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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 proved several times, by Subbarao, Erdős, and Hardy & Subbarao. References *. *. *https://planetmath.org/pillaiprime, PlanetMath PlanetMath is a free, collaborative, mathematics online encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be c ... Classes of prime numbers Factorial and binomial topics [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of 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 are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...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 a super-prime. The previous prime is 107, making them both twin primes. 109 is a centered triangular number. 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 108-digit cycle are 853211, the first six Fibonacci numbers in descending order. 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, and 109 squares on an infinite chessboard that can be reached by a knight within three moves. See also *109 (other) 109 ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PlanetMath
PlanetMath is a free, collaborative, mathematics online encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. 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 encyclopedic entries. It formerly operated a self-hosted forum, but now encourages discussion via Gitter. , the encyclopedia hosted about 9,289 entries and over 16,258 ''concepts'' (a concept may be for example a specific notion defined within a more general entry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' 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. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...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 (, abbr. AP) is a state in the south-eastern coastal region of India. It is the seventh-largest state by area covering an area of and tenth-most populous state with 49,386,799 inhabitants. It is bordered by Telangana to the ..., India. 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 maj ... [...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 a prime number, and a Pierpont prime, implying that a 193-gon can be constructed using a compass, straightedge, and angle trisector. It is the only odd prime p known for which 2 is not a primitive root of 4p^2 + 1. It is the number of compositions of 14 into distinct parts. It is also part of the prime quadruplet (191, 193, 197, 199). See also * 193 (other) 193 A.D. is a year. 193 may also refer to: * 193 Ambrosia * Connecticut Route 193 * Maryland Route 193 * West Virginia Route 193 * Alabama State Route 193 * California State Route 193 * Ohio State Route 193 * Georgia State Route 193 * Maine S ... References {{DEFAULTSORT:193 (Number) Integers ... [...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 a 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. See also * The year AD 149 or 149 BC * List of highways numbered 149 * References Externa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
139 (number)
139 (One hundred ndthirty-nine) is the natural number following 138 and preceding 140. In mathematics 139 is the 34th prime number. It is a twin prime with 137. Because 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 + 23 + 29 + 31 + 37). It is the smallest factor of 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. In the military * RUM-139 VL-ASROC is a United States Navy ASROC anti-submarine missile * was a United States Navy ''Admirable''-class minesweeper during World War II * was a United States Navy ''Haskell''-class attack transport during World War II * was a United States Navy destroyer during World War II * was a United States Navy transpor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred ndthirty-seven) is the natural number following 136 and preceding 138. In mathematics 137 is: * the 33rd prime number; the next is 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 4''n'' + 1, where ''n'' = 34 (137 = 4x34 + 1) or the sum of two squares 112 + 42 (121 + 16). * 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) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°. * 1/137 = 0.007299270072992700..., so its period value is palindromic and has a period length of only 8. In physics * Since the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
83 (number)
83 (eighty-three) is the natural number following 82 and preceding 84. In mathematics 83 is: * the sum of three consecutive primes (23 + 29 + 31). * the sum of five consecutive primes (11 + 13 + 17 + 19 + 23). * the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89. * a Sophie Germain prime. * a safe prime. * a Chen prime. * an Eisenstein prime with no imaginary part and real part of the form 3''n'' − 1. * a highly cototient number. * there number of primes that are right-truncatable. * a super-prime, because 23 is prime. In science Chemistry *The atomic number of bismuth (Bi) Astronomy * Messier object M83, a magnitude 8.5 spiral galaxy in the constellation Hydra, also known as the Southern Pinwheel Galaxy *The New General Catalogue object NGC 83, a magnitude 12.3 elliptical galaxy in the constellation Andromeda In religion Judaism * When someone reaches 83 they may celebrate a second bar mitzvah In music * M83 is the debut a ... [...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] |
