|
Weakly Prime Number
A delicate prime, digitally delicate prime, or weakly prime number is a prime number where, under a given radix but generally decimal, replacing any one of its digits with any other digit always results in a composite number. Definition A prime number is called a ''digitally delicate prime number'' when, under a given radix but generally decimal, replacing any one of its digits with any other digit always results in a composite number. A weakly prime base-''b'' number with ''n'' digits must produce (b - 1) \times n composite numbers after every digit is individually changed to every other digit. There are infinitely many weakly prime numbers in any base. Furthermore, for any fixed base there is a positive proportion of such primes. History In 1978, Murray S. Klamkin posed the question of whether these numbers existed. Paul Erdős proved that there exists an infinite number of "delicate primes" under any base. In 2007, Jens Kruse Andersen found the 1000-digit weakly prime ( ... [...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] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics". Life and career Family Tao's parents are first-generation immigrants from Hong Kong to Australia.''Wen Wei Po'', Page A4, 24 Au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murray S
Murray may refer to: Businesses * Murray (bicycle company), an American manufacturer of low-cost bicycles * Murrays, an Australian bus company * Murray International Trust, a Scottish investment trust * D. & W. Murray Limited, an Australian wholesale drapery business * John Murray (publishing house), a British publishing house Fictional characters * Murray Monster, a muppet in ''Sesame Street'' *Little Murray Sparkles, a cat in ''Sesame Street'' * Murray (''Monkey Island''), a character in the video game series * Murray (''Sly Cooper''), a character in the video game series *Murray Slaughter, a regular character in ''The Mary Tyler Moore Show'' *Murray, the mascot of the band Dio *Murray, in the 2015 Netflix series '' Richie Rich'' *Murray, a ''Hotel Transylvania'' character *Murray the Cop, in ''Fat Pizza'' *Murray Smith, in ''Swift and Shift Couriers'' People *Murray (surname) *Murray (given name) Places Australia * Division of Murray, federal electoral district in Victo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classes Of Prime Numbers
Class or The Class may refer to: Common uses not otherwise categorized * Class (biology), a taxonomic rank * Class (knowledge representation), a collection of individuals or objects * Class (philosophy), an analytical concept used differently from such group phenomena as "types" or "kinds" * Class (set theory), a collection of sets that can be unambiguously defined by a property that all its members share * Hazard class, a dangerous goods classification * Social class, the hierarchical arrangement of individuals in society, usually defined by wealth and occupation * Working class, can be defined by rank, income or collar Arts, entertainment, and media * "The Class" (song), 1959 Chubby Checker song *Character class in role-playing games and other genres *Class 95 (radio station), a Singaporean radio channel Films * ''Class'' (film), 1983 American film * ''The Class'' (2007 film), 2007 Estonian film * ''The Class'' (2008 film), 2008 film (''Entre les murs'') Television * ''Clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
