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23 (number)
23 (twenty-three) is the natural number following 22 and preceding 24. It is a prime number. In mathematics Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet ( 7, 11, 13, 17, 19, 23). Twenty-three is also the next to last member of the first Cunningham chain of the first kind ( 2, 5, 11, 23, 47), and the sum of the prime factors of the second set of consecutive discrete semiprimes, ( 21, 22). 23 is the smallest odd prime to be a highly cototient number, as the solution to x-\phi(x) for the integers 95, 119, 143, and 529. * 23 is the second Smarandache–Wellin prime in base ten, as it is the concatenation of the decimal representations of the first two primes (2 and 3) and is itself also prime, and a happy number. * The sum of the first nine primes up to 23 is a square: 2 + ... [...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] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
14 (number)
14 (fourteen) is the natural number following 13 (number), 13 and preceding 15 (number), 15. Mathematics Fourteen is the seventh composite number. Properties 14 is the third distinct semiprime, being the third of the form 2 \times q (where q is a higher prime). More specifically, it is the first member of the second cluster of two discrete semiprimes (14, 15 (number), 15); the next such cluster is (21 (number), 21, 22 (number), 22), members whose sum is the fourteenth prime number, 43 (number), 43. 14 has an aliquot sum of 10 (number), 10, within an aliquot sequence of two composite numbers (14, 10 (number), 10, 8 (number), 8, 7 (number), 7, 1 (number), 1, 0) in the prime 7-aliquot tree. 14 is the third Pell number, companion Pell number and the fourth Catalan number. It is the lowest even n for which the Euler totient \varphi(x) = n has no solution, making it the first even nontotient. According to the Shapiro inequality, 14 is the least number n such that there exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Prime
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! + 1 or 1! + 1), 3 (2! + 1), 5 (3! − 1), 7 (3! + 1), 23 (4! − 1), 719 (6! − 1), 5039 (7! − 1), 39916801 (11! + 1), 479001599 (12! − 1), 87178291199 (14! − 1), ... ''n''! − 1 is prime for : :''n'' = 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, 147855, 208003, 632760, ... (resulting in 28 factorial primes) ''n''! + 1 is prime for : :''n'' = 0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, 110059, 150209, 288465, 308084, 422429, ... (resulting in 24 factorial primes - the prime 2 is repeated) No other factori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
874 (number)
800 (eight hundred) is the natural number following 799 and preceding 801. It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal 40. Integers from 801 to 899 800s * 801 = 32 × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins * 802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number, sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231) * 803 = 11 × 73, sum of three consecutive primes (263 + 269 + 271), sum of nine consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), Harshad number, number of partitions of 34 into Fibonacci parts * 804 = 22 × 3 × 67, nontotient, Harshad number, refactorable number ** "The 804" is a local nickname for the Greater Richmond Region of the U.S. state of Virginia, derived from its telephone area code (although the area code covers a larg ... [...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] |
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] |
Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
529 (number)
500 (five hundred) is the natural number following 499 and preceding 501. Mathematical properties 500 = 22 × 53. It is an Achilles number and a Harshad number, meaning it is divisible by the sum of its digits. It is the number of planar partitions of 10. Other fields Five hundred is also *the number that many NASCAR races often use at the end of their race names (e.g., Daytona 500), to denote the length of the race (in miles, kilometers or laps). *the longest advertised distance (in miles) of the IndyCar Series and its premier race, the Indianapolis 500. Slang names * Monkey (UK slang for £500; US slang for $500) Integers from 501 to 599 500s 501 501 = 3 × 167. It is: * the sum of the first 18 primes (a term of the sequence ). * palindromic in bases 9 (6169) and 20 (15120). 502 * 502 = 2 × 251 * vertically symmetric number 503 503 is: * a prime number. * a safe prime. * the sum of three consecutive primes (163 + 167 + 17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
143 (number)
143 (one hundred ndforty-three) is the natural number following 142 and preceding 144. It is one less than a gross. In media * On '' Mister Rogers' Neighborhood'': "Transformations", 143 is used to mean "I love you". 1 meaning I for 1 letter, 4 meaning Love for the 4 letters, and 3 meaning You for the 3 letters. Reportedly, Fred Rogers maintained his weight at exactly for the last thirty years of his life, and associated the number with the phrase "I love you". * Jake Shimabukuro released the song "143" based on his experience in high school when 143 was sent on a pager to indicate "I Love You". * Sal Governale of '' The Howard Stern Show'' had a long running saga on the show about his wife who had an emotional friend. He discovered the severity of their relationship when he read their text messages and emails which included "143", shorthand for "I love you". * " Case 143", song by Stray Kids. In popular culture *143. A popular pager number to communicate "I love you" (b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
119 (number)
119 (one hundred [and] nineteen) is the natural number following 118 (number), 118 and preceding 120 (number), 120. Mathematics * 119 is a Perrin number, preceded in the sequence by 51, 68, 90 (it is the sum of the first two mentioned). * 119 is the sum of five consecutive Prime number, primes (17 + 19 + 23 + 29 + 31). * 119 is the sum of seven consecutive Prime number, primes (7 + 11 + 13 + 17 + 19 + 23 + 29). * 119 is a highly cototient number. * 119 is one of five numbers to hold a Divisor function, sum-of-divisors of 144 (number), 144 = 12 (number), 122 (the others are 66 (number), 66, 70 (number), 70, 94 (number), 94, and 115 (number), 115). * 119 is the Order (group theory), order of the largest Cyclic group, cyclic subgroups of the monster group. * 119 is the smallest composite number that is 1 less than a factorial (120 is 5!). * 119 is a semiprime, and the fourth in the family. Telephony * 119 (emergency telephone number), 119 is an emergency telephone number in some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
