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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] |
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] |
Persian Language
Persian (), also known by its endonym Farsi (, ', ), is a Western Iranian language belonging to the Iranian branch of the Indo-Iranian subdivision of the Indo-European languages. Persian is a pluricentric language predominantly spoken and used officially within Iran, Afghanistan, and Tajikistan in three mutually intelligible standard varieties, namely Iranian Persian (officially known as ''Persian''), Dari Persian (officially known as ''Dari'' since 1964) and Tajiki Persian (officially known as ''Tajik'' since 1999).Siddikzoda, S. "Tajik Language: Farsi or not Farsi?" in ''Media Insight Central Asia #27'', August 2002. It is also spoken natively in the Tajik variety by a significant population within Uzbekistan, as well as within other regions with a Persianate history in the cultural sphere of Greater Iran. It is written officially within Iran and Afghanistan in the Persian alphabet, a derivation of the Arabic script, and within Tajikistan in the Tajik alphabet, a der ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Telugu Language
Telugu (; , ) is a Dravidian language spoken by Telugu people predominantly living in the Indian states of Andhra Pradesh and Telangana, where it is also the official language. It is the most widely spoken member of the Dravidian language family and one of the twenty-two scheduled languages of the Republic of India. It is one of the few languages that has primary official status in more than one Indian state, alongside Hindi and Bengali. Telugu is one of six languages designated as a classical language (of India) by the Government of India. Telugu is also a linguistic minority in the states of Karnataka, Tamil Nadu, Maharashtra, Gujarat, Chhattisgarh, Orissa, West Bengal, and the union territories of Puducherry and Andaman and Nicobar Islands. It is also spoken by members of the Telugu diaspora spread across countries like United States, Australia, United Kingdom, Canada, New Zealand in the Anglosphere; Myanmar, Malaysia, South Africa, Mauritius; and the Arabian Gulf count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 = 28. This definition is ancient, appearing as early as Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby q(q+1)/2 is an even perfect number whenever q is a prime of the form 2^p-1 for positive integer p—what is now called a Mersenne prime. Two millennia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bengali Language
Bengali ( ), generally known by its endonym Bangla (, ), is an Indo-Aryan languages, Indo-Aryan language native to the Bengal region of South Asia. It is the official, national, and most widely spoken language of Bangladesh and the second most widely spoken of the 22 scheduled languages of India. With approximately 300 million native speakers and another 37 million as second language speakers, Bengali is the List of languages by number of native speakers, fifth most-spoken native language and the List of languages by total number of speakers, seventh most spoken language by total number of speakers in the world. Bengali is the fifth most spoken Indo-European language. Bengali is the official language, official and national language of Bangladesh, with 98% of Bangladeshis using Bengali as their first language. Within India, Bengali is the official language of the states of West Bengal, Tripura and the Barak Valley region of the state of Assam. It is also a second official lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Devanāgarī
Devanagari ( ; , , Sanskrit pronunciation: ), also called Nagari (),Kathleen Kuiper (2010), The Culture of India, New York: The Rosen Publishing Group, , page 83 is a left-to-right abugida (a type of segmental writing system), based on the ancient ''Brāhmī'' script, used in the northern Indian subcontinent. It was developed and in regular use by the 7th century CE. The Devanagari script, composed of 47 primary characters, including 14 vowels and 33 consonants, is the fourth most widely adopted writing system in the world, being used for over 120 languages.Devanagari (Nagari) , Script Features and Description, SIL International (2013), United States The |
Saraiki Language
Saraiki ( '; also spelt Siraiki, or Seraiki) is an Indo-Aryan language of the Lahnda group, spoken by 26 million people primarily in the south-western half of the province of Punjab in Pakistan. It was previously known as Multani, after its main dialect. Saraiki has partial mutual intelligibility with Standard Punjabi, and it shares with it a large portion of its vocabulary and morphology. At the same time in its phonology it is radically different (particularly in the lack of tones, the preservation of the voiced aspirates and the development of implosive consonants), and has important grammatical features in common with the Sindhi language spoken to the south. The Saraiki language identity arose in the 1960s, encompassing more narrow local earlier identities (like Multani, Derawi or Riasati), and distinguishing itself from broader ones like that of Punjabi. Name The present extent of the meaning of ' is a recent development, and the term most probably gained its curr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senary
A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary. In turn, the senary logic refers to an extension of Jan Łukasiewicz's and Stephen Cole Kleene's ternary logic systems adjusted to explain the logic of statistical tests and missing data patterns in sciences using empirical methods. Formal definition The standard set of digits in senary is given by \mathcal_6 = \lbrace 0, 1, 2, 3, 4, 5\rbrace, with a linear order 0 < 1 < 2 < 3 < 4 < 5. Let be the |
Central Kurdish
Central Kurdish (), also called Sorani (), is a Kurdish dialect or a language that is spoken in Iraq, mainly in Iraqi Kurdistan, as well as the provinces of Kurdistan, Kermanshah, and West Azerbaijan in western Iran. Sorani is one of the two official languages of Iraq, along with Arabic, and is in administrative documents simply referred to as "Kurdish". The term Sorani, named after the former Soran Emirate, is used especially to refer to a written, standardized form of Central Kurdish written in the Sorani alphabet developed from the Arabic alphabet in the 1920s by Sa'ed Sidqi Kaban and Taufiq Wahby. History Tracing back the historical changes that Sorani has gone through is difficult. No predecessors of Kurdish are yet known from Old and Middle Iranian times. The extant Kurdish texts may be traced back to no earlier than the 16th century CE. Sorani originates from the Sulaymaniyah region. 1700s-1918 The oldest written literature in Sorani is reported to have been ''Mahdî ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Numeral
Chinese numerals are words and characters used to denote numbers in Chinese. Today, speakers of Chinese use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as Korean, Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials. The other indigenous system is the Suzhou numerals, or ''huama'', a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in Hong Kong until the 1990s, but we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew (language)
Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved throughout history as the main liturgical language of Judaism (since the Second Temple period) and Samaritanism. Hebrew is the only Canaanite language still spoken today, and serves as the only truly successful example of a dead language that has been revived. It is also one of only two Northwest Semitic languages still in use, with the other being Aramaic. The earliest examples of written Paleo-Hebrew date back to the 10th century BCE. Nearly all of the Hebrew Bible is written in Biblical Hebrew, with much of its present form in the dialect that scholars believe flourished around the 6th century BCE, during the time of the Babylonian captivity. For this reason, Hebrew has been referred to by Jews as '' Lashon Hakodesh'' (, ) since an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
