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The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
The most common way is to use tangent lines; the critical choices are how to divide the arc and where to place the tangent points. An efficacious way to divide the arc from y = 1 to y = 100 is geometrically: for two intervals, the bounds of the intervals are the square root of the bounds of the original interval, 1×100, i.e. [1, 2 √ 100 ...
y-cruncher can also be used to calculate other constants and holds world records for several of them. PiFast by Xavier Gourdon was the fastest program for Microsoft Windows in 2003. According to its author, it can compute one million digits in 3.5 seconds on a 2.4 GHz Pentium 4. [100]
One way to speed up these methods (and all the others mentioned below) is to pre-compute and store a list of all primes up to a certain bound, such as all primes up to 200. (Such a list can be computed with the Sieve of Eratosthenes or by an algorithm that tests each incremental m {\displaystyle m} against all known primes ≤ m {\displaystyle ...
In this same way the tables for subtracting digits from 10 or 9 are to be memorized. And whenever the rule calls for adding half of the neighbor, always add 5 if the current digit is odd. This makes up for dropping 0.5 in the next digit's calculation.
There’s no hard-and-fast rule for how high your current ratio should be, but ideally it should be over 1.0 — and the higher, the better. If your current ratio is below 1.0, you may want to ...
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.