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7560 (number)
7000 (seven thousand) is the natural number following 6999 and preceding 7001. Selected numbers in the range 7001–7999 7001 to 7099 * 7021 – triangular number * 7043 – Sophie Germain prime * 7056 = 842 * 7057 – cuban prime of the form ''x'' = ''y'' + 1, super-prime * 7073 – Leyland number * 7079 – Sophie Germain prime, safe prime 7100 to 7199 * 7103 – Sophie Germain prime, sexy prime with 7109 * 7106 – octahedral number * 7109 – super-prime, sexy prime with 7103 * 7121 – Sophie Germain prime * 7140 – triangular number, also a pronic number and hence = 3570 is also a triangular number, tetrahedral number * 7151 – Sophie Germain prime * 7187 – safe prime * 7192 – weird number * 7193 – Sophie Germain prime, super-prime 7200 to 7299 * 7200 – pentagonal pyramidal number * 7211 – Sophie Germain prime * 7225 = 852, centered octagonal number * 7230 = 362 + 372 + 382 + 392 + 402 = 412 + 422 + 432 + 442 * 7246 – centered heptagonal number * 7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonagonal Number
A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical. Specifically, the ''n''th nonagonal number counts the number of dots in a pattern of ''n'' nested nonagons, all sharing a common corner, where the ''i''th nonagon in the pattern has sides made of ''i'' dots spaced one unit apart from each other. The nonagonal number for ''n'' is given by the formula: :\frac . Nonagonal numbers The first few nonagonal numbers are: :0 (number), 0, 1 (number), 1, 9 (number), 9, 24 (number), 24, 46 (number), 46, 75 (number), 75, 111 (number), 111, 154 (number), 154, 204 (number), 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089 (number), 1089, 1216, 1350, 1491, 1639, 1794, 1956, 2125, 2301, 2484, 2674, 2871, 3075, 3286, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is (n^3+n)/2. The largest magic constant of normal magic square which is also a: *triangular number is 15 (solve the Diophantine equation x^2=y^3+16y+16, where y is divisible by 4); *square number is 1 (solve the Diophantine equation x^2=y^3+4y, where y is even); *generalized pentagonal number is 171535 (solve the Diophanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7825 (number)
7825 (seven thousand, eight hundred ndtwenty-five) is the natural number following 7824 and preceding 7826. In mathematics * 7825 is the smallest number n when it is impossible to assign two colors to natural numbers 1 through n such that every Pythagorean triple is multicolored, i.e. where the Boolean Pythagorean triples problem The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members. The Boolean Pythagorean triples problem w ... becomes false. The 200-terabyte proof to verify this is the largest ever made. * 7825 is a magic constant of ''n'' × ''n'' normal magic square and n-Queens Problem for ''n'' = 25. References Integers {{Number-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Organization For Standardization
The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Article 3 of the ISO Statutes. ISO was founded on 23 February 1947, and (as of November 2022) it has published over 24,500 international standards covering almost all aspects of technology and manufacturing. It has 809 Technical committees and sub committees to take care of standards development. The organization develops and publishes standardization in all technical and nontechnical fields other than electrical and electronic engineering, which is handled by the IEC.Editors of Encyclopedia Britannica. 3 June 2021.International Organization for Standardization" ''Encyclopedia Britannica''. Retrieved 2022-04-26. It is headquartered in Geneva, Switzerland, and works in 167 countries . The three official languages of the ISO are English, Fren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 7810
ISO/IEC 7810 ''Identification cards — Physical characteristics'' is an international standard that defines the physical characteristics for identification cards. The characteristics specified include: * Physical dimensions * Resistance to bending, chemicals, temperature, and humidity * Toxicity The standard includes test methods for resistance to heat. Card sizes The standard defines four card sizes: ID-1, ID-2, ID-3 and ID-000. All card sizes have a thickness of minimum and maximum. The standard defines both metric and imperial measurements, noting that: ID-1 The ID-1 format specifies a size of and rounded corners with a radius of 2.88–3.48 mm (about in). It is commonly used for payment cards ( ATM cards, credit cards, debit cards, etc.). Today it is also used for driving licences and personal identity cards in many countries, automated fare collection system cards for public transport, in retail loyalty cards, and even crew member certificates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7744 (number)
7744 is the natural number following 7743 and preceding 7745. In mathematics 7744 is: *the square of 88, and is the smallest nonzero square each of whose decimal digits occur exactly twice. *the sum of two fifth powers: 7744 = 65 + (−2)5. *a Harshad number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers ... in bases 5, 9, 10, 12, 14 and 15. *the aliquot sum of both 10316 and 15482. *part of the 29-aliquot tree. The complete aliquot sequence starting at 7716 is: 7716, 10316, 7744, 9147, 3053, 115, 29, 1, 0 References {{DEFAULTSORT:7744 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padovan Sequence
In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... A Padovan prime is a Padovan number that's also prime. The first Padovan primes are: :2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719, ... . The Padovan sequence is named after Richard Padovan who attributed its discovery to Netherlands, Dutch architect Hans van der Laan in his 1994 essay ''Dom. Hans van der Laan : Modern Primitive''.Richard Padovan. ''Dom Hans van der Laan: modern primitive'': Architectura & Natura Press, . The sequence was described by Ian Stewart (mathematician), Ian Stewart in his Scientific Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Pyramidal Number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes. As well as counting spheres in a pyramid, these numbers can be described algebraically as a sum of the first n positive square numbers, or as the values of a cubic polynomial. They can be used to solve several other counting problems, including counting squares in a square grid and counting acute triangles formed from the vertices of an odd regular polygon. They equal the sums of consecutive tetrahedral numbers, and are one-fourth of a larger tetrahedral number. The sum of two consecutive square pyramidal numbers is an octahedral number. History The pyramidal numbers were one of the few types of three-dimensional figurate num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emirp
An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, ... . All non-palindromic permutable primes are emirps. , the largest known emirp is 1010006+941992101×104999+1, found by Jens Kruse Andersen in October 2007. The term 'emirpimes' (singular) is used also in places to treat semiprimes in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits. It is an open problem whether there are infinitely many emirps. Other bases The emirps in base 12 are (using rotated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Prime
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are : 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... appearing as coordinates of the Markov triples :(1, 1, 1), (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), (1, 13, 34), (1, 34, 89), (2, 29, 169), (5, 13, 194), (1, 89, 233), (5, 29, 433), (1, 233, 610), (2, 169, 985), (13, 34, 1325), ... There are infinitely many Markov numbers and Markov triples. Markov tree There are two simple ways to obtain a new Markov triple from an old one (''x'', ''y'', ''z''). First, one may permute the 3 numbers ''x'',''y'',''z'', so in particular one can normalize the triples so that ''x'' ≤ ''y'' ≤ ''z''. Second, if (''x'', ''y'', ''z'') is a Markov triple then by Vieta jumping so is (''x'', ''y'', 3''xy''&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highly Composite Number
__FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually composite numbers; however, all further terms are. The late mathematician Jean-Pierre Kahane has suggested that Plato must have known about highly composite numbers as he deliberately chose 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it. Ramanujan wrote and titled his paper on the subject in 1915. Examples The initial or smallest 38 highly composite numbers are listed in the table below . The number of divisors is given in the column labeled ''d''(''n''). Asterisks indicate superior highly composite numbers. The divisors of the first 15 highly composite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
