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Palindromic Primes
In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such concerns. The first few decimal palindromic primes are: : 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, … Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is not known if there are infinitely many palindromic primes in base 10. The largest known is :101888529 - 10944264 - 1. which has 1,888,529 digits, and was found on 18 October 2021 by Ryan Propper and Serge Batalov. On the other hand, it is known that, for any base, almost all palindromic numbers are composite, i.e. the ratio between palindromic composites and all palindromes below ''n' ... [...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] |
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 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–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chudnovsky Algorithm
The Chudnovsky algorithm is a fast method for calculating the digits of , based on Ramanujan’s formulae. It was published by the Chudnovsky brothers in 1988. It was used in the world record calculations of 2.7 trillion digits of in December 2009, 10 trillion digits in October 2011, 22.4 trillion digits in November 2016, 31.4 trillion digits in September 2018–January 2019, 50 trillion digits on January 29, 2020, 62.8 trillion digits on August 14, 2021, and 100 trillion digits on March 21, 2022. Algorithm The algorithm is based on the negated Heegner number d = -163 , the ''j''-function j \left(\tfrac\right) = -640320^3, and on the following rapidly convergent generalized hypergeometric series: : \frac = 12 \sum^\infty_ \frac A detailed proof of this formula can be found here: For a high performance iterative implementation, this can be simplified to : \frac=\frac = \sum^\infty_ \frac There are 3 big integer terms (the multinomial term ''Mq'', the linear term ''Lq'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paulo Ribenboim
Paulo Ribenboim (born March 13, 1928) is a Brazilian-Canadian mathematician who specializes in number theory. Biography Ribenboim was born into a Jewish family in Recife, Brazil. He received his BSc in mathematics from the University of São Paulo in 1948, and won a fellowship to study with Jean Dieudonné in France at the University of Nancy in the early 1950s, where he became a close friend of Alexander Grothendieck. He has contributed to the theory of ideals and of valuations. Ribenboim has authored 246 publications including 13 books. He has been at Queen's University in Kingston, Ontario, since the 1960s, where he remains a professor emeritus. Jean Dieudonné was one of his doctoral advisors. Andrew Granville has been a doctoral student of Ribenboim. The Ribenboim Prize of the Canadian Number Theory Association is named in his honor. Personal life In 1951, Ribenboim married Huguette Demangelle, a French Catholic woman whom he met in France. The couple have two c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
13 (number)
13 (thirteen) is the natural number following 12 and preceding 14. Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition. In mathematics The number 13 is the sixth prime number. It is a twin prime with 11, as well as a cousin prime with 17. It is the second Wilson prime, of three known (the others being 5 and 563), and the smallest emirp in decimal. 13 is: *The second star number: *The third centered square number: * A happy number and a lucky number. *A Fibonacci number, preceded by 5 and 8. *The smallest number whose fourth power can be written as a sum of two consecutive square numbers (1192 + 1202). *The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
666 (number)
666 (six hundred ndsixty-six) is the natural number following 665 and preceding 667. In Christianity, 666 is called the " number of the beast" in (most manuscripts of) chapter 13 of the Book of Revelation of the New Testament.Beale, Gregory K. (1999). The Book of Revelation: A Commentary on the Greek Text. Grand Rapids, Michigan: Wm. B. Eerdmans Publishing. p. 718. . Retrieved 9 July 2012. In Mathematics 666 is the sum of the first 36 natural numbers (\sum_^ i, i.e. ), and thus it is a triangular number. Because 36 is also triangular, 666 is a doubly triangular number. Also, ; 15 and 21 are also triangular numbers, and . In base 10, 666 is a repdigit (and therefore a palindromic number) and a Smith number. A prime reciprocal magic square based on 1/149 in base 10 has a magic total of 666. The prime factorization of 666 is 2 ⋅ 32 ⋅ 37. Also, 666 is the sum of the squares of the first seven primes: 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 The number of integers whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hell
In religion and folklore, hell is a location in the afterlife in which evil souls are subjected to punitive suffering, most often through torture, as eternal punishment after death. Religions with a linear divine history often depict hells as eternal destinations, the biggest examples of which are Christianity and Islam, whereas religions with reincarnation usually depict a hell as an intermediary period between incarnations, as is the case in the dharmic religions. Religions typically locate hell in another dimension or under Earth's surface. Other afterlife destinations include heaven, paradise, purgatory, limbo, and the underworld. Other religions, which do not conceive of the afterlife as a place of punishment or reward, merely describe an abode of the dead, the grave, a neutral place that is located under the surface of Earth (for example, see Kur, Hades, and Sheol). Such places are sometimes equated with the English word ''hell'', though a more correct translatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belphegor
In Christian demonology, Belphegor (or Beelphegor, he, בַּעַל-פְּעוֹר ''Báʿal-pəʿór'' - Lord of the Gap) is a demon. In later Kabbalah Belphegor is a demon who helps people make discoveries. He seduces people by suggesting to them ingenious inventions that will make them rich, stagnating that which could not be accredited to it. Auxiliary Bishop and witch-hunter Peter Binsfeld believed that Belphegor tempts by means of laziness. Also, according to Peter Binsfeld's Classification of Demons, Belphegor is the chief demon of the deadly sin known as Sloth in Christian tradition. Literature The novella by Italian diplomat Niccolò Machiavelli was first published in 1549, and regales how the demon comes to earth to find a mate. Belphegor figures in ''Paradise Lost'' by John Milton, 1667. According to the 1818 by Collin de Plancy Belphegor was Hell's ambassador to France. The same claim was repeated by Victor Hugo in '' Toilers of the Sea'' (1866). In the gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superstition
A superstition is any belief or practice considered by non-practitioners to be irrational or supernatural, attributed to fate or magic, perceived supernatural influence, or fear of that which is unknown. It is commonly applied to beliefs and practices surrounding luck, amulets, astrology, fortune telling, spirits, and certain paranormal entities, particularly the belief that future events can be foretold by specific (apparently) unrelated prior events. Also, the word ''superstition'' is often used to refer to a religion not practiced by the majority of a given society regardless of whether the prevailing religion contains alleged superstitions or to all religions by the antireligious. Contemporary use Definitions of the term vary, but commonly describe superstitions as irrational beliefs at odds with scientific knowledge of the world. Stuart Vyse proposes that a superstition's "presumed mechanism of action is inconsistent with our understanding of the physical world", wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duodecimal
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (decimal 14). Similarly, in duodecimal, "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth", respectively). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and , as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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