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1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic numbers in two different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan.
The pairs of summands of the Hardy–Ramanujan number Ta(2) = 1729 were first mentioned by Bernard Frénicle de Bessy, who published his observation in 1657. 1729 was made famous as the first taxicab number in the early 20th century by a story involving Srinivasa Ramanujan in claiming it to be the smallest for his particular example of two summands.
The nth Ramanujan prime is the least integer R n for which () (/), for all x ≥ R n. [2] In other words: Ramanujan primes are the least integers R n for which there are at least n primes between x and x/2 for all x ≥ R n. The first five Ramanujan primes are thus 2, 11, 17, 29, and 41.
In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy [1] states that the normal order of the number () of distinct prime factors of a number is . Roughly speaking, this means that most numbers have about this number of distinct prime factors.
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...
Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If ( a , b , c ) is a Pythagorean triple, then so is ( ka , kb , kc ) for any positive integer k . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle .
In number theory, a superior highly composite number is a natural number which, ... The term was coined by Ramanujan (1915). [1] For example, the number with the most ...