<Dd> π = ∑ k = 0 ∞ 1 16 k (4 8 k + 1 − 2 8 k + 4 − 1 8 k + 5 − 1 8 k + 6) (\ displaystyle \ pi = \ sum _ (k = 0) ^ (\ infty) (\ frac (1) (16 ^ (k))) \ left ((\ frac (4) (8k + 1)) - (\ frac (2) (8k + 4)) - (\ frac (1) (8k + 5)) - (\ frac (1) (8k + 6)) \ right)) </Dd> <P> This formula, unlike others before it, can produce any individual hexadecimal digit of π without calculating all the preceding digits . Individual binary digits may be extracted from individual hexadecimal digits, and octal digits can be extracted from one or two hexadecimal digits . Variations of the algorithm have been discovered, but no digit extraction algorithm has yet been found that rapidly produces decimal digits . An important application of digit extraction algorithms is to validate new claims of record π computations: After a new record is claimed, the decimal result is converted to hexadecimal, and then a digit extraction algorithm is used to calculate several random hexadecimal digits near the end; if they match, this provides a measure of confidence that the entire computation is correct . </P> <P> Between 1998 and 2000, the distributed computing project PiHex used Bellard's formula (a modification of the BBP algorithm) to compute the quadrillionth (10 th) bit of π, which turned out to be 0 . In September 2010, a Yahoo! employee used the company's Hadoop application on one thousand computers over a 23 - day period to compute 256 bits of π at the two - quadrillionth (2 × 10 th) bit, which also happens to be zero . </P> <P> Because π is closely related to the circle, it is found in many formulae from the fields of geometry and trigonometry, particularly those concerning circles, spheres, or ellipses . Other branches of science, such as statistics, physics, Fourier analysis, and number theory, also include π in some of their important formulae . </P>

As of today pi has been calculated out to how many digits