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Largest Number
A large number or the largest number are terms that may refer to: * Large numbers, for notations to exactly specify very large numbers * Names of large numbers, for the largest numbers with names In mathematics and physics * Infinity, a concept which can be used as a largest number in some contexts * Graham's number, once claimed as the largest number ever used in a serious mathematical proof * Largest known prime number, for the largest known primes * Dirac large numbers hypothesis, for cosmology. In computing * Arbitrary-precision arithmetic * The constant 127, 32767, 2147483647, or 9223372036854775807, in a byte, a word of 16, 32, or 64 bits in two's-complement format * The constant 255, 65535, 4294967295, or 18446744073709551615, in a byte, a word of 16, 32, or 64 bits with no sign bit * The constant 3.4028235e+38 or 1.7976931348623157e+308, in a word of 32 or 64 bits using the binary IEEE 754-2008 floating-point representation See also *Infinitesimal In mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Numbers
Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics. They are typically large positive integers, or more generally, large positive real numbers, but may also be other numbers in other contexts. Googology is the study of nomenclature and properties of large numbers. In the everyday world Scientific notation was created to handle the wide range of values that occur in scientific study. 1.0 × 109, for example, means one billion, or a 1 followed by nine zeros: 1 000 000 000. The reciprocal, 1.0 × 10−9, means one billionth, or 0.000 000 001. Writing 109 instead of nine zeros saves readers the effort and hazard of counting a long series of zeros to see how large the number is. Examples of large numbers describing everyday real-world objects include: * The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Names Of Large Numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. These naming procedures are based on taking the number ''n'' occurring in 103''n''+3 (short scale) or 106''n'' (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix ''-illion''. Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as ''10'' with a numeric superscript. Indian English does not use millions, but has its own system of large numbers including lakhs and crores. English also has many words, such as "zillion", used informally to mean large but unspecified amoun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graham's Number
Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of ''that'' number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers of the form a ^. How ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Known Prime Number
The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilise a specialised primality test that is faster than the general one. , the eight largest known primes are Mersenne primes. The last seventeen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all 1's, since the binary form of 2''k'' − 1 is simply ''k'' 1's. Current record The record is currently held by with 24,862,048 digits, found by GIMPS in December 2018. The first and last 120 digits of its val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Large Numbers Hypothesis
The Dirac large numbers hypothesis (LNH) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch. According to Dirac's hypothesis, the apparent similarity of these ratios might not be a mere coincidence but instead could imply a cosmology with these unusual features: *The strength of gravity, as represented by the gravitational constant, is inversely proportional to the age of the universe: G \propto 1/t\, *The mass of the universe is proportional to the square of the universe's age: M \propto t^2. *Physical constants are actually not constant. Their values depend on the age of the Universe. Background LNH was Dirac's personal response to a set of large number "coincidences" that had intrigued other theorists of his time. The "coincidences" began with Hermann Weyl (1919), who speculated that the obse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbitrary-precision Arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should not be confu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
32767
30,000 (thirty thousand) is the natural number that comes after 29,999 and before 30,001. Selected numbers in the range 30001–39999 30001 to 30999 * 30029 = primorial prime * 30030 = primorial * 30031 = smallest composite number which is one more than a primorial * 30203 = safe prime * 30240 = harmonic divisor number * 30323 = Sophie Germain prime and safe prime * 30420 = pentagonal pyramidal number * 30537 = Riordan number * 30694 = open meandric number * 30941 = first base 13 repunit prime 31000 to 31999 * 31116 = octahedral number * 31337 = cousin prime, pronounced ''elite'', an alternate way to spell ''1337'', an obfuscated alphabet made with numbers and punctuation, known and used in the gamer, hacker, and BBS cultures. * 31395 = square pyramidal number * 31397 = prime number followed by a record prime gap of 72, the first greater than 52 * 31688 = the number of years approximately equal to 1 trillion seconds * 31721 = start of a prime quadruplet * 31929 = Zeisel nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2147483647
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on Pietro Cataldi's method, so that at most 372 divisions were needed. It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the largest known prime until 1867. In computing, this number is the largest value that a signed 32-bit integer field can hold. Barlow's prediction At the time of its discovery, 2,147,483,647 was the largest known prime number. In 1811, Peter Barlow, not anticipating future interest in perfect numbers, wrote (in ''An Elementary Investigation of the Theory of Numbers''): Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9223372036854775807
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In a context where only integers are considered, is restricted to non-negative values, so there are 1, 2, and 2 multiplied by itself a certain number of times. The first ten powers of 2 for non-negative values of are: : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system. Computer science Two to the exponent of , written as , is the number of ways the bits in a binary word of length can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 () to () inclusively. Corresponding signed integer values can be positive, negative and zero; see signed number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
65535
65535 is the integer after 65534 and before 65536. It is the maximum value of an unsigned 16-bit integer. In mathematics 65535 is the product of the first four Fermat primes: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1). Because of this property, it is possible to construct with compass and straightedge a regular polygon with 65535 sides. See constructible polygon. 65535 is the sum of 20 through 215 (20 + 21 + 22 + ... + 215) and is therefore a repdigit in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF). 65535 is the 15th 626- gonal number, the 5th 6555-gonal number, and the 3rd 21846-gonal number. In computing *65535 occurs frequently in the field of computing because it is 2^ - 1 (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bit binary number. Some computer programming environments may have predefined constant values representing 65535, with names like . *In older computers with processo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4294967295
The number 4,294,967,295 is an integer equal to 2 − 1. It is a perfect totient number. It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of 3 \cdot 5 \cdot 17 \cdot 257 \cdot 65537. It is the highest unsigned 32-bit integer. In geometry Since the prime factors of 2 − 1 are exactly the five known Fermat primes, this number is the largest known odd value ''n'' for which a regular ''n''-sided polygon is constructible using compass and straightedge. Equivalently, it is the largest known odd number ''n'' for which the angle 2\pi/n can be constructed, or for which \cos(2\pi/n) can be expressed in terms of square roots. Not only is 4,294,967,295 the largest known odd number of sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers ''n'' for which an ''n''-sided polygon is constructible begins with the list of factors of 4,294,967,295. If there are no more Fermat primes, then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
