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8,000
8000 (eight thousand) is the natural number following 7000 (number), 7999 and preceding #8001 to 8099, 8001. 8000 is the cube (arithmetic), cube of 20 (number), 20, as well as the sum of four consecutive integers cubed, 113 + 123 + 133 + 143. The fourteen tallest mountains on Earth, which exceed 8000 meters in height, are sometimes referred to as eight-thousanders. Selected numbers in the range 8001–8999 8001 to 8099 * 8001 – triangular number * 8002 – Mertens function zero * 8011 – Mertens function zero, super-prime * 8012 – Mertens function zero * 8017 – Mertens function zero * 8021 – Mertens function zero * 8039 – safe prime * 8059 – super-prime * 8069 – Sophie Germain prime * 8093 – Sophie Germain prime 8100 to 8199 * 8100 = 902 * 8101 – super-prime * 8111 – Sophie Germain prime * 8117 – super-prime, balanced prime * 8119 – octahedral number; 8119/5741 ≈ square root of 2, √2 * 8125 – pentagonal pyramidal number * 8128 (number), 8128 – p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight-thousander
The eight-thousanders are the 14 mountains recognized by the International Mountaineering and Climbing Federation (UIAA) as being more than in height above sea level, and sufficiently independent of neighbouring peaks. There is no precise definition of the criteria used to assess independence, and at times, the UIAA has considered whether the list should be expanded to 20 mountain peaks by including the major satellite peaks of eight-thousanders. All of the eight-thousanders are located in the Himalayas, Himalayan and Karakoram mountain ranges in Asia, and their summits lie in the altitude range known as the death zone. From 1950 to 1964, all 14 eight-thousanders were first summited by Expedition climbing, expedition climbers in the summer (the first to be summited was Annapurna I in 1950, and the last was Shishapangma in 1964), and from 1980 to 2021, all 14 were summited in the winter (the first to be summited in winter being Mount Everest in 1980, and the last being K2 in 2021 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armenian Numerals
Armenian numerals form a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet. There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the ancient Greek numerals and Hebrew numerals. In modern Armenia, the familiar Arabic numerals are used. In contemporary writing, Armenian numerals are used more or less like Roman numerals in modern English, e.g. Գարեգին Բ. means Garegin II and Գ. գլուխ means ''Chapter III'' (as a headline). The final two letters of the Armenian alphabet, "o" (Օ) and "fe" (Ֆ), were added to the Armenian alphabet only after Arabic numerals were already in use, to facilitate transliteration of other languages. Thus, they sometimes have a numerical value assigned to them. Notation As in Hebrew and ancient notation, in Armenian numerals distinct symbols represent multiples of po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect numbers are 6 (number), 6, 28 (number), 28, 496 (number), 496 and 8128 (number), 8128. The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. This definition is ancient, appearing as early as Euclid's Elements, Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby \frac is an even perfect number whenever q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Octagonal Number
A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the odd number, odd square numbers. Thus, the ''n''th odd square number and ''t''th centered octagonal number is given by the formula :O_n=(2n-1)^2 = 4n^2-4n+1 , (2t+1)^2=4t^2+4t+1. The first few centered octagonal numbers are :1 (number), 1, 9 (number), 9, 25 (number), 25, 49 (number), 49, 81 (number), 81, 121 (number), 121, 169 (number), 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089 (number), 1089, 1225 Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number. O_n is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their Permanent (mathematics), permanent. See also * Octagonal number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonagonal Number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical. Specifically, the ''n''th nonagonal number counts the dots in a pattern of ''n'' nested nonagons, all sharing a common corner, where the ''i''th nonagon in the pattern has sides made of ''i'' dots spaced one unit apart from each other. The nonagonal number for ''n'' is given by the formula: :\frac . Nonagonal numbers The first few nonagonal numbers are: :0 (number), 0, 1 (number), 1, 9 (number), 9, 24 (number), 24, 46 (number), 46, 75 (number), 75, 111 (number), 111, 154 (number), 154, 204 (number), 204, 261 (number), 261, 325 (number), 325, 396 (number), 396, 474 (number), 474, 559 (number), 559, 651 (number), 651, 750 (number), 750, 856 (number), 856, 96 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuban Prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''. First series This is the first of these equations: :p = \frac,\ x = y + 1,\ y>0, i.e. the difference between two successive cubes. The first few cuban primes from this equation are : 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227 The formula for a general cuban prime of this kind can be simplified to 3y^2 + 3y + 1. This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal. the largest known has 3,153,105 digits with y = 3^ - 1, found by R. Propper and S. Batalov. Second series The second of these equations is: :p = \frac,\ x = y + 2,\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Heptagonal Number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by the formula :\over2. The first few centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 Centered heptagonal prime A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are :43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... The centered heptagonal twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ... numbers are :43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twin Prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime'' is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved. Properties Usually the pair is not considered to be a pair of twin primes. Since 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Narcissistic Number
In number theory, a narcissistic number 1 F_ : \mathbb \rightarrow \mathbb to be the following: : F_(n) = \sum_^ d_i^k. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and : d_i = \frac is the value of each digit of the number. A natural number n is a narcissistic number if it is a fixed point for F_, which occurs if F_(n) = n. The natural numbers 0 \leq n < b are trivial narcissistic numbers for all , all other narcissistic numbers are nontrivial narcissistic numbers. For example, the number 153 in base is a narcissistic number, because and . A natural number is a sociable narcissistic number if it is a for , where for a positive |
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] |
8192 (number)
8192 is the natural number following 8191 and preceding 8193. 8192 is a 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^ ...: 2^ (2 to the 13th power). Because it is two times a sixth power (8192 = 2 × 46), it is also a Bhaskara twin. That is, 8192 has the property that twice its square is a cube and twice its cube is a square.. In computing * 8192 (213) is the maximum number of fragments for IPv4 datagram. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that should be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
