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Pillai Prime
In number theory, a Pillai prime is a prime number ''p'' for which there is an integer ''n'' > 0 such that the factorial of ''n'' is one less than a multiple of the prime, but the prime is not one more than a multiple of ''n''. To put it algebraically, n! \equiv -1 \mod p but p \not\equiv 1 \mod n. The first few Pillai primes are : 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, ... Pillai primes are named after the mathematician Subbayya Sivasankaranarayana Pillai, who studied these numbers. Their infinitude has been proven several times, by Subbarao, Erdős, and Hardy & Subbarao. References *. *. *https://planetmath.org/pillaiprime, PlanetMath PlanetMath is a free content, free, collaborative, mathematics online encyclopedia. Intended to be comprehensive, the project is currently hosted by the University of Waterloo. The site is owned by a US-based nonprofit corporation, "PlanetMath.org ... Classes of prime numbers Eponymous numbers in mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred [and] thirty-seven) is the natural number following 136 (number), 136 and preceding 138 (number), 138. Mathematics 137 is: * the 33rd prime number; the next is 139 (number), 139, with which it comprises a twin prime, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4n+1, where n=34 (137=4\times 34+1) or the sum of two squares 11^+4^ = (121+16). * a combination of three terms 4^+3^-2^ = (64+81-8), cube of 4 + Triangular number T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link) * a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73 (number), 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classes Of Prime Numbers
Class, Classes, 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'') Telev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PlanetMath
PlanetMath is a free content, free, collaborative, mathematics online encyclopedia. Intended to be comprehensive, the project is currently hosted by the University of Waterloo. The site is owned by a US-based nonprofit corporation, "PlanetMath.org, Ltd". PlanetMath was started when the popular free online mathematics encyclopedia MathWorld was temporarily taken offline for 12 months by a court injunction as a result of the CRC Press lawsuit against the Wolfram Research company and its employee (and MathWorld's author) Eric Weisstein. Materials The main PlanetMath focus is on encyclopedia, encyclopedic entries. It formerly operated a self-hosted forum, but now encourages discussion via Gitter. An all-inclusive PlanetMath ''Free Encyclopedia'' book of 2,300 pages is available for the encyclopedia contents up to 2006 as a free download PDF file. Content development model PlanetMath implements a specific content creation system called ''authority model''. An author who starts a ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The editor-in-chief heads all departments of the organization and is held accoun ... is Vadim Ponomarenko ( San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathukumalli V
Mathukumalli is a village in Savalyapuram mandal of Guntur district in Andhra Pradesh Andhra Pradesh (ISO 15919, ISO: , , AP) is a States and union territories of India, state on the East Coast of India, east coast of southern India. It is the List of states and union territories of India by area, seventh-largest state and th ..., India. References Villages in Guntur district {{Guntur-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subbayya Sivasankaranarayana Pillai
Subbayya Sivasankaranarayana Pillai (5 April 1901 – 31 August 1950) was an Indian mathematician specialising in number theory. His contribution to Waring's problem was described in 1950 by K. S. Chandrasekharan as "almost certainly his best piece of work and one of the very best achievements in Indian Mathematics since Ramanujan". Biography Subbayya Sivasankaranarayana Pillai was born to parents Subbayya Pillai and Gomati Ammal. His mother died a year after his birth and his father when Pillai was in his last year at school. Pillai did his intermediate course and B.Sc. Mathematics in the Scott Christian College at Nagercoil and managed to earn a B.A. degree from Maharaja's college, Trivandrum. In 1927, Pillai was awarded a research fellowship at the University of Madras to work among professors K. Ananda Rau and Ramaswamy S. Vaidyanathaswamy. He was from 1929 to 1941 at Annamalai University where he worked as a lecturer. It was in Annamalai University that he did his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
193 (number)
193 (one hundred ndninety-three) is the natural number following 192 and preceding 194. In mathematics 193 is the number of compositions of 14 into distinct parts. In decimal, it is the seventeenth full repetend prime, or ''long prime''. * It is the only odd prime p known for which 2 is not a primitive root of 4p^2 + 1. * It is the thirteenth Pierpont prime, which implies that a regular 193-gon can be constructed using a compass, straightedge, and angle trisector. * It is part of the fourteenth pair of twin primes (191, 193), the seventh trio of prime triplets (193, 197, 199), and the fourth set of prime quadruplets (191, 193, 197, 199). Aside from itself, the '' friendly giant'' (the largest sporadic group) holds a total of 193 conjugacy classes. It also holds at least 44 maximal subgroups aside from the double cover of \mathbb (the forty-fourth prime number is 193). 193 is also the eighth numerator of convergents to Euler's number; correct to three decimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
149 (number)
149 (one hundred [and] forty-nine) is the natural number between 148 (number), 148 and 150 (number), 150. In mathematics 149 is the 35th prime number, the first prime whose difference from the previous prime is exactly 10, an emirp, and an irregular prime. After 1 and 127, it is the third smallest de Polignac number, an odd number that cannot be represented as a prime plus a power of two. More strongly, after 1, it is the second smallest number that is not a sum of two prime powers. It is a tribonacci number, being the sum of the three preceding terms, 24, 44, 81. There are exactly 149 integer points in a closed circular disk of radius 7, and exactly 149 ways of placing six queens (the maximum possible) on a 5 × 5 chess board so that each queen attacks exactly one other. The barycentric subdivision of a tetrahedron produces an abstract simplicial complex with exactly 149 simplices. References External links {{DEFAULTSORT:149 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
139 (number)
139 (one hundred [and] thirty-nine) is the natural number following 138 (number), 138 and preceding 140 (number), 140. In mathematics 139 is the 34th prime number. It is a twin prime with 137 (number), 137. Because 141 (number), 141 is a semiprime, 139 is a Chen prime. 139 is the smallest prime before a prime gap of length 10. This number is the sum of five consecutive prime numbers (19 (number), 19 + 23 (number), 23 + 29 (number), 29 + 31 (number), 31 + 37 (number), 37). It is the smallest factorization, factor of 64079 (number), 64079 which is the smallest Lucas number with prime index which is not prime. It is also the smallest factor of the first nine terms of the Euclid–Mullin sequence, making it the tenth term. 139 is a happy number and a strictly non-palindromic number. References External links Psalm 139 {{DEFAULTSORT:139 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
109 (number)
109 (one hundred ndnine) is the natural number following 108 and preceding 110. In mathematics 109 is the 29th prime number. As 29 is itself prime, 109 is the tenth super-prime. The previous prime is 107, making them both twin primes. 109 is a centered triangular number. There are exactly: *109 different families of subsets of a three-element set whose union includes all three elements. *109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements. *109 squares on an infinite chessboard that can be reached by a knight within three moves. There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings. The decimal expansion of 1/109 can be computed using the alternating series, with F(n) the n^ Fibonacci number: ::\frac=\sum_^\infty\times (-1)^=0.00917431\dots The decimal expansion of 1/109 has 108 digits, making 109 a full reptend prime in decimal. The last six digits of the 10 ... [...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 (mathematics), 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 factorization, 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 primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
