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I need to express the value of $\pi$ as numerator/denominator. What is the best pair considering that the numerator should be less than or equal to $2^{62}$? Or how to get this pair?

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    See http://en.wikipedia.org/wiki/Continued_fraction#Continued_fraction_expansions_of_.CF.80 .2011-02-21
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    See also http://demonstrations.wolfram.com/ApproximatingPiWithContinuedFractions/2011-02-21
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    See http://stackoverflow.com/questions/4637967/algorithm-challenge-generate-continued-fractions-for-a-float2011-02-21

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