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Quartan Prime
In mathematics, a quartan prime is a prime number of the form ''x''4 + ''y''4 where ''x'' and ''y'' are positive integers. The odd quartan primes are of the form 16''n'' + 1. For example, 17 is the smallest odd quartan prime: 14 + 24 = 1 + 16 = 17. With the exception of 2 (''x'' = ''y'' = 1), one of ''x'' and ''y'' will be odd, and the other will be even. If both are odd or even, the resulting integer will be even, and 2 is the only even prime. The first few quartan primes are : 2, 17, 97, 257, 337, 641, 881 __NOTOC__ Year 881 ( DCCCLXXXI) was a common year starting on Sunday of the Julian calendar. Events By place Europe * February 12 – King Charles the Fat, the third son of the late Louis the German, is crowned as Holy Roman Emper ..., … . See also * Fourth power * Quartic References * Neil Sloane, A Handbook of Integer Sequences', Academic Press, NY, 1973. {{Prime number classes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...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 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 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, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...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; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2 (number)
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. Evolution Arabic digit The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method. The Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was completely vertical, and the digit looked like a dotless closing question mark. Restoring the bottom line to its original horizonta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
17 (number)
17 (seventeen) is the natural number following 16 (number), 16 and preceding 18 (number), 18. It is a prime number. Seventeen is the sum of the first four prime numbers. In mathematics 17 is the seventh prime number, which makes seventeen the fourth super-prime, as seven is itself prime. The next prime is 19 (number), 19, with which it forms a twin prime. It is a cousin prime with 13 (number), 13 and a sexy prime with 11 (number), 11 and 23 (number), 23. It is an emirp, and more specifically a permutable prime with 71 (number), 71, both of which are also supersingular prime (moonshine theory), supersingular primes. Seventeen is the sixth Mersenne prime exponent, yielding 131,071. Seventeen is the only prime number which is the sum of four consecutive primes: 2,3,5,7. Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. Seventeen can be written in the form x^y + y^x and x^y - y^x, and, as such, it is a Leyland ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
97 (number)
97 (ninety-seven) is the natural number following 96 and preceding 98. It is a prime number and the only prime in the nineties. In mathematics 97 is: * the 25th prime number (the largest two-digit prime number in base 10), following 89 and preceding 101. * a Proth prime and a Pierpont prime as it is 3 × 25 + 1. * the eleventh member of the Mian–Chowla sequence. * a self number in base 10, since there is no integer that added to its own digits, adds up to 97. * the smallest odd prime that is not a cluster prime. * the highest two-digit number where the sum of its digits is a square. * the number of primes <= 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all s. However, 9000007 (read as ''nine million seven'') is |
257 (number)
257 (two hundred ndfifty-seven) is the natural number following 256 and preceding 258. In mathematics 257 is a prime number of the form 2^+1, specifically with ''n'' = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime. Analogously, 257 is the third Sierpinski prime of the first kind, of the form n^ + 1 ➜ 4^ + 1 = 257. It is also a balanced prime, an irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number. There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes). In other fields *The years 257 and 257 BC *257 is the country calling code for Burundi. See List of country calling codes. *.257 Roberts, rifle cartridge *There is a Pac-Man themed restaurant called Level 257 located in Schaumburg, Illinois. It is in reference to the kill screen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
337 (number)
300 (three hundred) is the natural number following 299 and preceding 301. Mathematical properties The number 300 is a triangular number and the sum of a pair of twin primes (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is palindromic in 3 consecutive bases: 30010 = 6067 = 4548 = 3639, and also in base 13. Factorization is 30064 + 1 is prime Other fields Three hundred is: * In bowling, a perfect score, achieved by rolling strikes in all ten frames (a total of twelve strikes) * The lowest possible Fair Isaac credit score * Three hundred ft/s is the maximum legal speed of a shot paintball * In the Hebrew Bible, the size of the military force deployed by the Israelite judge Gideon against the Midianites () * According to Islamic tradition, 300 is the number of ancient Israeli king Thalut's soldiers victorious against Goliath's soldiers * According to Herodotus, 300 is the number of ancient Spartan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
641 (number)
600 (six hundred) is the natural number following 599 and preceding 601. Mathematical properties Six hundred is a composite number, an abundant number, a pronic number and a Harshad number. Credit and cars * In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate. * NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race. * The Fiat 600 is a car, the SEAT 600 its Spanish version. Integers from 601 to 699 600s * 601 = prime number, centered pentagonal number * 602 = 2 × 7 × 43, nontotient, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623 * 603 = 32 × 67, Harshad number, Riordan number, area code for New Hampshire * 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) * 605 = 5 × ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
881 (number)
881 (eight hundred ndeighty-one) is the natural number following 880 and preceding 882. 881 is: * the 152nd prime number * a Paid Toll Free telephone number prefix in the USA * the Port of Los Angeles Long Wharf, California State Historic Landmark #881 * In astronomy, NGC 881 is an Sc type galaxy in the constellation Cetus. * A bilingual play on words when text chatting in Mandarin Chinese or bilingually Mandarin Chinese and English. "881" is pronounced ''ba ba yi'' in Mandarin, and thus puns on "bye-bye." Probably an elaboration of the similar pun on "88" (''ba-ba''). See 88 (number). * The international telephone dialing code for the Global Mobile Satellite System The Global Mobile Satellite System (GMSS) consists of several satellite phone providers serving private customers. It can be compared to PLMN ( wireless telephony carriers) and PSTN (traditional wire-based telephony). As of 2008, ranges of numbers ... * A musical comedy-drama film. References {{DEFAULTSORT:881 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourth Power
In arithmetic and algebra, the fourth power of a number ''n'' is the result of multiplying four instances of ''n'' together. So: :''n''4 = ''n'' × ''n'' × ''n'' × ''n'' Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. The sequence of fourth powers of integers (also known as biquadrates or tesseractic numbers) is: :0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736, 28561, 38416, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000, ... . Properties The last digit of a fourth power in decimal can only be 0 (in fact 0000), 1, 5 (in fact 0625), or 6. Every positive integer can be expressed as the sum of at most 19 fourth powers; every integer larger than 13792 can be expressed as the sum of at most 16 fourth powers (see Waring's problem). Fermat knew that a fourth power cannot be the sum of two other fourth powers (the ''n'' = 4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
