + 12 = 72 + 42. It appears in the Padovan sequence, preceded by the terms 28, 37, 49 (it is the sum of the first two of these). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
67 (number)
67 (sixty-seven) is the natural number following 66 (number), 66 and preceding 68 (number), 68. It is an Parity (mathematics), odd and prime number. In mathematics 67 is: *the 19th prime number (the next is 71 (number), 71). * a Chen prime. *an irregular prime. *a lucky prime. *the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). *a Heegner number. *a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. *palindromic in quinary (2325) and senary (1516). *a super-prime. (19 is prime) *an Twin prime#Isolated prime, isolated prime. (65 and 69 are not prime) *a sexy prime with 61 and 73 References External links Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphenic Number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definition A sphenic number is a product ''pqr'' where ''p'', ''q'', and ''r'' are three distinct prime numbers. In other words, the sphenic numbers are the square-free 3- almost primes. Examples The smallest sphenic number is 30 = 2 × 3 × 5, the product of the smallest three primes. The first few sphenic numbers are : 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, ... The largest known sphenic number at any time can be obtained by multiplying together the three largest known primes. Divisors All sphenic numbers have exactly eight divisors. If we express the sphenic number as n = p \cdot q \cdot r, where ''p'', ''q'', and ''r'' are distinct primes, then the set of divisors of ''n'' will be: :\left\. The converse does not hold. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiperfect Number
In number theory, a semiperfect number or pseudoperfect number is a natural number ''n'' that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. The first few semiperfect numbers are: 6, 12, 18, 20, 24, 28, 30, 36, 40, ... Properties * Every multiple of a semiperfect number is semiperfect. A semiperfect number that is not divisible by any smaller semiperfect number is called ''primitive''. * Every number of the form 2''m''''p'' for a natural number ''m'' and an odd prime number ''p'' such that ''p'' < 2''m''+1 is also semiperfect. ** In particular, every number of the form 2''m''(2''m''+1 − 1) is semiperfect, and indeed perfect if 2''m''+1 − 1 is a . * The sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Woods Number
In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property: there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common factor with one of the endpoints. In other words, is an Erdős–Woods number if there exists a positive integer such that for each integer between and , at least one of the greatest common divisors or is greater than . Examples 16 is an Erdős–Woods number because the 15 numbers between 2184 and each share a prime factor with one of and These 15 numbers and their shared prime factor(s) are: The first Erdős–Woods numbers are Although all of these initial numbers are even, odd Erdős–Woods numbers also exist. They include Prime partitions The Erdős–Woods numbers can be characterized in terms of certain partitions of the prime numbers. A number is an Erdős–Woods number if and only if the prime numbers less than c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in the triangular arrangement with dots on each side, and is equal to the sum of the natural numbers from 1 to . The first 100 terms sequence of triangular numbers, starting with the 0th triangular number, are Formula The triangular numbers are given by the following explicit formulas: where \textstyle is notation for a binomial coefficient. It represents the number of distinct pairs that can be selected from objects, and it is read aloud as " plus one choose two". The fact that the nth triangular number equals n(n+1)/2 can be illustrated using a visual proof. For every triangular number T_n, imagine a "half-rectangle" arrangement of objects corresponding to the triangular number, as in the figure below. Copying this arrangement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Number
A hexagonal number is a figurate number. The ''n''th hexagonal number ''h''''n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex (geometry), vertex. The formula for the ''n''th hexagonal number :h_n= 2n^2-n = n(2n-1) = \frac. The first few hexagonal numbers are: :1 (number), 1, 6 (number), 6, 15 (number), 15, 28 (number), 28, 45 (number), 45, 66 (number), 66, 91 (number), 91, 120 (number), 120, 153 (number), 153, 190 (number), 190, 231 (number), 231, 276 (number), 276, 325 (number), 325, 378, 435, 496 (number), 496, 561 (number), 561, 630, 703, 780, 861, 946... Every hexagonal number is a triangular number, but only every ''other'' triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Front Side Bus
The front-side bus (FSB) is a computer communication interface (bus) that was often used in Intel-chip-based computers during the 1990s and 2000s. The EV6 bus served the same function for competing AMD CPUs. Both typically carry data between the central processing unit (CPU) and a memory controller hub, known as the northbridge. Depending on the implementation, some computers may also have a back-side bus that connects the CPU to the cache. This bus and the cache connected to it are faster than accessing the system memory (or RAM) via the front-side bus. The speed of the front side bus is often used as an important measure of the performance of a computer. The original front-side bus architecture was replaced by HyperTransport, Intel QuickPath Interconnect, and Direct Media Interface, followed by Intel Ultra Path Interconnect and AMD's Infinity Fabric. History The term came into use by Intel Corporation about the time the Pentium Pro and Pentium II products were announced, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Processing Unit
A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs). The form, CPU design, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic operation, arithmetic and Bitwise operation, logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the #Fetch, fetching (from memory), #Decode, decoding and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Motherboard
A motherboard, also called a mainboard, a system board, a logic board, and informally a mobo (see #Nomenclature, "Nomenclature" section), is the main printed circuit board (PCB) in general-purpose computers and other expandable systems. It holds and allows communication between many of the crucial electronic components of a system, such as the central processing unit (CPU) and computer memory, memory, and provides connectors for other peripherals. Unlike a backplane, a motherboard usually contains significant sub-systems, such as the CPU, the chipset's input/output and Memory controller, memory controllers, interface (computing), interface connectors, and other components integrated for general use. Nomenclature ''Oxford English Dictionary'' traces the origin of the word ''motherboard'' to 1965, its earliest-found attestation occurring in the magazine ''Electronics (magazine), Electronics''. The term alludes to its importance and size compared to the components attached to i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
