103 (number)
103 (one hundred ndthree) is the natural number following 102 and preceding 104. In mathematics 103 is a prime number, and the largest prime factor of 6!+1=721=7\cdot 103. The previous prime is 101. This makes 103 a twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' .... It is the fifth irregular prime, because it divides the numerator of the Bernoulli number B_=-\frac=-\frac. The equation 64^3+94^3=103^3+1 makes 103 part of a "Fermat near miss". There are 103 different connected series-parallel partial orders on exactly six unlabeled elements. 103 is conjectured to be the smallest number for which repeatedly reversing the digits of its ternary representation, and adding the number to its reversal, does not eventually reach a ternary palindrome. References ... [...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]   |
|
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
102 (number)
102 (one hundred [and] two) is the natural number following 101 (number), 101 and preceding 103 (number), 103. In mathematics 102 is an abundant number and a semiperfect number. It is a sphenic number. The sum of Euler's totient function φ(''x'') over the first eighteen integers is 102. 102 is the first three-digit base 10 polydivisible number, since 1 is divisible by 1, 10 is divisible by 2 and 102 is divisible by 3. This also shows that 102 is a Harshad number. 102 is the first 3-digit number divisible by the numbers 3, 6, 17, 34 and 51. oeis:A006316, 10264 + 1 is a prime number. There are 102 vertices in the Biggs–Smith graph. In other fields 102 is also: * The emergency telephone number for police in Azerbaijan, Mongolia, Ukraine and Belarus * The emergency telephone number for fire in Israel * The emergency telephone number for ambulance in parts of India * The emergency telephone number for ambulance in Maldives References * Wells, D. ''The Penguin Dictionary of ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
104 (number)
104 (one hundred ndfour) is the natural number following 103 and preceding 105. In mathematics 104 is a refactorable number and a primitive semiperfect number. The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at every vertex. The second largest sporadic group \mathbb has a McKay–Thompson series, representative of a principal modular function is T_(\tau), with constant term a(0) = 104: :j_(\tau) = T_(\tau)+104 = \frac + 104 + 4372q + 96256q^2 + \cdots The Tits group \mathbb , which is the only finite simple group to classify as either a ''non-strict'' group of Lie type or sporadic group, holds a minimal faithful complex representation in 104 dimensions. References * Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
101 (number)
101 (one hundred ndone) is the umberfollowing 100 and preceding 102. It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one". As an ordinal number, 101st (one hundred ndfirst), rather than 101th, is the correct form. 101 is a prime number and the smallest integer above 100. It is also a palindromic number, and hence, a palindromic prime. In mathematics 101 is an alternating factorial, sexy prime and 101 is also the smallest number that can be expressed as the sum of three distinct nonzero squares in more than two ways: 9^2+4^2+2^2, 8^2+6^2+1^2 or 7^2+6^2+4^2 (see image). For a 3-digit number in decimal, this number has a relatively simple divisibility test. The candidate number is split into groups of four, starting with the rightmost four, and added up to produce a 4-digit number. If this 4-digit number is of the form 1000a+100b+10a+b (where and are integers from 0 to 9), such as 3232 or 9797 ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Twin Prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime'' is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved. Properties Usually the pair is not considered to be a pair of twin primes. Since 2 ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Irregular Prime
In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class number (number theory), class numbers or of Bernoulli numbers. The first few regular odd primes are: : 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, ... . History and motivation In 1850, Kummer proved that Fermat's Last Theorem is true for a prime exponent ''p'' if ''p'' is regular. This focused attention on the irregular primes. In 1852, Angelo Genocchi, Genocchi was able to prove that the First case of Fermat's last theorem, first case of Fermat's Last Theorem is true for an exponent ''p'', if is not an irregular pair. Kummer improved this further in 1857 by showing that for the "first case" of Fermat's Last Theorem (see Sophie Germain's theorem) i ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Bernoulli Number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of ''m''-th powers of the first ''n'' positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function. The values of the first 20 Bernoulli numbers are given in the adjacent table. Two conventions are used in the literature, denoted here by B^_n and B^_n; they differ only for , where B^_1=-1/2 and B^_1=+1/2. For every odd , . For every even , is negative if is divisible by 4 and positive otherwise. The Bernoulli numbers are special values of the Bernoulli polynomials B_n(x), with B^_n=B_n(0) and B^+_n=B_n(1). The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, an ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Series-parallel Partial Order
In order theory, order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two simple composition operations... The series-parallel partial orders may be characterized as the N-free finite partial orders; they have order dimension at most two.. They include weak orders and the reachability relationship in Tree (graph theory), directed trees and directed series–parallel graphs. The comparability graphs of series-parallel partial orders are cographs. Series-parallel partial orders have been applied in job shop scheduling, machine learning of event sequencing in time series data, transmission sequencing of multimedia data, and throughput maximization in dataflow programming. Series-parallel partial orders have also been called multitrees;. however, that name is ambiguous: multitrees also refer to partial orders with no four-element diamond suborder and to other structures formed from multiple tree ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Ternary Numeral System
A ternary numeral system (also called base 3 or trinary) has 3 (number), three as its radix, base. Analogous to a bit, a ternary numerical digit, digit is a trit (trinary digit). One trit is equivalent to binary logarithm, log2 3 (about 1.58496) bits of Units of information, information. Although ''ternary'' most often refers to a system in which the three digits are all non–negative numbers; specifically , , and , the adjective also lends its name to the balanced ternary system; comprising the digits −1, 0 and +1, used in comparison logic and ternary computers. Comparison to other bases Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary numeral system, binary. For example, decimal 365 (number), 365 or senary corresponds to binary (nine bits) and to ternary (six digits). However, they are still far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codi ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Palindrome
A palindrome (Help:IPA/English, /ˈpæl.ɪn.droʊm/) is a word, palindromic number, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as ''madam'' or ''racecar'', the date "Twosday, 02/02/2020" and the sentence: "A man, a plan, a canal – Panama". The 19-letter Finnish language, Finnish word ''saippuakivikauppias'' (a soapstone vendor) is the longest single-word palindrome in everyday use, while the 12-letter term ''tattarrattat'' (from James Joyce in ''Ulysses (novel), Ulysses'') is the longest in English. The word ''palindrome'' was introduced by English poet and writer Henry Peacham (born 1578), Henry Peacham in 1638.Henry Peacham, ''The Truth of our Times Revealed out of One Mans Experience'', 1638p. 123 The concept of a palindrome can be dated to the 3rd-century BCE, although no examples survive. The earliest known examples are the 1st-century CE Latin acrostic word square, the Sator Square (which contains both word and senten ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |