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2seventy Bio
70 (seventy) is the natural number following 69 and preceding 71. Mathematics Properties of the integer 70 is the fourth discrete sphenic number, as the first of the form 2 \times 5 \times r. It is the smallest weird number, a natural number that is abundant but not semiperfect, where it is also the second-smallest primitive abundant number, after 20. 70 is in equivalence with the sum between the smallest number that is the sum of ''two'' abundant numbers, and the largest that is not ( 24, 46). 70 is the tenth Erdős–Woods number, since it is possible to find sequences of seventy consecutive integers such that each inner member shares a factor with either the first or the last member. It is also the sixth Pell number, preceding the tenth prime number 29, in the sequence \. 70 is a palindromic number in bases 9 (779), 13 (5513) and 34 (2234). Happy number 70 is the thirteenth happy number in decimal, where 7 is the first such number greater than 1 in base ten: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew Numerals
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals sometime between 200 and 78 BCE, the latter being the date of the earliest archeological evidence. The current numeral system is also known as the ''Hebrew alphabetic numerals'' to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from in the Samaria Ostraca. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BCE. In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2, ..., 9) is assigned a separate letter, each tens (10, 20, ..., 90) a separate letter, and the first four hundreds (100, 200, 300, 400) a separate letter. The later hundreds (500, 600, 700, 8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. In other words, if prime numbers are matched with ordinal numbers, starting with prime number 2 matched with ordinal number 1, then the primes matched with prime ordinal numbers are the super-primes. The subsequence begins :3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, ... . That is, if ''p''(''n'') denotes the ''n''th prime number, the numbers in this sequence are those of the form ''p''(''p''(''n'')). In 1975, Robert Dressler and Thomas Parker used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
74 (number)
74 (seventy-four) is the natural number following 73 and preceding 75. In mathematics 74 is: * the twenty-first distinct semiprime and the eleventh of the form (2.''q''), where q is a higher prime. * with an aliquot sum of 40, within an aliquot sequence of three composite numbers (74, 40, 50, 43, 1,0) to the Prime in the 43-aliquot tree. * a palindromic number in bases 6 (2026) and 36 (2236). * a nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie .... * the number of collections of subsets of that are closed under union and intersection. * φ(74) = φ(σ(74)). There are 74 different non-Hamiltonian polyhedra with a minimum number of vertices. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number. Examples For example, the proper divisors of 12 (that is, the positive divisors of 12 that are not equal to 12) are , and 6, so the aliquot sum of 12 is 16 i.e. (). The values of for are: :0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 36, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 55, 1, 22, 17, 50, 1, 54, 1, 40, 33, 26, 1, 76, 8, 43, ... Characterization of classes of numbers The aliquot sum function can be used to characterize several notable classes of numbers: *1 is the only number whose aliquot sum is 0. *A number is prime if and only if its aliquot sum is 1. *The aliquot sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Prime
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because the sequence starting with 4^2=16 and 1^2+6^2=37 eventually reaches 2^2+0^2=4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the Perfect digital invariant, perfect digital invariant function for p = 2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" . Ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
97 (number)
97 (ninety-seven) is the natural number following 96 (number), 96 and preceding 98 (number), 98. It is a prime number and the only prime in the nineties. In mathematics 97 is: * the 25th prime number (the largest two-digit prime number in Base 10, base 10), following 89 (number), 89 and preceding 101 (number), 101. * a Proth prime and a Pierpont prime as it is 3 × 25 + 1. * the eleventh member of the Mian–Chowla sequence. * a self number in base 10, since there is no integer that added to its own digits, adds up to 97. * the smallest odd prime that is not a cluster prime. * the highest two-digit number where the sum of its digits is a square. * the number of primes less than 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all happy primes. However, 9000007 (read as ''nine million seven'') is composite number, composite and has the factorization 277 (number), 277 × 32491. * an emirp with 79 (number), 79. * an isolated p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of Figurate number, figurate numbers (other examples being Cube (algebra), cube numbers and triangular numbers). In the Real number, real number system, square numbers are non-negative. A non-negative integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A decimal numeral (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because the sequence starting with 4^2=16 and 1^2+6^2=37 eventually reaches 2^2+0^2=4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" . Happy numbers and perfect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palindromic Number
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palindromic'' is derived from palindrome, which refers to a word (such as ''rotor'' or ''racecar'') whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers (in decimal) are: : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, ... . Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain property ''and'' are palindromic. For instance: * The palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, ... . * The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, ... . In any base there are infinitely many palindromic numbers, since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
29 (number)
29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number. 29 is the number of days February has on a leap year. Mathematics 29 is the tenth prime number. Integer properties 29 is the fifth primorial prime, like its twin prime 31. 29 is the smallest positive whole number that cannot be made from the numbers \, using each digit exactly once and using only addition, subtraction, multiplication, and division. None of the first twenty-nine natural numbers have more than two different prime factors (in other words, this is the longest such consecutive sequence; the first sphenic number or triprime, 30 is the product of the first three primes 2, 3, and 5). 29 is also, * the sum of three consecutive squares, 22 + 32 + 42. * the sixth Sophie Germain prime. * a Lucas prime, a Pell prime, and a tetranacci number. * an Eisenstein prime with no imaginary part and real part of the form 3n − 1. * a Markov number, appearing in the solution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell Number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell–Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + . As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
